hypothesis rejected and accepted

What is The Null Hypothesis & When Do You Reject The Null Hypothesis

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A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating the dependent variable or due to random chance.

How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

Examples of Null Hypotheses

When do we reject the null hypothesis .

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected.

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a p -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Probability and statistical significance in ab testing. Statistical significance in a b experiments

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist.

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null.

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter.

Purpose of a Null Hypothesis

The primary purpose of the null hypothesis is to disprove an assumption.
Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true.

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study.

What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”). However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing. Political research quarterly , 52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method. American Psychologist , 56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing. Behavior research methods , 43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods , 5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological bulletin , 57 (5), 416.

Hypothesis Testing (cont...)

Hypothesis testing, the null and alternative hypothesis.

In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen ( hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the mean exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the distributions , medians , amongst other things. As such, we can state:

Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.

Significance levels

The level of statistical significance is often expressed as the so-called p -value . Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p -value) of observing your sample results (or more extreme) given that the null hypothesis is true . Another way of phrasing this is to consider the probability that a difference in a mean score (or other statistic) could have arisen based on the assumption that there really is no difference. Let us consider this statement with respect to our example where we are interested in the difference in mean exam performance between two different teaching methods. If there really is no difference between the two teaching methods in the population (i.e., given that the null hypothesis is true), how likely would it be to see a difference in the mean exam performance between the two teaching methods as large as (or larger than) that which has been observed in your sample?

So, you might get a p -value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

Whilst there is relatively little justification why a significance level of 0.05 is used rather than 0.01 or 0.10, for example, it is widely used in academic research. However, if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).

One- and two-tailed predictions

When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:

The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.

Sarah predicted that her teaching method (independent variable: teaching method), whereby she not only required her students to attend lectures, but also seminars, would have a positive effect (that is, increased) students' performance (dependent variable: exam marks). If an alternative hypothesis has a direction (and this is how you want to test it), the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:

In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition (going to seminar classes as well as lectures) would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect. However, this is just our opinion (and hope) and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction (i.e., and testing for it this way) is frowned upon as it usually reflects the hope of a researcher rather than any certainty that it will happen. Notable exceptions to this rule are when there is only one possible way in which a change could occur. This can happen, for example, when biological activity/presence in measured. That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" (i.e., it cannot possibly reduce the activity of a "dormant" protein). In addition, for some statistical tests, one-tailed tests are not possible.

Rejecting or failing to reject the null hypothesis

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

Statistics Made Easy

When Do You Reject the Null Hypothesis? (3 Examples)

A hypothesis test is a formal statistical test we use to reject or fail to reject a statistical hypothesis.

We always use the following steps to perform a hypothesis test:

Step 1: State the null and alternative hypotheses.

The null hypothesis , denoted as H 0 , is the hypothesis that the sample data occurs purely from chance.

The alternative hypothesis , denoted as H A , is the hypothesis that the sample data is influenced by some non-random cause.

2. Determine a significance level to use.

Decide on a significance level. Common choices are .01, .05, and .1.

3. Calculate the test statistic and p-value.

Use the sample data to calculate a test statistic and a corresponding p-value .

4. Reject or fail to reject the null hypothesis.

If the p-value is less than the significance level, then you reject the null hypothesis.

If the p-value is not less than the significance level, then you fail to reject the null hypothesis.

You can use the following clever line to remember this rule:

“If the p is low, the null must go.”

In other words, if the p-value is low enough then we must reject the null hypothesis.

The following examples show when to reject (or fail to reject) the null hypothesis for the most common types of hypothesis tests.

Example 1: One Sample t-test

A one sample t-test is used to test whether or not the mean of a population is equal to some value.

For example, suppose we want to know whether or not the mean weight of a certain species of turtle is equal to 310 pounds.

We go out and collect a simple random sample of 40 turtles with the following information:

Sample size n = 40
Sample mean weight x = 300
Sample standard deviation s = 18.5

We can use the following steps to perform a one sample t-test:

Step 1: State the Null and Alternative Hypotheses

We will perform the one sample t-test with the following hypotheses:

H 0 : μ = 310 (population mean is equal to 310 pounds)
H A : μ ≠ 310 (population mean is not equal to 310 pounds)

We will choose to use a significance level of 0.05 .

We can plug in the numbers for the sample size, sample mean, and sample standard deviation into this One Sample t-test Calculator to calculate the test statistic and p-value:

t test statistic: -3.4187
two-tailed p-value: 0.0015

Since the p-value (0.0015) is less than the significance level (0.05) we reject the null hypothesis .

We conclude that there is sufficient evidence to say that the mean weight of turtles in this population is not equal to 310 pounds.

Example 2: Two Sample t-test

A two sample t-test is used to test whether or not two population means are equal.

For example, suppose we want to know whether or not the mean weight between two different species of turtles is equal.

We go out and collect a simple random sample from each population with the following information:

Sample size n 1 = 40
Sample mean weight x 1 = 300
Sample standard deviation s 1 = 18.5
Sample size n 2 = 38
Sample mean weight x 2 = 305
Sample standard deviation s 2 = 16.7

We can use the following steps to perform a two sample t-test:

We will perform the two sample t-test with the following hypotheses:

H 0 : μ 1 = μ 2 (the two population means are equal)
H 1 : μ 1 ≠ μ 2 (the two population means are not equal)

We will choose to use a significance level of 0.10 .

