kid friendly meaning of hypothesis

Hypothesis For Kids

Crafting a hypothesis isn’t just for scientists in white lab coats; even young budding researchers can join in the fun! When kids learn to frame their curious wonders as hypothesis statements, they pave the way for exciting discoveries. Our guide breaks down the world of hypothesis writing into kid-friendly chunks, complete with relatable thesis statement examples and easy-to-follow tips. Dive in to spark a love for inquiry and nurture young scientific minds!

What is an example of a Hypothesis for Kids?

Question: Do plants grow taller when they are watered with coffee instead of water?

Hypothesis: If I water a plant with coffee instead of water, then the plant will not grow as tall because coffee might have substances that aren’t good for plants.

This hypothesis is based on a simple observation or question a child might have, and it predicts a specific outcome (the plant not growing as tall) due to a specific condition (being watered with coffee). It’s presented in simple language suitable for kids.

100 Kids Hypothesis Statement Examples

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Children’s innate curiosity lays the foundation for numerous questions about the world around them. Framing these questions as good hypothesis statements can transform them into exciting learning experiments. Presented below are relatable and straightforward examples crafted especially for young minds, offering them a structured way to articulate their wonders and predictions.

• Sunlight & Plant Growth : If a plant gets more sunlight, then it will grow taller.
• Sugary Drinks & Tooth Decay : Drinking sugary drinks daily will lead to faster tooth decay.
• Chocolates & Energy : Eating chocolate will make me feel more energetic.
• Moon Phases & Sleep : I’ll sleep more during a full moon night.
• Homework & Weekend Moods : If I finish my homework on Friday, I’ll be happier over the weekend.
• Pets & Happiness : Owning a pet will make a child happier.
• Rain & Worms : Worms come out more after it rains.
• Shadows & Time of Day : Shadows are longer in the evening than at noon.
• Snow & School Holidays : More snow means there’s a better chance of school being canceled.
• Ice Cream & Brain Freeze : Eating ice cream too fast will give me a brain freeze.
• Video Games & Dreams : Playing video games before bed might make my dreams more vivid.
• Green Vegetables & Strength : Eating more green vegetables will make me stronger.
• Bicycles & Balance : The more I practice, the better I’ll get at riding my bike without training wheels.
• Stars & Wishes : If I wish on the first star I see at night, my wish might come true.
• Cartoons & Laughing : Watching my favorite cartoon will always make me laugh.
• Soda & Bone Health : Drinking soda every day will make my bones weaker.
• Beach Visits & Sunburn : If I don’t wear sunscreen at the beach, I’ll get sunburned.
• Loud Noises & Pet Behavior : My cat hides when she hears loud noises.
• Bedtime & Morning Energy : Going to bed early will make me feel more energetic in the morning.
• Healthy Snacks & Hunger : Eating a healthy snack will keep me full for longer. …
• Toys & Sharing : The more toys I have, the more I want to share with my friends.
• Homemade Cookies & Taste : Homemade cookies always taste better than store-bought ones.
• Books & Imagination : The more books I read, the more adventures I can imagine.
• Jumping & Height : The more I practice, the higher I can jump.
• Singing & Mood : Singing my favorite song always makes me happy.
• Snowmen & Temperature : If the temperature rises, my snowman will melt faster.
• Costumes & Play : Wearing a costume will make playtime more fun.
• Gardening & Patience : Waiting for my plants to grow teaches me patience.
• Night Lights & Sleep : Having a night light makes it easier for me to sleep.
• Handwriting & Practice : The more I practice, the better my handwriting will become.
• Painting & Creativity : Using more colors in my painting lets me express my creativity better.
• Puzzles & Problem Solving : The more puzzles I solve, the better I become at problem-solving.
• Dancing & Coordination : The more I dance, the more coordinated I will become.
• Stargazing & Constellations : If I stargaze every night, I’ll recognize more constellations.
• Bird Watching & Species Knowledge : The more I watch birds, the more species I can identify.
• Cooking & Skill : If I help in the kitchen often, I’ll become a better cook.
• Swimming & Confidence : The more I swim, the more confident I become in the water.
• Trees & Birds’ Nests : The taller the tree, the more likely it is to have birds’ nests.
• Roller Skating & Balance : If I roller skate every weekend, I’ll improve my balance.
• Drawing & Observation : The more I draw, the better I become at observing details.
• Sandcastles & Water : If I use wet sand, I can build a stronger sandcastle.
• Hiking & Endurance : The more I hike, the farther I can walk without getting tired.
• Camping & Outdoor Skills : If I go camping often, I’ll learn more about surviving outdoors.
• Magic Tricks & Practice : The more I practice a magic trick, the better I’ll get at performing it.
• Stickers & Collection : If I collect stickers, my album will become more colorful.
• Board Games & Strategy : The more board games I play, the better strategist I’ll become.
• Pets & Responsibility : The more I take care of my pet, the more responsible I become.
• Music & Concentration : Listening to calm music while studying will help me concentrate better.
• Photographs & Memories : The more photos I take, the more memories I can preserve.
• Rainbows & Rain : If it rains while the sun is out, I might see a rainbow.
• Museums & Knowledge : Every time I visit a museum, I learn something new.
• Fruits & Health : Eating more fruits will keep me healthier.
• Stories & Vocabulary : The more stories I listen to, the more new words I learn.
• Trees & Fresh Air : The more trees there are in a park, the fresher the air will be.
• Diary & Feelings : Writing in my diary helps me understand my feelings better.
• Planets & Telescopes : If I look through a telescope, I’ll see more planets clearly.
• Crafting & Creativity : The more crafts I make, the more creative I become.
• Snowflakes & Patterns : Every snowflake has a unique pattern.
• Jokes & Laughter : The funnier the joke, the louder I’ll laugh.
• Riddles & Thinking : Solving riddles makes me think harder.
• Nature Walks & Observations : The quieter I am on a nature walk, the more animals I’ll spot.
• Building Blocks & Structures : The more blocks I use, the taller my tower will be.
• Kites & Wind : If there’s more wind, my kite will fly higher.
• Popcorn & Movie Nights : Watching a movie with popcorn makes it more enjoyable.
• Stars & Wishes : If I see a shooting star, I should make a wish.
• Diets & Energy : Eating a balanced diet gives me more energy for playtime.
• Clay & Sculptures : The more I play with clay, the better my sculptures will be.
• Insects & Magnifying Glass : Using a magnifying glass will let me see more details of tiny insects.
• Aquarium Visits & Marine Knowledge : Every time I visit the aquarium, I discover a new marine creature.
• Yoga & Flexibility : If I practice yoga daily, I’ll become more flexible.
• Toothpaste & Bubbles : The more toothpaste I use, the more bubbles I’ll get while brushing.
• Journals & Memories : Writing in my journal every day helps me remember special moments.
• Piggy Banks & Savings : The more coins I save, the heavier my piggy bank will get.
• Baking & Measurements : If I measure ingredients accurately, my cake will turn out better.
• Coloring Books & Art Skills : The more I color, the better I get at staying inside the lines.
• Picnics & Outdoor Fun : Having a picnic makes a sunny day even more enjoyable.
• Recycling & Environment : The more I recycle, the cleaner my environment will be.
• Treasure Hunts & Discoveries : Every treasure hunt has a new discovery waiting.
• Milk & Bone Health : Drinking milk daily will make my bones stronger.
• Puppet Shows & Stories : The more puppet shows I watch, the more stories I learn.
• Field Trips & Learning : Every field trip to a new place teaches me something different.
• Chores & Responsibility : The more chores I do, the more responsible I feel.
• Fishing & Patience : Fishing teaches me to be patient while waiting for a catch.
• Fairy Tales & Imagination : Listening to fairy tales expands my imagination.
• Homemade Pizza & Toppings : The more toppings I add, the tastier my homemade pizza will be.
• Gardens & Butterflies : If I plant more flowers, I’ll see more butterflies in my garden.
• Raincoats & Puddles : Wearing a raincoat lets me jump in puddles without getting wet.
• Gymnastics & Balance : The more I practice gymnastics, the better my balance will be.
• Origami & Craft Skills : The more origami I fold, the better my craft skills become.
• Basketball & Shooting Skills : The more I practice, the better I get at shooting baskets.
• Fireflies & Night Beauty : Catching fireflies makes summer nights magical.
• Books & Knowledge : The more books I read, the smarter I become.
• Pillows & Forts : With more pillows, I can build a bigger fort.
• Lemonade & Summers : Drinking lemonade makes hot summer days refreshing.
• Bicycles & Balance : The more I practice, the better I get at riding my bike without training wheels.
• Pencils & Drawings : If I have colored pencils, my drawings will be more colorful.
• Ice Cream & Happiness : Eating ice cream always makes me happy.
• Beach Visits & Shell Collections : Every time I visit the beach, I find new shells for my collection.
• Jump Ropes & Fitness : The more I jump rope, the fitter I become.
• Tea Parties & Imagination : Hosting tea parties lets my imagination run wild.

Simple Hypothesis Statement Examples for Kids

Simple hypothesis are straightforward predictions that can be tested easily. They help children understand the relationship between two variables. Here are some examples tailored just for kids.