We can plug in the numbers for the sample sizes, sample means, and sample standard deviations into this Two Sample t-test Calculator to calculate the test statistic and p-value:

t test statistic: -1.2508
two-tailed p-value: 0.2149

Since the p-value (0.2149) is not less than the significance level (0.10) we fail to reject the null hypothesis .

We do not have sufficient evidence to say that the mean weight of turtles between these two populations is different.

Example 3: Paired Samples t-test

A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.

For example, suppose we want to know whether or not a certain training program is able to increase the max vertical jump of college basketball players.

To test this, we may recruit a simple random sample of 20 college basketball players and measure each of their max vertical jumps. Then, we may have each player use the training program for one month and then measure their max vertical jump again at the end of the month:

We can use the following steps to perform a paired samples t-test:

We will perform the paired samples t-test with the following hypotheses:

H 0 : μ before = μ after (the two population means are equal)
H 1 : μ before ≠ μ after (the two population means are not equal)

We will choose to use a significance level of 0.01 .

We can plug in the raw data for each sample into this Paired Samples t-test Calculator to calculate the test statistic and p-value:

t test statistic: -3.226
two-tailed p-value: 0.0045

Since the p-value (0.0045) is less than the significance level (0.01) we reject the null hypothesis .

We have sufficient evidence to say that the mean vertical jump before and after participating in the training program is not equal.

Bonus: Decision Rule Calculator

You can use this decision rule calculator to automatically determine whether you should reject or fail to reject a null hypothesis for a hypothesis test based on the value of the test statistic.

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Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

Clear and precise
Capable of being tested
Able to relate to a variable
Stated in simple terms
Consistent with known facts
Limited in scope and specific
Tested in a limited timeframe
Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A null hypothesis is a hypothesis when there is no significant relationship between the dependent and the participants’ independent variables .

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

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How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to gather the data obtained through a large number of samples from a specific population.

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance.

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

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Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided.

If the significance level is minimum, then it prevents the researchers from false claims.

The significance level is denoted by P, and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the outcomes of your study . You need to ensure whether you have met the objectives of your research or not.

In the discussion section and conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis?

Always remember that you either conclude to reject Ho in favor of Haor do not reject Ho . It would help if you never rejected Ha or even accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude reject Ho in favor of Haor do not reject Ho, then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

One-Sample Test : Compare sample data to a known population value.
Two-Sample Test : Compare means between two sample groups.
ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

9.8: Hypothesis: Accept or Fail to Reject?

Chapter 1: understanding statistics, chapter 2: summarizing and visualizing data, chapter 3: measure of central tendency, chapter 4: measures of variation, chapter 5: measures of relative standing, chapter 6: probability distributions, chapter 7: estimates, chapter 8: distributions, chapter 9: hypothesis testing, chapter 10: analysis of variance, chapter 11: correlation and regression, chapter 12: statistics in practice.

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In an experiment, a farm with infected plants is subjected to a widely applicable insecticide.

This insecticide is expected to increase the number of healthy plants after its application. However, at the end of the experiment, the proportion of healthy and infected plants remained the same.

Here, the null hypothesis that the insecticide has no effect seems to hold, but should one accept the hypothesis or fail to reject it?

Accepting this hypothesis would mean that the insecticide is ineffective and cannot improve the plants' health.

This decision actually overlooks the other plausible explanations for the observed results.

In this case, using an unprescribed amount or concentration of insecticide might have resulted in no effect.

There is a possibility of plants being infected by something that the insecticide cannot target.

Failing to reject a null hypothesis means there is no sufficient evidence for the expected or the observed effect.

Today, if scientists had accepted null hypotheses, the discovery of plant viruses or the rediscovery of many extinct species would not have been possible.

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P -values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?

There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null hypothesis and 'fail to reject' the null hypothesis. Superficially, both these phrases mean the same, but in statistics, the meanings are somewhat different. The phrase 'accept the null hypothesis' implies that the null hypothesis is by nature true, and it is proved. But a hypothesis test simply provides information that there is no sufficient evidence in support of the alternative hypothesis, and therefore the null hypothesis cannot be rejected. The null hypothesis cannot be proven, although the hypothesis test begins with an assumption that the hypothesis is true, and the final result indicates the failure of the rejection of the null hypothesis. Thus, it is always advisable to state 'fail to reject the null hypothesis' instead of 'accept the null hypothesis.'

'Accepting' a hypothesis may also imply that the given hypothesis is now proven, so there is no need to study it further. Nevertheless, that is never the case, as newer scientific evidence often challenges the existing studies. Discovery of viruses and fossils, rediscovery of presumed extinct species, criminal trials, and novel drug tests follow the same principles of testing hypotheses. In those cases, 'accepting' a hypothesis may lead to severe consequences.

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What 'Fail to Reject' Means in a Hypothesis Test

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In statistics , scientists can perform a number of different significance tests to determine if there is a relationship between two phenomena. One of the first they usually perform is a null hypothesis test. In short, the null hypothesis states that there is no meaningful relationship between two measured phenomena. After a performing a test, scientists can:

Reject the null hypothesis (meaning there is a definite, consequential relationship between the two phenomena), or
Fail to reject the null hypothesis (meaning the test has not identified a consequential relationship between the two phenomena)

Key Takeaways: The Null Hypothesis

• In a test of significance, the null hypothesis states that there is no meaningful relationship between two measured phenomena.

• By comparing the null hypothesis to an alternative hypothesis, scientists can either reject or fail to reject the null hypothesis.

• The null hypothesis cannot be positively proven. Rather, all that scientists can determine from a test of significance is that the evidence collected does or does not disprove the null hypothesis.

It is important to note that a failure to reject does not mean that the null hypothesis is true—only that the test did not prove it to be false. In some cases, depending on the experiment, a relationship may exist between two phenomena that is not identified by the experiment. In such cases, new experiments must be designed to rule out alternative hypotheses.

Null vs. Alternative Hypothesis

The null hypothesis is considered the default in a scientific experiment . In contrast, an alternative hypothesis is one that claims that there is a meaningful relationship between two phenomena. These two competing hypotheses can be compared by performing a statistical hypothesis test, which determines whether there is a statistically significant relationship between the data.

For example, scientists studying the water quality of a stream may wish to determine whether a certain chemical affects the acidity of the water. The null hypothesis—that the chemical has no effect on the water quality—can be tested by measuring the pH level of two water samples, one of which contains some of the chemical and one of which has been left untouched. If the sample with the added chemical is measurably more or less acidic—as determined through statistical analysis—it is a reason to reject the null hypothesis. If the sample's acidity is unchanged, it is a reason to not reject the null hypothesis.

When scientists design experiments, they attempt to find evidence for the alternative hypothesis. They do not try to prove that the null hypothesis is true. The null hypothesis is assumed to be an accurate statement until contrary evidence proves otherwise. As a result, a test of significance does not produce any evidence pertaining to the truth of the null hypothesis.

Failing to Reject vs. Accept

In an experiment, the null hypothesis and the alternative hypothesis should be carefully formulated such that one and only one of these statements is true. If the collected data supports the alternative hypothesis, then the null hypothesis can be rejected as false. However, if the data does not support the alternative hypothesis, this does not mean that the null hypothesis is true. All it means is that the null hypothesis has not been disproven—hence the term "failure to reject." A "failure to reject" a hypothesis should not be confused with acceptance.

In mathematics, negations are typically formed by simply placing the word “not” in the correct place. Using this convention, tests of significance allow scientists to either reject or not reject the null hypothesis. It sometimes takes a moment to realize that “not rejecting” is not the same as "accepting."

Null Hypothesis Example

In many ways, the philosophy behind a test of significance is similar to that of a trial. At the beginning of the proceedings, when the defendant enters a plea of “not guilty,” it is analogous to the statement of the null hypothesis. While the defendant may indeed be innocent, there is no plea of “innocent” to be formally made in court. The alternative hypothesis of “guilty” is what the prosecutor attempts to demonstrate.

The presumption at the outset of the trial is that the defendant is innocent. In theory, there is no need for the defendant to prove that he or she is innocent. The burden of proof is on the prosecuting attorney, who must marshal enough evidence to convince the jury that the defendant is guilty beyond a reasonable doubt. Likewise, in a test of significance, a scientist can only reject the null hypothesis by providing evidence for the alternative hypothesis.

If there is not enough evidence in a trial to demonstrate guilt, then the defendant is declared “not guilty.” This claim has nothing to do with innocence; it merely reflects the fact that the prosecution failed to provide enough evidence of guilt. In a similar way, a failure to reject the null hypothesis in a significance test does not mean that the null hypothesis is true. It only means that the scientist was unable to provide enough evidence for the alternative hypothesis.

For example, scientists testing the effects of a certain pesticide on crop yields might design an experiment in which some crops are left untreated and others are treated with varying amounts of pesticide. Any result in which the crop yields varied based on pesticide exposure—assuming all other variables are equal—would provide strong evidence for the alternative hypothesis (that the pesticide does affect crop yields). As a result, the scientists would have reason to reject the null hypothesis.

Hypothesis Test for the Difference of Two Population Proportions
Type I and Type II Errors in Statistics
Null Hypothesis and Alternative Hypothesis
Null Hypothesis Examples
How to Conduct a Hypothesis Test
An Example of a Hypothesis Test
What Is a P-Value?
The Difference Between Type I and Type II Errors in Hypothesis Testing
What Is a Hypothesis? (Science)
Null Hypothesis Definition and Examples
Hypothesis Test Example
What Level of Alpha Determines Statistical Significance?
The Runs Test for Random Sequences
How to Do Hypothesis Tests With the Z.TEST Function in Excel
Scientific Method Vocabulary Terms
What Is the Difference Between Alpha and P-Values?

How to accept or reject a hypothesis?

A hypothesis is a proposed statement to explore a possible theory. Many studies in the fields of social sciences, sciences, and mathematics make use of hypothesis testing to prove a theory. Assumptions in a hypothesis help in making predictions. It is presented in the form of null and alternate hypotheses. When a hypothesis is presented negatively (for example, TV advertisements do not affect consumer behavior), it is called a null hypothesis. This article explains the conditions to accept or reject a hypothesis.

Why is it important to reject the null hypothesis?

A null hypothesis is a statement that describes that there is no difference in the assumed characteristics of the population. For example, in a study wherein the impact of the level of education on the efficiency of the employee need to be determined, null (Ho) and alternate (HA) hypothesis would be:

In the above-stated null hypothesis, there is very little chance of a relationship between both the variables (education and employee’s efficiency). When a null hypothesis is accepted, it shows that the study has a lack of evidence in showing any significant connection between the variables. This could be due to problems with the data such as:

high variability,
small sample size,
inappropriate sample and,
wrong data testing method.

Hence, for efficient, appropriate, and reliable results, it is suggested to reject the null hypothesis.