• Plants & Sunlight : Plants placed near the window will grow taller than those in the dark.
• Chocolates & Happiness : Eating chocolates can make kids feel happier.
• Rain & Puddles : The more it rains, the bigger the puddles become.
• Homework & Learning : Doing homework helps kids understand lessons better.
• Toys & Sharing : Sharing toys with friends makes playtime more fun.
• Pets & Care : Taking care of a pet fish helps it live longer.
• Storytime & Sleep : Listening to a bedtime story helps kids sleep faster.
• Brushing & Cavity : Brushing teeth daily prevents cavities.
• Games & Skill : Playing a new game every day improves problem-solving skills.
• Baking & Patience : Waiting for cookies to bake teaches patience.

Hypothesis Statement Examples for Kids Psychology

Child psychology hypothesis delves into how kids think, behave, and process emotions. These hypotheses help understand the psychological aspects of children’s behaviors.

• Emotions & Colors : Kids might feel calm when surrounded by blue and energetic with red.
• Friendship & Self-esteem : Making friends can boost a child’s self-confidence.
• Learning Styles & Memory : Some kids remember better by seeing, while others by doing.
• Play & Development : Pretend play is crucial for cognitive development.
• Rewards & Motivation : Giving small rewards can motivate kids to finish tasks.
• Music & Mood : Listening to soft music can calm a child’s anxiety.
• Sibling Bonds & Sharing : Having siblings can influence a child’s willingness to share.
• Feedback & Performance : Positive feedback can improve a kid’s academic performance.
• Outdoor Play & Attention Span : Playing outside can help kids concentrate better in class.
• Dreams & Reality : Kids sometimes can’t differentiate between dreams and reality.

Hypothesis Examples in Kid Friendly Words

Phrasing hypothesis in simple words makes it relatable and easier for kids to grasp. Here are examples with kid-friendly language.

• Socks & Warmth : Wearing socks will keep my toes toasty.
• Jumping & Energy : The more I jump, the more energy I feel.
• Sandcastles & Water : A little water makes my sandcastle stand tall.
• Stickers & Smiles : Getting a sticker makes my day shine brighter.
• Rainbows & Rain : After the rain, I might see a rainbow.
• Slides & Speed : The taller the slide, the faster I go.
• Hugs & Love : Giving hugs makes me and my friends feel loved.
• Stars & Counting : The darker it is, the more stars I can count.
• Paint & Mess : The more paint I use, the messier it gets.
• Bubbles & Wind : If I blow my bubble wand, the wind will carry them high.

Hypothesis Statement Examples for Kids in Research

Even in a research setting, research hypothesis should be age-appropriate for kids. These examples focus on concepts children might encounter in structured studies.

• Reading & Vocabulary : Kids who read daily might have a richer vocabulary.
• Games & Math Skills : Playing number games can improve math skills.
• Experiments & Curiosity : Conducting science experiments can make kids more curious.
• Doodles & Creativity : Drawing daily might enhance a child’s creativity.
• Learning Methods & Retention : Kids who learn with visuals might remember lessons better.
• Discussions & Understanding : Talking about a topic can deepen understanding.
• Observation & Knowledge : Observing nature can increase a kid’s knowledge about the environment.
• Puzzles & Cognitive Skills : Solving puzzles regularly might enhance logical thinking.
• Music & Rhythmic Abilities : Kids who practice music might develop better rhythm skills.
• Teamwork & Social Skills : Group projects can boost a child’s social skills.

Hypothesis Statement Examples for Kids Science Fair

Science fairs are a chance for kids to delve into the world of experiments and observations. Here are hypotheses suitable for these events.

• Magnet & Metals : Certain metals will be attracted to a magnet.
• Plants & Colored Light : Plants might grow differently under blue and red lights.
• Eggs & Vinegar : An egg in vinegar might become bouncy.
• Solar Panels & Sunlight : Solar panels will generate more power on sunny days.
• Volcanoes & Eruptions : Mixing baking soda and vinegar will make a mini eruption.
• Mirrors & Reflection : Shiny surfaces can reflect light better than dull ones.
• Battery & Energy : Fresh batteries will make a toy run faster.
• Density & Floating : Objects with lower density will float in water.
• Shadows & Light Source : Moving the light source will change the shadow’s direction.
• Freezing & States : Water turns solid when kept in the freezer.

Hypothesis Statement Examples for Science Experiments

Experiments let kids test out their predictions in real-time. Here are hypotheses crafted for various scientific tests.

• Salt & Boiling Point : Adding salt will make water boil at a higher temperature.
• Plants & Music : Playing music might affect a plant’s growth rate.
• Rust & Moisture : Metals kept in a moist environment will rust faster.
• Candles & Oxygen : A candle will burn out faster in an enclosed jar.
• Fruits & Browning : Lemon juice can prevent cut fruits from browning.
• Yeast & Sugar : Adding sugar will make yeast activate more vigorously.
• Density & Layers : Different liquids will form layers based on their density.
• Acids & Bases : Red cabbage juice will change color in acids and bases.
• Soil Types & Water : Sandy soil will drain water faster than clay.
• Thermometers & Temperatures : Thermometers will show higher readings in the sun.

Hypothesis Statement Examples for Kids At Home

These hypotheses are crafted for experiments and observations kids can easily make at home, using everyday items.

• Chores & Time : Setting a timer will make me finish my chores faster.
• Pets & Behavior : My cat sleeps more during the day than at night.
• Recycling & Environment : Recycling more can reduce the trash in my home.
• Cooking & Tastes : Adding spices will change the taste of my food.
• Family Time & Bonding : Playing board games strengthens our family bond.
• Cleaning & Organization : Organizing my toys daily will keep my room tidier.
• Watering & Plant Health : Watering my plant regularly will keep its leaves green.
• Decor & Mood : Changing the room decor can influence my mood.
• Journals & Memories : Writing in my journal daily will help me remember fun events.
• Photos & Growth : Taking monthly photos will show how much I’ve grown.

How do you write a hypothesis for kids? – A Step by Step Guide

Step 1: Start with Curiosity Begin with a question that your child is curious about. This could be something simple, like “Why is the sky blue?” or “Do plants need sunlight to grow?”

Step 2: Observe and Research Before formulating the hypothesis, encourage your child to observe the world around them. If possible, read or watch videos about the topic to gather information. The idea is to get a general understanding of the subject.

Step 3: Keep it Simple For kids, it’s essential to keep the hypothesis straightforward and concise. Use language that is easy to understand and relatable to their age.

Step 4: Make a Predictable Statement Help your child frame their hypothesis as an “If… then…” statement. For example, “If I water a plant every day, then it will grow taller.”

Step 5: Ensure Testability Ensure that the hypothesis can be tested using simple experiments or observations. It should be something they can prove or disprove through hands-on activities.

Step 6: Avoid Certainty Teach kids that a hypothesis is not a definitive statement of fact but rather a best guess based on what they know. It’s okay if the hypothesis turns out to be wrong; the learning process is more important.

Step 7: Review and Refine After forming the initial hypothesis, review it with your child. Discuss if it can be made simpler or clearer. Refinement aids in better understanding and testing.

Step 8: Test the Hypothesis This is the fun part! Plan an experiment or set of observations to test the hypothesis. Whether the hypothesis is proven correct or not, the experience provides a learning opportunity.

Tips for Writing Hypothesis for Kids

• Encourage Curiosity : Always encourage your child to ask questions about the world around them. It’s the first step to formulating a hypothesis.
• Use Familiar Language : Use words that the child understands and can relate to. Avoid jargon or technical terms.
• Make it Fun : Turn the process of forming a hypothesis into a game or a storytelling session. This will keep kids engaged.
• Use Visual Aids : Kids often respond well to visuals. Drawing or using props can help in understanding and formulating the hypothesis.
• Stay Open-minded : It’s essential to teach kids that it’s okay if their hypothesis is wrong. The process of discovery and learning is what’s crucial.
• Practice Regularly : The more often kids practice forming hypotheses, the better they get at it. Use everyday situations as opportunities.
• Link to Real-life Scenarios : Relate the hypothesis to real-life situations or personal experiences. For instance, if discussing plants, you can relate it to a plant you have at home.
• Collaborate : Sometimes, two heads are better than one. Encourage group activities where kids can discuss and come up with hypotheses together.
• Encourage Documentation : Keeping a journal or notebook where they document their hypotheses and results can be a great learning tool.
• Celebrate Efforts : Regardless of whether the hypothesis was correct, celebrate the effort and the learning journey. This reinforces the idea that the process is more important than the outcome.

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Hypothesis facts for kids

A hypothesis is a proposed explanation for some event or problem.

Cardinal Bellarmine gave a well known example of the older sense of the word in his warning to Galileo in the early 17th century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.

Today, a hypothesis refers to an idea that needs to be tested . A hypothesis needs more work by the researcher in order to check it. A tested hypothesis that works, may become part of a theory or become a theory itself. The testing should be an attempt to prove the hypothesis is wrong. That is, there should be a way to falsify the hypothesis, at least in principle.

People often call a hypothesis an "educated guess".

Experimenters may test and reject several hypotheses before solving the problem.

A 'working hypothesis' is just a rough kind of hypothesis that is provisionally accepted as a basis for further research. The hope is that a theory will be produced, even if the hypothesis ultimately fails.

Hypotheses are especially important in science. Several philosophers have said that without hypotheses there could be no science. In recent years, philosophers of science have tried to integrate the various approaches to testing hypotheses, and the scientific method in general, to form a more complete system. The point is that hypotheses are suggested ideas which are then tested by experiments or observations .

In statistics , people talk about correlation : correlation is how closely related two events or phenomena are. A proposition (or hypothesis) that two events are related cannot be tested in the same way as a law of nature is tested. An example would be to see if some drug is effective to treat a given medical condition. Even if there is a strong correlation that indicates that this is the case, some samples would still not fit the hypothesis.

There are two hypotheses in statistical tests, called the null hypothesis and the alternative hypothesis. The null hypothesis states that there is no link between the phenomena. The alternative hypothesis states that there is some kind of link. The alternative hypothesis may take several forms. It can be two-sided (for example: there is some effect, in a yet unknown direction) or one-sided (the direction of the supposed relation, positive or negative, is fixed in advance).

Related pages

• Falsifiability
• Thought experiment
• This page was last modified on 16 October 2023, at 16:53. Suggest an edit .

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Scientific Method For Kids With Examples

Kids have questions about the world around them every day, and there is so much to learn through experimentation with simple materials. You can begin using the scientific method with elementary kids. Below we’ll share with you how and when to introduce the scientific method, the steps of the scientific method, and some easy scientific method experiments. There are so many great ways to enjoy science projects with kids!

What Is The Scientific Method?

The scientific method is a process or method of research. A problem is identified, information about the problem is gathered, a hypothesis or question is formulated from the information, and the hypothesis is put to the test with an experiment to prove or disprove its validity.

Sounds heavy… What in the world does that mean?!? It means you don’t need to try and solve the world’s biggest science questions! The scientific method is all about studying and learning things right around you.

As children develop practices that involve creating, gathering data evaluating, analyzing, and communicating, they can apply these critical thinking skills to any situation.

Note: The use of the best Science and Engineering Practices is also relevant to the topic of using the scientific method. Read more here and see if it fits your science planning needs.

Can Young Kids Use the Scientific Method?

Kids are great scientists at any age, and can use the scientific method in context to what they are learning. It can be adapted for any age!

The scientific method is a valuable tool for introducing kids to a logical way to solve scientific problems. Scientists use the scientific method to study, learn, and come up with an answer!

The scientific method is a process that helps double-check that answers are correct and the correct results are obtained through careful planning. Sometimes the guesses and questions change as you run your experiments.

Kids can use the scientific method too on questions that are relevant to them!

Let’s break the scientific method for kids down into six parts, and you can quickly see how each can be incorporated into your next science experiment.

What Are The Steps In The Scientific Method?

• Make initial observations.
• Come up with a question of interest that is based on the observations.
• Develop a hypothesis or prediction to go along with the question.
• Experiment and test.
• Gather and record results of tests and experiments and draw conclusions.
• Share and discuss results.

Whoa… Wait A  Minute! That sounds like a lot for a young kid!

You are correct. Depending on your kid’s abilities, following all the scientific method steps precisely will not go well. Someone will get frustrated, bored, and turned off by just how cool science can be. We do not want that to happen!

Using The Scientific Method For Preschool and Kindergarten

Use the scientific method steps as a guideline in the back of your mind. You can cover most of the steps by talking with your kids about…

• What do they think will happen?
• What is happening ?
• What happened compared to what they thought would happen ?

No writing is required! It’s also best to pick pretty straightforward ideas that aren’t overly involved or complicated to set up and test. Kids always have burning questions and “what ifs.”

See if you can tackle their next “what if” using the scientific method by listening carefully to their conversations. You can even have them keep a journal with their “what if” questions for your next science time.

Learn more about Science Activities For Preschoolers and Kindergarten Science Experiments .

Now on to how to apply the scientific method for elementary kiddos and beyond.

Scientific Method Steps In Action

Learn more about the steps of the scientific method below, which are great for science at home with your kids or in the classroom! We have also included some simple scientific method experiments for you to enjoy.

Ice Science Experiments are perfect for this! Try these 3 today !

STEP 1: Make Observations

Tons of everyday activities would make for cool science experiments using the scientific method. Listen to what your kids talk about and see happening. My son noticed that ice melted pretty fast in his water.

Observation is simply noticing what’s happening through our senses or with tools like a magnifying glass. Observation is used to collect and record data, enabling scientists to construct and test hypotheses and theories.

Learn more about observations in science.

STEP 2: Come Up With A Question 

Your kids’ observations should lead to some sort of question. For my son and his ice observations, he came up with questions. Does ice melt faster in different liquids? His curiosity about what happens to the ice in liquids is a simple science experiment perfect for using the scientific method.

Next! Do some research and come up with ideas!

STEP 3: Develop A Prediction or Hypothesis

You have made your observations, you have your question, and now you need to make a prediction about what you think will happen.

A prediction is a guess at what might happen in an experiment based on observation or other information.

A hypothesis is not simply a guess! It’s a statement of what you believe will happen based on the information you have gathered.

My son hypothesizes that ice will melt faster in juice than in water.

STEP 4: Conduct An Experiment

We made a prediction that ice will melt faster in juice than it will in water, and now we have to test our hypothesis. We set up an experiment with a glass of juice, a glass of water, and an ice cube for each.

For the best experiments, only one thing should change! All the things that can be changed in a science experiment are called variables. There are three types of variables; independent, dependent, and controlled.

The independent variable is the one that is changed in the experiment and will affect the dependent variable. Here we will use different types of liquids to melt our ice cube in.

The dependent variable is the factor that is observed or measured in the experiment. This will be the melting of the ice cubes. Set up a stopwatch or set a time limit to observe the changes!

The controlled variable stays constant in the experiment. The liquids should be roughly the same temperature (as close as possible) for our ice melting experiment and measured to the same amount. So we left them out to come to room temperature. They could also be tested right out of the fridge!

You can find simple science experiments here with dependent and controlled variables.

STEP 5: Record Results and Draw Conclusions

Make sure to record what is happening as well as the results—note changes at specific time intervals or after one set time interval.

For example…

• Record when each ice cube is completely melted.
• Add drawings if you wish of the setup up and the end results.
• Was your prediction accurate? If it was inaccurate, record why.
• Write out a final conclusion to your experiment.

STEP 6: Communicate Your Results

This is the opportunity to talk about your hypothesis, experiment, results, and conclusion!

ALTERNATIVE IDEAS: Switch out an ice cube for a lollipop or change the liquids using vinegar and cooking oil.

Now you have gone through the steps of the scientific method, read on for more fun scientific method experiments to try!

Free printable scientific method worksheets!

Fun Scientific Method Experiments

Sink or float experiment.

A Sink or Float experiment is great for practicing the steps of the scientific method with younger kids.

Grab this FREE printable sink or float experiment

Here are a few of our favorite scientific method experiments, which are great for elementary-age kids . Of course, you can find tons more awesome and doable science projects for kids here!

Magic Milk Experiment

Start with demonstrating this delightful magic milk experiment. Then get kids to apply the steps of the scientific method by coming up with a question to investigate. What happens when you change the type of milk used?

What Dissolves In Water

Investigate  what solids dissolve in water  and what do not. Here’s a super fun science experiment for kids that’s very easy to set up! Learn about solutions, solutes, and solvents through experimenting with water and common kitchen ingredients.

Apple Browning Experiment

Investigate how to keep apples from turning brown with this apple oxidation experiment . What can you add to cut apples to stop or slow the oxidation process?

Freezing Water Experiment

Will it freeze? What happens to the freezing point of water when you add salt?

Viscosity Experiment

Learn about the viscosity of fluids with a simple  viscosity experiment . Grab some marbles and add them to different household liquids to find out which one will fall to the bottom first. 

Seed Germination Experiment

Set up a simple seed germination experiment .

Catapult Experiment

Make a simple popsicle stick catapult and use one of our experiment ideas to investigate from rubber band tension to changes in launch angle and more. How far can you fling your objects? Take measurements and find out.

Floating Orange

Investigate whether an orange floats or sinks in water, and what happens if you use different types of oranges. Learn about buoyancy and density with a simple ingredient from the kitchen, an orange.

Bread Mold Experiment

Grow mold on bread for science, and investigate how factors such as moisture, temperature, and air affect mold growth. 

Eggshell Strength Experiment

Test how strong an egg is with this eggshell strength experiment . Grab some eggs, and find out how much weight an egg can support.

Free Printable Science Fair Starter Guide

Are you looking to plan a science fair project, make a science fair board, or want an easy guide to set up science experiments?

Learn more about prepping for a science fair and grab this free printable science fair project pack here!

If you want a variety of science fair experiments with instructions, make sure to pick up a copy of our Science Project Pack in the shop.

Bonus STEM Projects For Kids

STEM activities include science, technology, engineering, and mathematics. As well as our kids science experiments, we have lots of fun STEM activities for you to try. Check out these STEM ideas below…

• Building Activities
• Engineering Projects For Kids
• What Is Engineering For Kids?
• Coding Activities For Kids
• STEM Worksheets
• Top 10 STEM Challenges For Kids

Printable Science Projects Pack

If you’re looking to grab all of our printable science projects in one convenient place plus exclusive worksheets and bonuses like a STEAM Project pack, our Science Project Pack is what you need! Over 300+ Pages!