Conditions for rejecting a null hypothesis

Rejection of the null hypothesis provides sufficient evidence for supporting the perception of the researcher. Thus, a statistician always prefers to reject the null hypothesis. However, there are certain conditions which need to be fulfilled for the required results i.e.

Condition 1: Sample data should be reasonably random

A random sample is the one every person in the sample universe has an equal possibility of being selected for the analysis. Random sampling is necessary for deriving accurate results and rejecting the null hypothesis. This is because when a sample is randomly selected, characteristic traits of each participant in the study are the same, so there is no error in decision making. For example, in the sample hypothesis, instead of collecting data from all employees, the data was collected from only the board members of the company. This hypothesis testing would not provide good results as the sample does not represent all the employees of the company.

Condition 2: Distribution of the sample should be known

A dataset can be of two types: normally distributed or skewed. Normally distributed datasets require application of parametric tests i.e. Z-test, T-test, χ2-test, and F-distribution. On the other hand, skewed dataset uses non-parametric test i.e. Wilcoxon rank sum test, Wilcoxon signed rank test, and Kruskal Wallis test. For reliable hypothesis test result, it is essential that the distribution of the sample be tested.

Condition 3: Value of test statistic should not fall in the rejection region

Test statistic value is compared with critical value when the null hypothesis is true (critical value). If the test statistic is more extreme as compared to the critical value, then the null hypothesis would be rejected.

For example, in the sample hypothesis if the sample size is 50 and the significance level of the study is 5% then the critical value for the given two-tailed test would be 1.960. Hence, null hypothesis would be rejected if,

Condition 4: P-value should be less than the significance of the study

P-value represents the probability that the null hypothesis true. In order to reject the null hypothesis, it is essential that the p-value should be less that the significance or the precision level considered for the study. Hence,

Reject null hypothesis (H0) if ‘p’ value < statistical significance (0.01/0.05/0.10)
Accept null hypothesis (H0) if ‘p’ value > statistical significance (0.01/0.05/0.10)

For example, in the sample hypothesis if the considered statistical significance level is 5% and the p-value of the model is 0.12. Hence, the hypothesis of having no significant impact would not be rejected as 0.12 > 0.05.

Important points to note

While making the final decision of the hypothesis, these points should be noted i.e.

A large sample size i.e. at least greater than 30 should be considered. As per the Central Limit Theorem (CLT) large sample size i.e. at least greater than 30 is considered to be approximately normally distributed.
For deriving the results either p-value approach or rejection approach could be used. However, the p-value is a more preferable approach.
Statistical significance should be maintained at a minimum level.
The choice of the rejection region should be appropriately made by verifying the direction of the alternative hypothesis.
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JEPS Bulletin

The Official Blog of the Journal of European Psychology Students

What happens to studies that accept the null hypothesis?

Source: Scargle, 2000

“The literature of social sciences contains horror stories of journal editors and others who consider a study worthwhile only if it reaches a statistically significant, positive conclusion; that is, an equally significant rejection of a hypothesis is not considered worthwhile” (Scargle, 2000).

This is a footnote in Jeffrey D. Scargle’s, an astrophysicist working for NASA, article about the publication bias in scientific journals . Usually, the psychologist in me would go all defensive of our precious little social science, but then one discovers this: a couple of researchers trying to publish a paper debunking Bem’s research on ESP (in layman terms, ESP means predicting the future). More precisely, their woes while trying to publish a paper with nonsignificant results. How many papers have you read that have nonsignificant results, that accept the null hypothesis? I have a feeling you have the same answer as me, and it’s frighteningly converging on zero. What happens to those papers? And what’s the implication of such a bias in publishing for science at large?

Before delving deeper into the subject, we should explicitly state what the publication’s bias (or its extreme formulation, the file-drawer problem) is, which was best explained in an influential work by Rosenthal (1979, p. 638; as cited in Scargle, 2000):

…researchers and statisticians have long suspected that the studies published in the behavioral sciences are a biased sample of the studies that are actually carried out… The extreme view of this problem, the “file-drawer problem”, is that the journals are filled with the 5% of the studies that show Type I errors, while the file drawers back at the lab are filled with the 95% of the studies that show nonsignificant (e.g., p > .05) results.

This is basically a problem with the untruthfulness of the publication process in science, especially in social sciences where almost all quantitative analysis is based on statistical (non)significance. In an ideal system, a statistically significant result means that the results are significantly different from the expected null hypothesis. But what if we’re fishing for results, which is precisely the case if a bias for publishing only significant results exists? To put it even more metaphorically: if we fish long enough, we will certainly score big game; whatever our research subject might be. Be it personality traits or precognition, as in Bem’s case.

Ritchie’s experience in trying to publish a study offering a proof that no precognition exists when replicating Bem’s research was, as stated in Tom Bartlett’s (2011) article , was rejected out of different reasons. No reviewer will hopefully openly state that a study is rejected specifically because it does not show a significant effect (contrary to Scargle’s horror story from the introduction). Still, the question is–what was the real reason of rejection? Even in such a controversial study as Bem’s, where the scientific community would make a statement by publishing nonsignificant results from a replication study, this study was rejected. By publishing it, the scientific community would back up their disdain of the pseudoscientific ESP research with sound empirically grounded data, and yet they still refuse to publish it?

All this makes it sound like there’s an intricate conspiracy within the scientific community, plotting in the shadows and disallowing the publication of marginal or no effect studies. I think that the absurdity in that is self evident.