• 90+ classic science activities  with journal pages, supply lists, set up and process, and science information.  NEW! Activity-specific observation pages!
• Best science practices posters  and our original science method process folders for extra alternatives!
• Be a Collector activities pack  introduces kids to the world of making collections through the eyes of a scientist. What will they collect first?
• Know the Words Science vocabulary pack  includes flashcards, crosswords, and word searches that illuminate keywords in the experiments!
• My science journal writing prompts  explore what it means to be a scientist!!
• Bonus STEAM Project Pack:  Art meets science with doable projects!
• Bonus Quick Grab Packs for Biology, Earth Science, Chemistry, and Physics

19 Comments

A great post and sure to help extend children’s thinking! I would like to download the 6 steps but the blue download button doesn’t seem to be working for me.

Thank you! All fixed. You should be able to download now!

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it is so great, thanks a lot.

This helped for a science project.Thanks so much.

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~ Projects to Try Now! ~

• Ask a question
• Gather information and observe (research)
• Make a hypothesis (guess the answer)
• Experiment and test your hypothesis
• Analyze your test results
• Modify your hypothesis, if necessary
• Present a conclusion
• Retest (often done by other scientists)

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What is a hypothesis?

No.  A hypothesis is sometimes described as an educated guess.  That's not the same thing as a guess and not really a good description of a hypothesis either.  Let's try working through an example.

If you put an ice cube on a plate and place it on the table, what will happen?  A very young child might guess that it will still be there in a couple of hours.  Most people would agree with the hypothesis that:

An ice cube will melt in less than 30 minutes.

You could put sit and watch the ice cube melt and think you've proved a hypothesis.  But you will have missed some important steps.

For a good science fair project you need to do quite a bit of research before any experimenting.  Start by finding some information about how and why water melts.  You could read a book, do a bit of Google searching, or even ask an expert.  For our example, you could learn about how temperature and air pressure can change the state of water.  Don't forget that elevation above sea level changes air pressure too.

Now, using all your research, try to restate that hypothesis.

An ice cube will melt in less than 30 minutes in a room at sea level with a temperature of 20C or 68F.

But wait a minute.  What is the ice made from?  What if the ice cube was made from salt water, or you sprinkled salt on a regular ice cube?  Time for some more research.  Would adding salt make a difference?  Turns out it does.  Would other chemicals change the melting time?

Using this new information, let's try that hypothesis again.

An ice cube made with tap water will melt in less than 30 minutes in a room at sea level with a temperature of 20C or 68F.

Does that seem like an educated guess?  No, it sounds like you are stating the obvious.

At this point, it is obvious only because of your research.  You haven't actually done the experiment.  Now it's time to run the experiment to support the hypothesis.

A hypothesis isn't an educated guess.  It is a tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation.

Once you do the experiment and find out if it supports the hypothesis, it becomes part of scientific theory.

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Hypothesizing: How Toddlers Use Scientific Thinking to Learn

Can Toddlers Hypothesize?

Yes, but it’s simplified at this age. Toddlers tend to be less vocal when they make an observation or a hypothesis, often internalizing their thoughts instead.

You might see your toddler dump and refill a container of blocks several times, focusing intently on watching the blocks fall out over and over again. As your little one watches, they might consider what will happen if they added more blocks to dump out, or if kicking the container over will have a different outcome than using their hands to tip it over.

Hypothesizing in the toddler years relies heavily on cause and effect awareness , which develops through toddlerhood and into the preschool years. Toddlers learn what happens when they do certain things, such as making banging sounds when they hit a box. Each time a toddler changes how they play with something, they see a different outcome, which lays the foundation for forming predictions.

So every time you see your little one repeating the same things, or switching them up slightly, they’re working on the cause and effect awareness that leads to scientific thinking!

Hypothesizing and Scientific Exploration at Work in Toddlerhood

Scientific exploration is much more than simply science! It involves planning, critical thinking, and problem-solving – skills at the heart of learning in general. Scientific exploration relies on observing, asking questions, making predictions, and testing things out.

Here’s how the scientific thinking process might look in a toddler who’s playing with toy trucks:

• Observing: Your toddler rolls the truck across the floor, watching its wheels move. Your cat walks by and pushes another truck with its paw, sending it soaring across the room as your toddler watches.
• Asking questions: Your toddler wonders why that truck moved faster than the one in their hands.
• Hypothesizing: Your toddler pushes the truck with one hand, sending the truck zooming across the floor.
• Predicting: Seeing the truck move faster, your toddler might think that pushing the truck with both hands could make it go even faster still.
• Testing: Your toddler uses their hands to push the toy across the floor again and again. Eventually, they try other ways of moving the truck, like kicking it with their feet and rolling it off the edge of a chair.

In this example, your little one made it through a complete cycle of scientific thinking with just one toy! Hypothesizing is a pivotal piece of that process, requiring them to problem-solve in. order to achieve a specific outcome.

How can you help your toddler hypothesize and think scientifically? Play! You could ask questions that help them think, such as, “What do you think would happen if…” or “Do you think your picture would look different if we colored it with markers instead of crayons?” Even if your toddler doesn’t have an answer, you’re engaging their thinking skills.

You can find fun ways to engage your little one’s scientific thinking in our BabySparks program!

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Hypothesis: A Science Process Skill

January 25, 2021 By Janice VanCleave

A Hypothesis is a Well Thoughtout Prediction.

Yes, asking groups of kids to guess what will happen can be fun. But, expecting a hypothesis for every experiment defeats the purpose for this science process skill.  A  hypothesis  relys on observations that have been previously made. Hypothesis are often called “educated” guesses. Please don’t require kids to give a hypothesis unless it can be based on previous knowledge.  In other words, a hypothesis must be based on  schema , which is previously learned information.

Using an Exploratory Experiment to provide needed schema for a hypothesis. 

Research  is any method used to learn more about a topic. Reading books, magazines as well as online sources and everyday observations of the world around you are good research methods. I suggest that research include exploratory experiments, such as those found in the science book shown. The following exploratory experiment was taken from , “201 Awesome, Magical, Bizarre & Incredible Experiments.” My intention in writing this and other experiment books was to provide fun experiments requiring around the house materials or materials easily found locally. These are exploratory experiments.

FYI:  My books are sold on Amazon as well as other online books suppliers. If you sell my books contact me and I will add a link to your website.

Facts:  Provide information that kids may not be familiar with before introducing the experiment.

• Pressure is the force pressing against a surface.
• Gas molecules move in a straight line until they collide with each other or their container. When colliding, the gas molecules, much like balls striking a wall changes direction and continues moving. Unlike a ball, each gas molecule collides, changes direction and continue at the same speed as before its collision.

 Exploratory Experiment #141 Increasing

Problem: How does temperature affect air pressure? Materials: empty glass soda bottle (any glass bottle with a small mouth) 9-inch (23-cm) round balloon

Something More

Now that kids are engaged –have their schema turned on– introduce a problem related to the previous exploratory experiment.

4. Observe and record the appearance of the balloon over the bottle.

5. Place the open bottle and the bottle with the balloon in a freezer for 15 or more minutes. Note: You can sit the bottles in an ice chest with ice. Make sure both bottles are equally cooled and the chest is closed.  Again, it is important for the air surrounding the bottles to be cold.

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• Science Process Skill: Identifying Variables
• How Salt Melts Ice
• Developing A Science Fair Project
• Coloring Changing Colorants
• Tutorial for Using Science Process Skills
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• Heat Energy
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A hypothesis is a proposed explanation for some event or problem. For a scientific hypothesis, the scientific method requires that one can test it. [1] [2]

• 2 Statistics
• 3 Hypothesis Media
• 4 Related pages
• 5 References
• 6 Other websites

In the early 17th century, Cardinal Bellarmine gave a well known example of the older sense of the word in his warning to Galileo : that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.

Today, a hypothesis refers to an idea that needs to be tested . A hypothesis needs more work by the researcher in order to check it. A tested hypothesis that works may become part of a theory —or become a theory itself. The testing should be an attempt to prove that the hypothesis is wrong. That is, there should be a way to falsify the hypothesis, at least in principle if not in practice.

People often call a hypothesis an "educated guess".

Experimenters may test and reject several hypotheses, before solving the problem or reaching a satisfactory theory.

A 'working hypothesis' is just a rough kind of hypothesis that is provisionally accepted as a basis for further research. [5] The hope is that a theory will be produced, even if the hypothesis ultimately fails. [6] [7]

Hypotheses are especially important in science. Several philosophers have said that without hypotheses, there could be no science. [8] In recent years, philosophers of science have tried to integrate the various approaches to testing hypotheses (and the scientific method in general), to form a more complete system. The point is that hypotheses are suggested ideas , which are then tested by experiments or observations .

In statistics , people talk about correlation : correlation is how closely related two events or phenomena are. A proposition (or hypothesis) that two events are related cannot be tested in the same way as a law of nature can be tested. An example would be to see if some drug is effective to treat a given medical condition. Even if there is a strong correlation that indicates that this is the case, some samples would still not fit the hypothesis.