My take on it is that this is yet another incarnation of human cognition in an institution, taken into a sophisticated extreme in the most elaborate human epistemological endeavor–science. This artifact of human cognition has been called by psychologists the confirmation bias for decades. What is it precisely?

… confirmation bias connotes a less explicit, less consciously one-sided case building process. It refers usually to unwitting selectivity in the acquisition and use of evidence. The line between deliberate selectivity in the use of evidence and unwitting molding of facts to fit hypotheses or beliefs is a difficult one to draw in practice, but the distinction is meaningful conceptually, and confirmation has more to do with latter than the former. The assumption that people can and do engage in case-building unwittingly, without intending to treat evidence in a biased way or even being aware of doing so, is fundamental to the concept. (Nickerson, 1998)

Science, as an organized endeavor of research, the ultimate epistemology of the modern world, just transformed this normal and typical artifact of human cognition into something compatible with the critical methodology it’s based on. The publication bias. Looking for and publishing only evidence that support your theories and hypotheses is ethically questionable at best, or an example of scientific dishonesty and data fishing at worst. But what if the publication process, the mechanism that guards the gates of cited scientific literature has the bias built into it? Then the scientists would remain true to their trade, and still fulfill their basic cognitive need. To publish results that support their theories and leave everything else in the ‘shadow’.

You do the research, you’re an honest researcher, but you only publish the research that supports your ideas. Not because you are dishonest, but because reviewers and journal editors are only interested in cutting edge, top notch and most importantly, significant studies. When you take such a system and couple it with statistical significance as the ultimate demarcation criterion of publishable and unpublishable – you get a science which has the confirmation bias systemically built into it.

On a practical level, you get a system of journals that will not publish Ritchie’s study, even if it proves something the true, proper scientists at large want proven – that ESP is a pseudoscientific research problem that should not be even considered for publication in ‘serious’ journals.

Barlett, T. (2011, Dec 6). Wait, maybe you can’t feel the future. The Chronicle of Higher Education. Retrieved from: http://chronicle.com/blogs/percolator/wait-maybe-you-cant-feel-the-future/27984

Flis, I. (2011, Feb 15). The ‘science’ in scientific peer-reviewed journals. JEPS Bulletin . Retrieved from: https://blog.efpsa.org/2011/02/15/the-science-in-scientific-peer-reviewed-journals/

Nickerson, R.S. (1998). Confirmation Bias: A Ubiquitous Phenomenon in Many Guises. Review of General Psychology, 2 (2), 175 – 220. Scargle, J.D. (2000). Publication Bias: The “File-Drawer” Problem in Scientific Inference . Journal of Scientific Exploration, 14 (1), 91-106.

The histogram in the introduction is taken from Jeffrey D. Scargle’s cited article, representing the unpublished/published studies ratio.

Ivan Flis is a PhD student in History and Philosophy of Science at the Descartes Centre, Utrecht University; and has a degree in psychology from the University of Zagreb, Croatia. His research focuses on quantitative methodology in psychology, its history and application, and its relation to theory construction in psychological research. He had been an editor of JEPS for three years in the previous mandates.

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The Null Hypothesis: Why it can never be accepted

One of the commonest uses of Biostatistics is null hypothesis significance testing .

This involves the following steps:

1. State the null hypothesis (H0)

2. State the alternative hypothesis (Ha) (one sided or two sided)

3. Choose a test of significance

4. Set the level of significance

5. Make observations and collect data

6. Run the test of significance

7. Take a decision regarding the null hypothesis.

Often, the last step is the trickiest- how does one interpret the test statistic ? Does one reject the null hypothesis?

In common usage, when one does not reject something, one is accepting it. This seems logical since accept and reject are antonyms (opposites).

However, in null hypothesis significance testing, one can never accept the null hypothesis. Here’s why:

Let us assume that a 4 year old asked you, “Why do men have larger hands than women?”

You don’t know the answer to that question, but you start wondering if all women have smaller hands than men. Being of a scientific bent of mind, you decide to find out for yourself.

Accordingly, you follow the steps outlined above:

Null hypothesis (H0): The hands of men are the same size as those of women

Alternative hypothesis ( Two sided ): Men and women do not have the same hand size

You decide to use the Chi-square test to test significance, and set the significance level at 5% (p= 0.05).

You then go around requesting men and women to provide an outline of their hands (on paper). To keep things simple, if you first encountered a woman, you’d then go looking for a man, and vice-versa. For the purpose of the study, it has been decided that a difference of 10% or more in size would qualify as being larger or smaller than the preceding/ succeeding hand.

After spending weeks, you do not find any difference in hand size between men and women (as per definition).

It’s time to conclude the study, you think to yourself.

What would you conclude at this point?

Since you failed to find a significantly larger or smaller hand, would you conclude that the null hypothesis was true and accept it?

Chances are, you’d say, “I’m not sure. Maybe it’s because of the way I collected the data; Maybe it is true in this location, but we’re talking about men and women in general;…”

You decide to obtain one last set of prints before finally concluding the study.

This time the man has a much larger hand than the woman. Point proven. Case closed.

Now what would you conclude?

The null hypothesis has been proven to be false, so it can be rejected.

From the above example we understand the following:

1. It is easier to reject the null hypothesis (because even a single observation to the contrary will disprove it)

2. Numerous factors influence the ability to disprove the null hypothesis

3. Due to this, there is uncertainty about the truth

4. Therefore, it is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it

5. It is always possible that investigators elsewhere might be able to disprove the null hypothesis. However, in order that they can do this, we must not accept the null hypothesis as true- there is no question of testing something that has already been proven.

6. It is safer (and preferable) to state that we failed to reject the null hypothesis (and leave it to others to test the null hypothesis subsequently), than accepting the null hypothesis as true and making a Type I error .

For these reasons, in null hypothesis significance testing, one can either reject the null hypothesis, or fail to reject it, but can never accept it.

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Gaza ceasefire uncertain, Israel vows to continue Rafah operation

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RAFAH HIT BY STRIKES

Palestinians react after Hamas accepted a ceasefire proposal from Egypt and Qatar, in Rafah

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Inside the Gaza ceasefire deal that was accepted by Hamas but rejected by Israel

Israel has rejected the ceasefire proposal as prime minister benjamin netanyahu says a withdrawal from the gaza strip would ‘leave hamas intact’, article bookmarked.

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Hamas has accepted the a proposed ceasefire deal over the war in Gaza – but Israel, who have just launched attacks on Rafah – the last remaining area of the Gaza Strip yet to be invaded – has rejected it. Talks over a truce are said to be continuing.

Israeli Prime Minister Benjamin Netanyahu said the proposal, which was agreed over the weekend and calls for the eventual complete withdrawal of Israel’s military from the Gaza Strip, would “leave Hamas intact” .

“Surrendering to the demands of Hamas would be a terrible defeat for the State of Israel," he said in a video statement.

Here we look at exactly what was included in the proposal.

The proposed plan is broken down into three 42-day stages, with the majority of requirements of both sides taking place during the first stage.

In the first 42 days, there would be “a temporary cessation of military operations between the two parties”, followed by a “withdrawal of Israeli forces eastward and away from densely populated areas”.

That withdrawal will happen in three stages. The first, after three days, should see Israel withdraw from strongholds in the northern half of the enclave and “dismantle military sites and installations in this area”.

The second stage, after 22 days of the ceasefire, which is when half the living civilian captives in Gaza, including female soldiers, should have been released, the Israeli military should withdraw from areas in central Gaza.

At the end of the first 42-day stage, Israel should be prepared to withdraw entirely from the Gaza Strip.

Internally displaced civilians in Gaza should be permitted to return to their homes as the Israeli military withdraws from the affected area.

The proposal, which Al Jazeera has seen, adds that Israel’s warplanes should cease flying over Gaza for 10 hours a day and 12 hours when Israeli hostages are being swapped for Palestinian prisoners.

Meanwhile, 600 trucks of humanitarian aid are due to be delivered on a daily basis, starting from the first day of the ceasefire.

The proposal reads: “Humanitarian aid, relief materials and fuel (600 trucks a day, including 50 fuel trucks, and 300 trucks for the north) shall be allowed into Gaza in an intensive manner and in sufficient quantities from the first day. This is to include the fuel needed to operate the power station, restart trade, rehabilitate and operate hospitals, health centres and bakeries in all parts of the Gaza Strip, and operate equipment needed to remove rubble. This shall continue throughout all stages.”

Infrastructure, including electricity, water, sewage, communications and roads, will be rebuilt and all equipment needed for reconstruction, as well as the removal of rubble and debris, should be allowed into Gaza.

A minimum of 60,000 caravans and 200,000 tents will also be allowed into the enclave to house those whose homes have been destroyed.

Regarding hostages, the text reads: “During the first phase, Hamas shall release 33 Israeli captives (alive or dead), including women (civilians and soldiers), children (under the age of 19 who are not soldiers), those over the age of 50, and the sick, in exchange for a number of prisoners in Israeli prisons and detention centres.”

The ratio of swaps would be one Israeli hostage for 30 Palestinian prisoners, and the swaps will be direct, namely one female soldier for one female prisoner.

The prisoners will be those being held in Israeli prisons and named on the release list by Hamas, a list that will also be approved by Israel.

The first three Israeli hostages will be released on the third day of the agreement, after which Hamas should release three additional hostages every seven days, starting with women, including female soldiers.

In the sixth week of exchanges, Hamas should “release all remaining civilian detainees”.

The second and third stages relate to Israel’s “complete withdrawal” from the Gaza Strip and the subsequent reconstruction of the enclave.

The proposal says the second stage concerns “a return to sustainable calm”, including a permanent cessation of military operations and the final exchanges of captives and prisoners, which should include all remaining living Israeli men, both civilian and military.

The third and final stage should involve the “exchange of the bodies and remains of the dead on both sides after they have been retrieved and identified”.

A reconstruction plan over a period of three to five years will then commence, including the rebuilding of homes, civilian facilities and infrastructure, under the supervision of Egypt, Qatar and the United Nations.

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Why has Israel rejected three-phase ceasefire deal accepted by Hamas? What comes next?

Hopes of peace remain a dream after Israel rejected the ceasefire proposal, which was earlier accepted by Hamas. The Benjamin Netanyahu-led government said the deal was not what they had agreed to and ‘has significant gaps’. Moreover, the Jewish nation has said it would continue its operation in Rafah, carrying out night airstrikes read more

On Monday (6 May), almost seven months into the Israel-Hamas war, came a sliver of hope that the war would come to an end as the Palestinian group, Hamas, approved a proposal for a ceasefire put forward by mediators Qatar and Egypt.

With the announcement, Palestinians celebrated in the streets of Gaza, while in Tel Aviv, hostage families and their supporters implored Israel’s leaders to accept the deal.