There are two hypotheses in statistical tests, called the null hypothesis , often written as [math]\displaystyle{ H_0 }[/math] , and the alternative hypothesis , often written as [math]\displaystyle{ H_a }[/math] . [9] The null hypothesis states that there is no link between the phenomena, [10] and is usually assumed to be true until it can be proven wrong beyond a reasonable doubt. [11] The alternative hypothesis states that there is some kind of link. It is usually the opposite of the null hypothesis, and is what one would conclude if null hypothesis is rejected. [12] The alternative hypothesis may take several forms. It can be two-sided (for example: there is some effect, in a yet unknown direction) or one-sided (the direction of the supposed relation, positive or negative, is fixed in advance). [11]

Hypothesis Media

The hypothesis of Andreas Cellarius , showing the planetary motions in eccentric and epicyclical orbits .

Related pages

• Falsifiability
• Gaia hypothesis
• Null hypothesis
• Occam's razor
• Statistical hypothesis test
• Thought experiment
• ↑ The term comes from the Greek , hypotithenai meaning "to put under" or "to suppose".
• ↑ Bunge, Mario 1967. Scientific research I: the search for system . Berlin: Springer Verlag, Chapter 5, p222.
• ↑ Richard Feynman (1965) The character of physical law . p156
• ↑ Oxford Dictionary of Sports Science & Medicine Eprint via Answers.com
• ↑ See in "hypothesis", Century Dictionary Supplement , v. 1, 1909, New York: Century Company. Reprinted, v. 11, p. 616 (via Internet Archive ) of the Century Dictionary and Cyclopedia , 1911.
• ↑ Schick, Theodore; Vaughn, Lewis (2002). How to think about weird things: critical thinking for a New Age . Boston: McGraw-Hill Higher Education. ISBN   0-7674-2048-9 .
• ↑ Medawar P.B. & J.S. 1983. Aristotle to zoos: a philosophical dictionary of biology . Harvard University Press, p148. ISBN   0-674-04537-8
• ↑ "List of Probability and Statistics Symbols" . Math Vault . 2020-04-26 . Retrieved 2020-09-22 .
• ↑ or that the link does not have the form given by the alternative hypothesis
• ↑ 11.0 11.1 "Null and Alternative Hypotheses | Introduction to Statistics" . courses.lumenlearning.com . Retrieved 2020-09-22 .
• ↑ "Introductory Statistics: Null and Alternative Hypotheses" . opentextbc.ca . Archived from the original on June 11, 2021 . Retrieved September 22, 2020 .

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• Analysis and synthesis - on scientific method, based on a study by Bernhard Riemann from the Swedish Morphological Society

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

About the author

Muhammad Hassan

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• Published: 14 June 2021

Children’s exploratory play tracks the discriminability of hypotheses

• Max H. Siegel   ORCID: orcid.org/0000-0003-4510-3145 1   na1 ,
• Rachel W. Magid 1   na1 ,
• Madeline Pelz 1 ,
• Joshua B. Tenenbaum 1 &
• Laura E. Schulz   ORCID: orcid.org/0000-0002-2981-8039 1  

Nature Communications volume  12 , Article number:  3598 ( 2021 ) Cite this article

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Effective curiosity-driven learning requires recognizing that the value of evidence for testing hypotheses depends on what other hypotheses are under consideration. Do we intuitively represent the discriminability of hypotheses? Here we show children alternative hypotheses for the contents of a box and then shake the box (or allow children to shake it themselves) so they can hear the sound of the contents. We find that children are able to compare the evidence they hear with imagined evidence they do not hear but might have heard under alternative hypotheses. Children (N = 160; mean: 5 years and 4 months) prefer easier discriminations (Experiments 1-3) and explore longer given harder ones (Experiments 4-7). Across 16 contrasts, children’s exploration time quantitatively tracks the discriminability of heard evidence from an unheard alternative. The results are consistent with the idea that children have an “intuitive psychophysics”: children represent their own perceptual abilities and explore longer when hypotheses are harder to distinguish.

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Introduction

Young children are remarkable learners, constructing intuitive theories that support prediction, explanation, intervention, and discovery. These early-emerging abilities arguably lay the foundation for scientific inquiry 1 , 2 . However, both scientific inquiry and everyday learning are difficult in part because we can often get only indirect evidence to test our hypotheses: we want to know the composition of stars but can only measure the light they emit and absorb; we want to understand the neural basis of cognition but can only observe changes in blood flow. In science, we bridge the gap between ordinary perception and the otherwise unobservable and unknown through extensive causal chains. In everyday life, we do not use fancy telescopes or imaging equipment but must bridge an analogous gap: we hear a crash in another room and infer that something heavy was dropped; we see a curtain move and infer the cat behind it. These are ordinary, common-sense inferences—ones even a child might make—but they depend on an extraordinary capacity: the ability to use our understanding of the physical world to reason back from what we perceive to its probable unobserved causes.

We focus on a paradigmatic case of everyday exploration: trying to figure out what is inside a box by shaking it. Most of us have shaken a wrapped present at some point to try to guess its contents, suggesting that we think we can imagine how different items would sound given the motion of the box. Consistent with this intuition, studies suggest that adults, and even infants 3 , 4 , 5 , can mentally simulate the physical interactions of moving objects on short timescales. Such simulations might help us guess what is in a box, but they might also let us estimate the relative discriminability of different hypotheses and thereby make critical decisions about how to explore (e.g., how long to shake the box, how hard to shake it, or which of multiple boxes might be most worth shaking). As in science, a rational learner should be able to estimate the sensitivity of her measurement apparatus (in this case, her perceptual system) to decide what would count as an informative experiment and amount of data, given the alternative hypotheses she is trying to discriminate among 6 , 7 , 8 , 9 . Here we ask whether such an “intuitive psychophysics” guides children’s exploration. Can children use their intuitive understanding of both the physical world and their own ability to make perceptual discriminations to engage in effective exploration? Do they compare the perceptual evidence they observe with the evidence they think they would have observed under different competing hypotheses?

Our proposal builds on three more basic capacities that we already know children possess: aspects of intuitive physics (i.e., the ability to represent the physical interactions among objects) and intuitive psychology (i.e., the ability to represent the relationship between seeing and knowing), and an ability to make psychophysical discriminations themselves (i.e., to hear the difference between two quite different sounds more easily than the difference between two similar ones). In asking whether children have an “intuitive psychophysics”, we are asking whether children can use these abilities to judge whether they themselves will be able to distinguish evidence for different physical interactions. Can children simulate the interactions among physical events and the perceptual consequences of these interactions with sufficient granularity to represent their own ability to discriminate among events? Note that having an intuitive psychophysics need not imply that children can explicitly explain or justify their own judgments (any more than having an intuitive physics requires that children be able to explain their own reasoning about objects and forces). However, to the degree that children have an intuitive psychophysics, they should be able to represent the relative difficulty of discriminating perceptual evidence and these representations should guide their judgment and exploration.

Our study connects to a growing literature in cognitive science, cognitive neuroscience, and AI investigating rational curiosity: learners’ tendency to explore more when the expected information gain is higher 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 . Classic 18 and contemporary 19 , 20 work has examined the extent to which adult learning and exploration can be considered to be rational, and developmental studies suggest that even young children explore more when evidence is surprising 21 , 22 , 23 , 24 , 25 , 26 , 27 or confounded 28 , 29 , 30 . However, such studies have provided children with perceptually unambiguous evidence and, with the exception of work showing a U-shaped relationship between infant looking-time and the predictability of events 31 , 32 (see also ref. 5 ), looked only at qualitative relationships between children’s uncertainty and exploration. In particular, previous studies looking at children’s sensitivity to their own uncertainty have considered cases where evidence is surprising (e.g., refs. 25 , 31 ), uninformative with respect to competing hypotheses (e.g., ref. 29 ), or cases where children simply do not know the answer to a query (e.g., refs. 16 , 33 , 34 ). In contrast, here we look at cases where evidence to distinguish hypotheses is available and, in principle, informative, and we ask whether children represent their own ability to make distinctions among the available evidence. Specifically, rather than asking whether children can distinguish two different observations (as one might in a psychophysics experiment), we allow children to observe only one kind of event and we ask whether they recognize that the observation is more discriminable from some hypotheses than others. That is, we are interested in whether children can simulate the evidence they might get under alternative hypotheses and compare the discriminability of observed evidence with unobserved alternatives. Finally, we ask whether there is a precise quantitative relationship between the discriminability of competing hypotheses and children’s active exploration.

We report two series of experiments probing children’s intuitive psychophysics, considering first children’s reasoning about exploration, and second, their decisions about how long to explore. In Experiments 1–3, the experimenter shakes two boxes, generating identical sounds (see Fig.  1 ). Children are asked to decide which box they want to open to find a target. The only difference between the boxes is the alternative item that might have been in the box and the degree to which it would have been distinguishable from the target based on the sounds. In Experiments 4–7, children get to shake the box themselves to guess which of two alternatives are inside. The alternatives differ only in numerical quantity (e.g., three marbles or six marbles), which we vary across trials, systematically manipulating the discriminability of the hypotheses. Children are allowed to shake the box for as long as they want, allowing us to investigate the extent to which children’s free exploration tracks the quantitative discriminability of the alternative hypotheses. In Experiments 1–3, we focus on 4- and 5-year-olds, consistent with previous work on children’s active exploration 21 , 22 , 23 , 24 , 28 , 30 , 35 . In Experiments 4–7, where we look at children’s response to graded numerosity contrasts, we expand the range to 4- to 8-year-olds given the possibility that developmental changes in children’s number representations across this age range 36 , 37 might impact their exploration. Throughout, we adopt the convention in developmental psychology of reporting children’s ages as years; months (e.g., mean age of 4 years and 4 months is written 4;4).

The leftmost item in each pair was the target. Only one item in each pair (the target) was placed in each box. Because the target was always placed in both boxes, the two boxes in each experiment made the same sound when shaken.

Experiment 1

Preliminary studies (see SI) established that children could guess which of two boxes contained a target when the boxes generated two very different sounds when shaken: 100% of children distinguished a soft bean bag from a hard ball, and 100% distinguished eight marbles from two marbles. To establish that children engage in a relatively rich mental simulation of the physics of the event, we also showed that children were able to distinguish two from eight marbles even when the eight-marble box contained a cloth, muffling the sound ( N  = 15; mean age: 4;4; 86.7% correct; 95% CI [0.67−1], Bernoulli normal approximation CI) and even when the experimenter shook the two-marble box but tilted the eight-marble box back and forth, rather than shaking it ( N  = 15; mean age: 4;11; 86.7% correct; 95% CI [0.67−1]).

Having established that children’s intuitive physics can support inferences about the hidden causes of auditory stimuli, we turned to the question of whether children could determine the extent to which perceptual cues are and are not informative, given different competing hypotheses about their latent causes. In Experiments 1 and 2, we looked at participants’ inferences when the content of the boxes differed in kind; in Experiment 3, we looked at children’s inferences when the contents differed in quantity.

In Experiment 1 (see Fig.  1 and SI for details), children were introduced to two boxes. A pair of objects were placed in front of each box. Each pair consisted of an exciting target object (a pencil with a shiny holographic coating) and a boring distractor. The target was identical in both pairs. In the less discriminable pair, the distractor was an object that would make a very similar sound when shaken inside the box (a standard No. 2 pencil). In the more discriminable pair, the distractor was an object that would make a very different sound when shaken inside the box (a small pillow). The experimenter pointed to the shiny pencil and the boring pencil and told the child, “I’m going to take just one object -- either the shiny pencil or the plain pencil -- and put it in this box here.” Then she pointed to the other pair and the other box and said, “And then I’m going to take just one object -- either the shiny pencil or the cotton pillow -- and put it in this box here.” She put up an opaque screen and removed all the objects from the child’s line of sight. She silently put a shiny pencil in each box and then returned the boxes to the table. She told the child, “Remember, inside this box, there could be either a cool shiny pencil or the plain yellow pencil”; “Remember, inside this box, there could be either a cool shiny pencil or the pillow”; (order and L/R position counterbalanced). The experimenter shook each box generating identical sounds. Children were asked which box they wanted to open to find the target. The experimenter was not blind to the contents of the box, so to avoid her influencing the child’s choice, the left/right positions of the box were fixed and the experimenter looked directly at the child during the prompt. Children ( N  = 16, mean age: 4;7) successfully chose the box where the unheard alternative, the pillow, would have been easier to discriminate from the target (81.2%; 95% CI [0.63–1]).

Experiment 2

In Experiment 2, we replicated the design of Experiment 1, except that the more discriminable pair consisted of a small and large plastic elephant; the less discriminable pair consisted of a small plastic elephant and a small plastic pig. Children were told that the baby elephants had been separated from their friends (other plastic elephants housed in a separate container) and were asked to find them. The small elephant was hidden in both boxes. As in Experiment 1, children ( N  = 24; mean age: 4;8) successfully chose the box where the target would be easier to discriminate from the unheard alternative (the large elephant) (79%; 95% CI [0.63–0.96]). Importantly, this is not because children thought this pair was more dissimilar overall; a separate group of children ( N  = 24; mean age: 4;8) asked only which pair was more similar (without a box-shaking task) thought the small elephant and small pig were more dissimilar than the small and large elephant (83%; 95% CI [0.67–0.96]).

Experiment 3

In Experiment 3, preregistered on the Open Science Framework ( https://osf.io/ytvse/?view_only=abe4554f3ace483490953768b58efbfc ), we looked at whether children could infer the more discriminable of two boxes when the contents differed only in quantity. The less discriminable pair consisted of 8 marbles and 6 marbles; the more discriminable pair consisted of 8 marbles and 2 marbles. Both boxes in fact contained 8 marbles. Children ( N  = 24; mean: 5;0), successfully chose the box associated with the more discriminable (8 vs. 2) pair (75%; 95% CI [0.58–0.92]).

The results of Experiments 1–3 suggest that 4- and 5-year-old children represent the relative discriminability of perceptual evidence. Critically, children’s choices were guided not by the evidence they observed (which was identical between choices) but by its contrast with the unheard alternatives, consistent with the idea that children can simulate novel physical interactions and the perceptual data that will result 3 . Children’s ability to represent their own ability to make these perceptual discriminations is consistent with emerging evidence for metacognitive monitoring in young children (see ref. 38 for review) and also suggests that, at least in simple, forced-choice contexts, children can exercise metacognitive control for effective decision-making 39 , 40 , 41 , 42 , 43 .

Experiments 4–7

In Experiments 4–7, we looked to see if children’s exploration times quantitatively tracked the discriminability of hypotheses. Because we wanted to test children on a range of discriminability contrasts (and because pilot work suggested it was impractical to test children on more than four contrasts at a time), we ran four separate experiments consisting of four contrasts each. The experiments differed only in the contrasts presented. The design and quantitative predictions for the last experiment (Experiment 7), as well as the overall analysis across all 16 contrasts, were preregistered ( https://osf.io/dxguw/?view_only=ba3ca1c5ff9346c0a39e731291aa5d5f ). See SI for details throughout.

The experimenter introduced two tubes of marbles; each tube contained a different number of marbles, varying in numerosity between one and nine (Fig.  2 ). Out of the children’s sight, the contents of one of the tubes were placed in the box. Children were allowed to shake the box for as long as they liked to try to guess its contents. After each trial, a new pair of tubes were introduced. Children were not given any feedback between trials.

The placement of contrasts corresponds to relative discriminability. The actual trial order was counterbalanced, as was the order in which the tubes of marbles were introduced and the contents hidden in the box (e.g., whether 1 or 7 marbles were hidden on the 7-vs.-1 trial), except in Experiment 6, where the content was held fixed at 8 and 3 for both high- and low-discriminability contrasts to provide a within-experiment test of whether content or contrast affected children’s exploration time.

Exploration time was coded from video by a human coder blind to contrast and, independently, by a motion sensor in the box (see SI). The experimenter was not blind to the contents of the box, but was blind to the precise predictions across all sixteen contrasts. The experimenter was positioned alongside the child, out of the child’s direct line of sight, and did not interact with the child or the box during the exploration period. The behavioral coding included the time from the moment the child first contacted the box until she identified the contents of the box on each trial. The motion sensor coded the time from the initial motion to the final motion on each trial. We also looked at the motion sensor data, including the only time when the box was actually in motion (i.e., excluding any pauses, see SI). Here we report the results of the behavioral coding since the relationship between uncertainty and exploration may be best indexed by including the time the children could have been planning subsequent actions and thinking about the data they generated, but the primary results hold for all measures (see SI).

To normalize for individual differences in children’s exploratory behavior, we computed the time each child spent exploring on each trial as a proportion of the child’s total playtime across all four trials and multiplied this proportion by the number of trials in the experiment. Thus, a proportion less than 1 represents less playtime (and a proportion more than 1, more playtime) than would be expected if children distributed their playtime evenly across trials. Although we use proportional playtime to control for individual differences in length of play, all results hold using untransformed (log) playtime reported in seconds (see SI).

To quantify the discriminability of different contrasts, we adopted a variant of the standard signal detection model in which shaking a box with m marbles in it would produce a perceptual trace drawn from some probability distribution over a high-dimensional acoustic space, which can be projected down to a one-dimensional space of abstract numerosity analogous to representations in the approximate number system 44 , 45 . We modeled the internal representation for each auditorily perceived number as a normal distribution on a log scale (see SI), with equal variances σ but logarithmically spaced means, and computed the discriminability of each contrast between l and m marbles presented in Experiments 4–7 in terms of the standard index

where \({\mu }_{l}={\rm{log}}\ l\) and \({\mu }_{m}={\rm{log }}\ m\) . See SI for a summary of these d ′ values (Supplementary Table  1 ), as well as a discussion of alternative ways of estimating discriminability (including different mathematical models, and an empirical estimate from independent adult psychophysical data). These produce nearly identical results for our purposes. We modeled children’s intuitions about task difficulty as proportional to this d’ measure. Note however those children hear only a single set of marbles in the box on each trial and have no way of judging directly from the auditory data the discriminability of the two set sizes being contrasted. Rather, we posit that children’s sense of discriminability depends on their ability to evaluate the contrast between the sounds they hear and their simulation of the sounds they would have heard had the alternative set of marbles been in the box.