However, it seems that peace will elude the region for longer.

That’s because Israel responded sceptically and said it would press on with its campaign in Gaza’s southernmost city, Rafah . The Israeli prime minister’s office said the war Cabinet had decided unanimously to push ahead with an Israel Defense Forces (IDF) operation in Rafah “in order to apply military pressure on Hamas, with the goal of making progress on freeing the hostages and the other war aims.”

Amid this confusion, we explore what is in three-phase ceasefire deal that Hamas accepted, why Israel rejected it and what this means for the ongoing war.

Hamas accepts ceasefire deal

On Monday, after days and days of negotiations, Hamas approved a ceasefire proposal put forth by Egypt and Qatar . The Palestinian group in a statement said that its supreme leader, Ismail Haniyeh , had expressed his agreement in a phone call with Qatar’s prime minister and Egypt’s intelligence minister.

Haniyeh said in a call with Qatar’s head of state that Israel should “seize the moment and accept the proposal.”

“After Hamas agreed to the mediators’ proposal for a ceasefire, the ball is now in the court of Israeli occupation, whether it will agree to the ceasefire agreement or obstruct it,” a senior Hamas official told AFP , soon after the office of Hamas leader Ismail Haniyeh had announced its acceptance.

It is reported that Hamas accepted the proposal only after mediators reworked it with CIA Director Bill Burns even travelling to Cairo last week and then on to Doha where he worked with the Qataris on the language, CNN reports.

Hamas’ acceptance of the proposal was the first glimmer of hope that further bloodshed — over 34,735 people have been killed — would be averted. There were celebrations in Gaza as Palestinians hoped this would finally bring an end to the bloody war.

The three-phase proposal

While it is not confirmed what exactly was Hamas agreeing to, officials involved in the negotiations said that the proposal comprised three phases, each being 42 days long.

In the first phase, Hamas would release 33 hostages — the group is believed to still hold 128 of the 250 hostages they had taken — in return for Israel releasing Palestinians from Israeli jails. Moreover, Israel would partially withdraw troops from Gaza and allow for free movement of Palestinians from south to north Gaza.

In phase two, which is another 42 days long, there would be a complete and permanent halt to military activity in Gaza.

And the final phase, phase three would see the completion of exchanging bodies and starting the implementation of reconstruction according to the plan overseen by Qatar, Egypt and the United Nations. It would also see the ending of the complete blockage in the Gaza Strip.

Israel rejects proposal

Shortly after Hamas announced it had approved the proposal, celebrations broke out in Gaza. Al Jazeera reported that people started celebrating near the Kuwaiti Hospital upon hearing the Hamas announcement. The announcement brought “a sense of relief and tranquility” among Palestinians who are “exhausted and traumatised”, said the news outlet.

However, confusion prevailed as Israel initially remained mum on the matter and then later stated that their operation in Rafah would continue.

It was later reported that Israeli officials said the terms Hamas claimed to have accepted did not match those that they had approved. A statement from Benjamin Netanyahu’s office said, “Hamas’s latest offer was “far from [meeting] Israel’s essential requirements.”

It further added that Israel would send working-level teams to hold talks with the mediators in order “to exhaust the possibility of achieving an agreement on terms that are acceptable to Israel.”

War Cabinet minister Benny Gantz also was quoted as telling the Times of Israel that the ceasefire proposal Hamas accepted “is inconsistent with the dialogue [Israel] held with the mediators to this point and has significant gaps [from Israel’s demands].”

Israel’s negotiators were “continuing their work at every moment” and “will leave no stone unturned,” Gantz promised. “Every decision will be brought before the war cabinet. There will be no political considerations” in the decision-making, he added (emphasis in original).

Israel officials, as per a Channel 12 report, said that this “was not the same proposal” that the Jewish nation and Egypt has agreed upon days ago.

An official also told Sky News that Hamas’ announcement “appears to be a ruse to cast Israel as the side refusing a deal”.

Israel has consistently asserted that it won’t accept any deal which provides for a permanent ceasefire and that it would resume its military campaign after any truce-for-hostages deal, in order to complete its two declared war goals: returning the hostages and destroying Hamas’ military and governance capabilities.

However, Benjamin Netanyahu’s decision to reject the deal prompted family members of the hostages to protest in Tel Aviv. They called on their government to accept the deal, with the Hostages and Missing Families Forum saying, “Hamas’s announcement must pave the way for the return of the 132 hostages held captive by Hamas for the past seven months. Now is the time for all that are involved to fulfil their commitment and turn this opportunity into a deal for the return of all the hostages.”

US officials at the White House and the State Department were repeatedly asked by journalists during news briefings about Hamas’s acceptance of the deal. But Matthew Miller, the State Department spokesperson, and John Kirby, the White House National Security spokesperson, refused to get into any details.

Uncertain and shaky future awaits

While Israel asserted that it would send its delegation for further talks, it also reiterated its commitment to an offensive in the southern Gaza city of Rafah, saying its war Cabinet had “unanimously decided” to continue with the operation “to exert military pressure on Hamas.”

The IDF said it was “conducting targeted strikes against Hamas terror targets in eastern Rafah in the southern Gaza Strip.” An AFP reporter in the city reported heavy bombardment throughout the night, while the Kuwaiti hospital there said on Tuesday in an updated toll that 11 people had been killed and dozens of others injured in Israeli strikes.