Each of Experiments 4–7 was analyzed separately for qualitative effects of discriminability, trial order, and the number of marbles in the box on exploration time (see SI). Here we focus on the preregistered joint analysis addressing our primary question about the effect of discriminability on exploration across all 16 contrasts in Experiments 4–7: Did children systematically explore longer when contrasts were less discriminable? The discriminability of the contrast quantitatively predicted children’s exploration time across the full range of contrasts ( β =0.24, 95% CI [0.18–0.30]). Children’s exploration time tracked the difficulty of distinguishing the heard and unheard alternative in a remarkably fine-grained way (Fig.  3A, B ), correlating strongly with the model whether exploration was coded from video ( r =0.95; 95% CI [0.78, 0.95]) or with the motion sensor (see SI).

Whether coded by hand ( A ) or by the motion sensor ( B ) children’s exploration correlated strongly with the difficulty of the discrimination. Error bars indicate SEMs. Source data are provided as a Source data file.

Strikingly, children’s exploration time was independent of the number of marbles actually in the box (Fig.  4 ; β =0.0065, 95% CI [−0.0094, 0.022]). Thus, although the sensorimotor experience of shaking a box containing only one or two marbles was quite different from shaking a box containing eight or nine marbles, children’s exploration depended not only on what they heard but also on what they did not hear: the contrast between the observed evidence and the unheard alternative.

There is no significant correlation between exploration time and number of marbles. Error bars indicate SEMs. Source data are provided as a Source data file.

We also analyzed other factors that might affect exploration. Across experiments, children’s exploration decreased only slightly over the four successive trials ( β =−0.051, 95% CI [−0.086, −0.016]); age had no effect on children’s tendency to explore the hardest contrast longer than the easiest one ( β =−0.041, 95% CI [−0.45, 0.40]). As expected, children’s accuracy increased with the discriminability of the contrast ( β =1.12, 95% CI [0.64, 1.46]); there was a marginal effect of age on children’s accuracy ( β =0.033, 95% CI [−0.0074, 0.069]).

Finally, we asked whether aggregate behavior in each individual experiment and each individual child’s behavior also tended to conform with the predictions of the discriminability model. There was substantial variability in individual children’s playtimes, but average playtimes within each experiment were qualitatively well-predicted by a linear fit to the discriminability model (Fig.  5 ). In addition, in each experiment, a significant majority of individual children explored more, on average, for more difficult discriminations (Fig.  5 ): for 19/24 children in Experiment 4 (79%; 95% CI [0.58–0.93]), 21/24 children in Experiment 5 (85%; 95% CI [0.68–0.97]), 18/24 children in Experiment 6 (75%; 95% CI [0.53−0.90]), and 19/24 children in Experiment 7 (79%; 95% CI [0.58–0.9]), a linear regression of that child’s playtimes onto discriminability had a positive slope. Hence, not only on average, but at the level of individuals as well, children systematically explored longer when contrasts were less discriminable.

Conditions ordered by discriminability ( n = 24 per experiment). Diamonds represent condition means, and box plots indicate medians, 25th and 75th percentiles, and outlier ranges. Blue lines show the predictions of the discriminability model under a linear fit to mean playtimes. Thin lines connect the responses of each individual child, with red lines indicating children who qualitatively followed the model’s predictions, exploring more on average when contrasts were harder (i.e., a linear regression of that child’s playtimes onto discriminability had a positive slope). Source data are provided as a Source data file.

Collectively, the results of these seven experiments suggest that, at least in familiar domains with simple tasks, children can simulate physical interactions and the perceptual data that will result. Furthermore, children can represent their own ability to make the perceptual discriminations needed to compare observed data with simulated, unobserved data under alternative hypotheses. Children represent the relative difficulty of different discrimination problems in ways that support effective decision-making and exploration: they prefer easier problems and explore more given harder ones. The precise, quantitative relationship between children’s exploratory play and the difficulty of perceptual discrimination problems suggests that starting in early childhood, human learners intuitively compute the value of evidence for discriminating alternative hypotheses, and use this sense of uncertainty to rationally calibrate their exploration.

Our account relies on mental simulation, and our quantitative results in Experiments 4–7 analyzed children’s exploratory behavior using idealized models of perceptual discriminability in these mental simulations. However, it is possible that children might have relied on some simpler cognitive mechanism or heuristic 46 , or a resource-constrained approximation to this ideal 47 , 48 . One natural alternative to consider for Experiments 4–7 is that children took into account only a simple contrast in the linguistically and graphically presented number of marbles in each pair, without attending at all to the rich perceptual data they obtained in shaking the box or imagining possible sounds they might hear via mental simulations of box shaking. We evaluated two such heuristic models that avoid the computational burden that might accompany mental simulation, based on the absolute difference and the (negative) ratio of the numbers of marbles in each pair. Both of these models perform well numerically (see SI, Additional Heuristic Models), and so it is indeed possible that children rely on such a mechanism in Experiments 4–7.

The current studies also open up provocative questions for future research. They suggest that children have some metacognitive knowledge about their own ability to make perceptual discriminations. Anecdotally, some children also proffered explicit accounts of their own reasoning. In piloting Experiment 1 for instance, a child said that he preferred the more discriminable box because the pair was “more not the same”. Likewise, in Experiments 4–7, children sometimes explained their own reasoning (e.g., “this one’s gonna be hard”). Given the sophistication of the judgment required here (in which children had to compare observed data with unobserved alternatives), we believe children’s choices and exploration were less likely to underestimate their reasoning than asking children to justify their choices. However, further research might look at the extent to which children can explicitly account for the reasoning behind their decisions.

Although it seems implausible that children store and retrieve precise representations of the sound of marbles shaken in boxes, we do not know how children (or adults) simulate physical interactions and the sounds they might make with sufficient richness to make these fine-grained discriminations. Intuitively, our ability to imagine what we might perceive given different novel interventions is arbitrarily generative: we can imagine not only how marbles might sound when shaken in a box, but how the sound might change if we added water to the box—or pennies—or a sock. Future work should target both the mechanisms that support these rich online simulations and the limits of our ability to imagine such interactions and their perceivable consequences.

We focused on learners’ ability to represent the difficulty of statistical discriminations in a psychophysical context, but our results might reflect a quite general ability to estimate how much data it would take to distinguish competing hypotheses. Future research might look at children’s sensitivity to their own ability to discriminate evidence in other domains, probing the extent to which children can engage in these behaviors more broadly.

We also do not know to what extent the abilities children showed here might emerge earlier in development, or in nonhuman animals. When confronted with easy and difficult problems, children as young as three adapt their behavior appropriately (i.e., opting out of difficult problems or asking for help 38 ); future research might look at whether young preschoolers—or in simpler contexts, even toddlers and infants—might, as here, also be able to anticipate the relative difficulty of different kinds of problems and adjust their choices and exploration accordingly. Similarly, macaques, capuchins, apes, and dolphins show some sensitivity to their uncertainty across a range of tasks (see ref. 49 and refs. 50 , 51 for reviews and discussion); the current paradigm might be adapted to test intuitive psychophysics across species. Would, for instance, a nonhuman primate be able to infer the probable contents of a container from the sound it made when it was shaken? If two containers were shaken and the animal heard a sloshing sound, would it preferentially open the box which could have contained the juice or a rock, or rather than the one which could have contained juice or water? Queries like these might allow us to test the extent to which our ability to recover the generative causes of perceptual stimuli, compare heard and unheard alternatives, and prefer more discriminable evidence emerges across species.

Finally, here we probed children’s ability to reason back a single step in a causal chain: from the sound objects made when shaken in a box to the objects making the sound. But as lay adults, we can reason backward through multiple steps in a causal chain to events increasingly remote from direct experience. We can see the lights go out and infer that a storm knocked over a tree branch and downed a power line, or we can see a pileup of traffic and infer that a ship is passing under a drawbridge, miles up the road. Our work suggests that young children can go from perceptual data to the physical causes that gave rise to them, and compare their observations with other evidence they might have observed, in order to make rational choices about how to explore. Future work might look at how these intuitive capacities develop into ones that can guide learning and discovery over a lifetime, culminating in the scientific practices that let us connect observations to events that are too big or too small, too fast or too slow, or too remote in space or time for direct perception. Progress on these questions has the potential to give us new insight into the origins of inquiry.

Participants

Across Experiments 1–7, we recruited 184 children (mean: 5;2, range 3;0–8;6) who were visiting a local children’s museum. Sixteen other participants were excluded from the analysis due to preferring the distractor object 12 , experimenter error 3 , failure to pass inclusion trial or attend to task 4 , and family interference 1 . All experiments were approved by an institutional review board for human subjects and all ethical guidelines were followed. The child’s parent or legal guardian was provided with a verbal description of the study. The experimenter answered any questions the parent had. The parent or legal guardian then provided written informed consent to participation and videotaping of the study consistent with the MIT IRB approval for the study. Children over age seven also provided verbal assent to participate.

In all preliminary studies, two cardboard shoeboxes covered with black electrical tape were used and a large cardboard screen (80 cm ×  60 cm) was used as an occluder. In the Object Identity study, a square beanbag and a plastic ball of equal weight were used (5-cm diameter). For all other preliminary studies, ten colored marbles and two translucent cylindrical tubes were used. A stuffed animal bunny was used as a character in the script. In the Volume Control experiment, a felt cloth fitted to the bottom of the shoebox was used to alter the sound of the marbles when shaken.