News agency AP also reported that Israeli tanks had entered Rafah, reaching as close as 200 metres from Rafah’s crossing with neighbouring Egypt.

It is also reported that US president Joe Biden spoke with Netanyahu and reiterated US concerns about an invasion of Rafah. Aid agencies and human rights activists have also warned that an offensive in Rafah would bring a surge of more civilian deaths in an Israeli campaign that has already killed over 34,000 people and devastated the territory. It could also wreck the humanitarian aid operation based out of Rafah that is keeping Palestinians across the Gaza Strip alive, they say.

With inputs from agencies

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Hamas accepts Qatari-Egyptian proposal for Gaza ceasefire

Israel says it will send a delegation to meet with mediators as its war cabinet approves continuing Rafah military operation.

Hamas says it has approved a proposal for a ceasefire in the seven-month Gaza war put forward by mediators Qatar and Egypt although Israel says the proposal falls short of its demands.

“Ismail Haniyeh, head of the political bureau of Hamas movement, conducted a telephone call with the prime minister of Qatar, Sheikh Mohammed bin Abdulrahman Al Thani, and with the Egyptian intelligence minister, Mr Abbas Kamel, and informed them of Hamas’s approval of their proposal regarding a ceasefire agreement,” the Palestinian group said in a statement published on its official website on Monday.

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Prime Minister Benjamin Netanyahu’s office said the proposed deal did not meet Israel’s demands and it would send a delegation to meet with negotiators.

“Although the Hamas proposal is far from Israel’s necessary requirements, Israel will send a working delegation to the mediators to exhaust the possibility of reaching an agreement under conditions acceptable to Israel,” it said in a post on X.

Full details of the proposal were not immediately clear.

Three phases

Khalil al-Hayya, a member of Hamas’s political bureau, told Al Jazeera Arabic that the Qatari-Egyptian proposal includes a withdrawal of Israeli forces from Gaza and a return of displaced Palestinians to their homes as well as an exchange of Israeli captives and Palestinian prisoners.

The proposal includes a three-stage truce, each phase lasting 42 days, according to al-Hayya.

In the first phase, indirect negotiations through mediators would resume on the exchange of captives and prisoners. A withdrawal of some Israeli troops from certain areas would also take place along with the unhindered return of displaced families to their homes and the flow of aid and fuel into Gaza, he said.

In the second phase, al-Hayya said, there would be a complete and permanent halt to military activity in Gaza.

The final phase would focus on beginning reconstruction in post-war Gaza, overseen by Egypt, Qatar, and United Nations agencies, he said.

“The ball is now in Israel’s court,” he said.

US Department of State spokesperson Matthew Miller said Washington will “withhold judgement” on Hamas’s announcement until it has time to fully review it.

“I can confirm that Hamas has issued a response. We are reviewing that response now and discussing it with our partners in the region,” he said.

“It’s something that is a top priority for everyone in this administration from the president on down,” Miller said.

Hamas’s statement was released after Israeli forces struck sites in the city of Rafah in the southern Gaza Strip after Israel ordered tens of thousands of people to evacuate. More than 1.4 million displaced Palestinians have sought shelter in the area.

Later on Monday, Israel said its war cabinet had approved continuing a military operation in the city.

“The war cabinet unanimously decided that Israel continue the operation in Rafah to exert military pressure on Hamas in order to advance the release of our hostages and the other goals of the war,” Netanyahu’s office said.

Palestinians in Rafah ‘optimistic’

Al Jazeera’s Tareq Abu Azzoum, reporting from Rafah, said people started celebrating near the Kuwaiti Hospital upon hearing the Hamas announcement.

“Everyone … is happy because they believe a Rafah invasion will bring an unspeakable humanitarian catastrophe,” Abu Azzoum said. “Now they are so optimistic.”

The announcement brought “a sense of relief and tranquility” among Palestinians who are “exhausted and traumatised”, he said.

Within the last couple of hours, Abu Azzoum said, Israel has intensified attacks in the eastern parts of Rafah.

“We have been hearing large explosions … they have been attacking farm lands,” he said.

According to Abu Azzoum, people have been hearing that there is a “great and general consensus” among Israeli officials that the war and military operations in Rafah will continue.

A displaced Palestinian in Rafah told Al Jazeera that he hopes he will be able to go back home.

“We hope we return to our homes. … I am from Gaza [City] itself,” he said.

Al Jazeera’s Alan Fisher, reporting from Washington, DC, said: “The Israelis have said they will conduct the war how they see fit.”

“Whether the US expresses concern or anger, it has made no difference to how the Israelis are conducting this war,” Fisher said.

Alon Liel, former director general of Israel’s Ministry of Foreign Affairs, told Al Jazeera that there is “strong pressure” on the Israeli government to send ground troops into Rafah.

“The mood here is very, very different than the mood in Gaza. Even if we have a deal, many people here will be frightened and think that we lost the war,” Liel said.

If Netanyahu accepts the deal, Liel said, it might be “the end of his political career”. And if he does not accept the deal, “we will have international calls by the UN and … sanctions,” he said.

At least 34,735 people, mostly women and children, have been killed and 78,018 wounded in Israel’s assault on Gaza since October, according to Palestinian authorities. The offensive has destroyed much of Gaza and a near-total siege has pushed parts of it to the brink of famine.

Israel launched the assault after Hamas led an attack on southern Israel on October 7, killing at least 1,139 people, according to an Al Jazeera tally based on Israeli statistics.

COMMENTS

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