For Experiments 1–3, the same tape-covered cardboard boxes and screen were used as in the preliminary studies, with the items being hidden differing between experiments. In Experiment 1, two pencils with a shiny, holographic coating were used as target objects. A standard yellow pencil and a small, cotton-filled fabric cushion were used as distractor objects. In Experiment 2, one large (approximately 8 cm by 5 cm) and six small (approximately 3 cm by 2 cm) plastic elephants were used. A small plastic pig (approximately 3 cm by 2 cm) was also used. A transparent, hexagonally partitioned container was used as the baby elephants’ home. In Experiment 3, four transparent cylinder tubes were used. Two tubes each contained eight different colored marbles, arranged to look identical to each other; one tube contained two white marbles, and one tube contained six white marbles. The tubes were sealed at the top with packing tape. Drawings of each of the marble tubes were also used as a memory cue. A stuffed animal bunny was used to occupy the children’s hands so that they did not reach for the stimuli or interfere with the demonstrations.

In Experiments 4–7, a single tape-covered shoebox (18 cm × 16 cm x 12 cm) was used. Four objects were used in the practice trials: a plastic duck, a star-shaped pillow, a flat glass bead, and a cotton ball. For the test trials, standard-size glass marbles in eight colors and eight translucent cylindrical tubes were used. The tubes were preloaded with the appropriate number of marbles and sealed at the top; although children were told that the tubes of marbles would be poured into the box, marbles were in fact added quietly by hand to ensure that children did not get any evidence about the sound until they themselves shook the box. A large cardboard screen (80 cm × 60 cm) was used both as an occluder and as an answer board with six Velcro tabs for children to provide their responses. Laminated pictures with Velcro tabs on the back, approximately to scale, were used to depict the possible contents of the box for both the practice trials and the test trials.

All children were tested individually in a private testing room off of the museum floor. The child and the experimenter sat on opposite sides of a child-sized table. All sessions were videotaped. Children’s responses were coded live by the experimenter and recoded by a coder blind to conditions from video. In addition to measuring children’s exploratory behavior via video coding, we developed an independent measure based on the time course of the motion of the box. We equipped a microcontroller with an accelerometer and placed the device in a small compartment of the box (the compartment was attached at the top corner of the box so as to minimize the possibility that it might interfere with box shaking). Custom software wirelessly transmitted the accelerometer readings, in real time, to a computer that recorded the measurements. The experimenter pressed a button at the start and end of every trial to record the time interval during which box shaking could have occurred.

Reporting summary

Further information on research design is available in the  Nature Research Reporting Summary linked to this article.

Data availability

A reporting summary is available as a Supplementary information file. All data are available at https://osf.io/n97fr/ . Source data underlying Figs.  3 – 5 are available as a Source data file.  Source data are provided with this paper.

Code availability

All source code for analysis is available at https://osf.io/n97fr/ .

See SI for detailed materials, methods, and procedures .

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Acknowledgements

We thank the Boston Children’s Museum and the families who participated in this research. We also thank Nancy Kanwisher, Josh McDermott, Drazen Prelec, and Rebecca Saxe for reviewing drafts of the paper, Angela Kim and Julia Simon for help with data collection, Kary Richardson for coding, Kevin Smith and Julian Jara-Ettinger for statistical assistance, and Regina Ebo for assistance with the references. This material is based on work supported by the Center for Brains, Minds, and Machines, funded by NSF STC award CCF-1231216 and an NSF Graduate Research Fellowship to R.W.M.

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These authors contributed equally: Max H. Siegel and Rachel W. Magid.

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Massachusetts Institute of Technology, Cambridge, MA, USA

Max H. Siegel, Rachel W. Magid, Madeline Pelz, Joshua B. Tenenbaum & Laura E. Schulz

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R.W.M. assisted with the study design, piloted Experiments 1–3, ran Experiments 4–7, and contributed to the data analysis and writing; M.H.S. conceived of the study, ran the preliminary experiments and Experiment 1, developed the model, and contributed to the data analysis and writing; M.P. ran Experiments 2–3 and contributed to the data analysis and writing; J.B.T. contributed to the study design, model, and writing; L.E.S. contributed to the study design and writing.

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Siegel, M.H., Magid, R.W., Pelz, M. et al. Children’s exploratory play tracks the discriminability of hypotheses. Nat Commun 12 , 3598 (2021). https://doi.org/10.1038/s41467-021-23431-2

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Explanation of Hypothesis

Contradiction, simple hypothesis, complex hypothesis, null hypothesis, alternative hypothesis, empirical hypothesis, statistical hypothesis, special example of hypothesis, solution part (a), solution part (b), hypothesis|definition & meaning.

A hypothesis is a claim or statement  that makes sense in the context of some information or data at hand but hasn’t been established as true or false through experimentation or proof.

In mathematics, any statement or equation that describes some relationship between certain variables can be termed as hypothesis if it is consistent with some initial supporting data or information, however, its yet   to be proven true or false by some definite and trustworthy experiment or mathematical law. 

Following example illustrates one such hypothesis to shed some light on this very fundamental concept which is often used in different areas of mathematics.

Figure 1: Example of Hypothesis

Here we have considered an example of a young startup company that manufactures state of the art batteries. The hypothesis or the claim of the company is that their batteries have a mean life of more than 1000 hours. Now its very easy to understand that they can prove their claim on some testing experiment in their lab.

However, the statement can only be proven if and only if at least one batch of their production batteries have actually been deployed in the real world for more than 1000 hours . After 1000 hours, data needs to be collected and it needs to be seen what is the probability of this statement being true .

The following paragraphs further explain this concept.

As explained with the help of an example earlier, a hypothesis in mathematics is an untested claim that is backed up by all the known data or some other discoveries or some weak experiments.

In any mathematical discovery, we first start by assuming something or some relationship . This supposed statement is called a supposition. A supposition, however, becomes a hypothesis when it is supported by all available data and a large number of contradictory findings.

The hypothesis is an important part of the scientific method that is widely known today for making new discoveries. The field of mathematics inherited this process. Following figure shows this cycle as a graphic:

Figure 2: Role of Hypothesis in the Scientific Method 

The above figure shows a simplified version of the scientific method. It shows that whenever a supposition is supported by some data, its termed as hypothesis. Once a hypothesis is proven by some well known and widely acceptable experiment or proof, its becomes a law. If the hypothesis is rejected by some contradictory results then the supposition is changed and the cycle continues.

Lets try to understand the scientific method and the hypothesis concept with the help of an example. Lets say that a teacher wanted to analyze the relationship between the students performance in a certain subject, lets call it A, based on whether or not they studied a minor course, lets call it B.

Now the teacher puts forth a supposition that the students taking the course B prior to course A must perform better in the latter due to the obvious linkages in the key concepts. Due to this linkage, this supposition can be termed as a hypothesis.

However to test the hypothesis, the teacher has to collect data from all of his/her students such that he/she knows which students have taken course B and which ones haven’t. Then at the end of the semester, the performance of the students must be measured and compared with their course B enrollments.

If the students that took course B prior to course A perform better, then the hypothesis concludes successful . Otherwise, the supposition may need revision.

The following figure explains this problem graphically.

Figure 3: Teacher and Course Example of Hypothesis

Important Terms Related to Hypothesis

To further elaborate the concept of hypothesis, we first need to understand a few key terms that are widely used in this area such as conjecture, contradiction and some special types of hypothesis (simple, complex, null, alternative, empirical, statistical). These terms are briefly explained below:

A conjecture is a term used to describe a mathematical assertion that has notbeenproved. While testing   may occasionally turn up millions of examples in favour of a conjecture, most experts in the area will typically only accept a proof . In mathematics, this term is synonymous to the term hypothesis.

In mathematics, a contradiction occurs if the results of an experiment or proof are against some hypothesis.  In other words, a contradiction discredits a hypothesis.

A simple hypothesis is such a type of hypothesis that claims there is a correlation between two variables. The first is known as a dependent variable while the second is known as an independent variable.

A complex hypothesis is such a type of hypothesis that claims there is a correlation between more than two variables.  Both the dependent and independent variables in this hypothesis may be more than one in numbers.

A null hypothesis, usually denoted by H0, is such a type of hypothesis that claims there is no statistical relationship and significance between two sets of observed data and measured occurrences for each set of defined, single observable variables. In short the variables are independent.

An alternative hypothesis, usually denoted by H1 or Ha, is such a type of hypothesis where the variables may be statistically influenced by some unknown factors or variables. In short the variables are dependent on some unknown phenomena .

An Empirical hypothesis is such a type of hypothesis that is built on top of some empirical data or experiment or formulation.

A statistical hypothesis is such a type of hypothesis that is built on top of some statistical data or experiment or formulation. It may be logical or illogical in nature.

According to the Riemann hypothesis, only negative even integers and complex numbers with real part 1/2 have zeros in the Riemann zeta function . It is regarded by many as the most significant open issue in pure mathematics.

Figure 4: Riemann Hypothesis

The Riemann hypothesis is the most well-known mathematical conjecture, and it has been the subject of innumerable proof efforts.

Numerical Examples

Identify the conclusions and hypothesis in the following given statements. Also state if the conclusion supports the hypothesis or not.

Part (a): If 30x = 30, then x = 1

Part (b): if 10x + 2 = 50, then x = 24

Hypothesis: 30x = 30

Conclusion: x = 10

Supports Hypothesis: Yes

Hypothesis: 10x + 2 = 50

Conclusion: x = 24

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