hypothesis graph maker

Enter either the p-value (represented by the blue area on the graph) or the test statistic (the coordinate along the horizontal axis) below to have the other value computed.

“extremely user friendly”

“truly amazing!”

“so easy to use!”

Statistics Calculator

You want to analyze your data effortlessly? DATAtab makes it easy and online.

Online Statistics Calculator

What do you want to calculate online? The online statistics calculator is simple and uncomplicated! Here you can find a list of all implemented methods!

Create charts online with DATAtab

Create your charts for your data directly online and uncomplicated. To do this, insert your data into the table under Charts and select which chart you want.

The advantages of DATAtab

Statistics, as simple as never before..

DATAtab is a modern statistics software, with unique user-friendliness. Statistical analyses are done with just a few clicks, so DATAtab is perfect for statistics beginners and for professionals who want more flow in the user experience.

Directly in the browser, fully flexible.

Directly in the browser, fully flexible. DATAtab works directly in your web browser. You have no installation and maintenance effort whatsoever. Wherever and whenever you want to use DATAtab, just go to the website and get started.

All the statistical methods you need.

DATAtab offers you a wide range of statistical methods. We have selected the most central and best known statistical methods for you and do not overwhelm you with special cases.

Data security is a top priority.

All data that you insert and evaluate on DATAtab always remain on your end device. The data is not sent to any server or stored by us (not even temporarily). Furthermore, we do not pass on your data to third parties in order to analyze your user behavior.

Many tutorials with simple examples.

In order to facilitate the introduction, DATAtab offers a large number of free tutorials with focused explanations in simple language. We explain the statistical background of the methods and give step-by-step explanations for performing the analyses in the statistics calculator.

Practical Auto-Assistant.

DATAtab takes you by the hand in the world of statistics. When making statistical decisions, such as the choice of scale or measurement level or the selection of suitable methods, Auto-Assistants ensure that you get correct results quickly.

Charts, simple and clear.

With DATAtab data visualization is fun! Here you can easily create meaningful charts that optimally illustrate your results.

New in the world of statistics?

DATAtab was primarily designed for people for whom statistics is new territory. Beginners are not overwhelmed with a lot of complicated options and checkboxes, but are encouraged to perform their analyses step by step.

Online survey very simple.

DATAtab offers you the possibility to easily create an online survey, which you can then evaluate immediately with DATAtab.

Our references

Alternative to statistical software like SPSS and STATA

DATAtab was designed for ease of use and is a compelling alternative to statistical programs such as SPSS and STATA. On datatab.net, data can be statistically evaluated directly online and very easily (e.g. t-test, regression, correlation etc.). DATAtab's goal is to make the world of statistical data analysis as simple as possible, no installation and easy to use. Of course, we would also be pleased if you take a look at our second project Statisty .

Extensive tutorials

Descriptive statistics.

Here you can find out everything about location parameters and dispersion parameters and how you can describe and clearly present your data using characteristic values.

Hypothesis Test

Here you will find everything about hypothesis testing: One sample t-test , Unpaired t-test , Paired t-test and Chi-square test . You will also find tutorials for non-parametric statistical procedures such as the Mann-Whitney u-Test and Wilcoxon-Test . mann-whitney-u-test and the Wilcoxon test

The regression provides information about the influence of one or more independent variables on the dependent variable. Here are simple explanations of linear regression and logistic regression .

Correlation

Correlation analyses allow you to analyze the linear association between variables. Learn when to use Pearson correlation or Spearman rank correlation . With partial correlation , you can calculate the correlation between two variables to the exclusion of a third variable.

Partial Correlation

The partial correlation shows you the correlation between two variables to the exclusion of a third variable.

Levene Test

The Levene Test checks your data for variance equality. Thus, the levene test is used as a prerequisite test for many hypothesis tests .

The p-value is needed for every hypothesis test to be able to make a statement whether the null hypothesis is accepted or rejected.

Distributions

DATAtab provides you with tables with distributions and helpful explanations of the distribution functions. These include the Table of t-distribution and the Table of chi-squared distribution

Contingency table

With a contingency table you can get an overview of two categorical variables in the statistics.

Equivalence and non-inferiority

In an equivalence trial, the statistical test aims at showing that two treatments are not too different in characteristics and a non-inferiority trial wants to show that an experimental treatment is not worse than an established treatment.

If there is a clear cause-effect relationship between two variables, then we can speak of causality. Learn more about causality in our tutorial.

Multicollinearity

Multicollinearity is when two or more independent variables have a high correlation.

Effect size for independent t-test

Learn how to calculate the effect size for the t-test for independent samples.

Reliability analysis calculator

On DATAtab, Cohen's Kappa can be easily calculated online in the Cohen’s Kappa Calculator . there is also the Fleiss Kappa Calculator . Of course, the Cronbach's alpha can also be calculated in the Cronbach's Alpha Calculator .

Analysis of variance with repeated measurement

Repeated measures ANOVA tests whether there are statistically significant differences in three or more dependent samples.

Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net

Hypothesis Maker

Ai-powered research hypothesis generator.

• Scientific Research: Generate a hypothesis for your experimental or observational study based on your research question.
• Academic Studies: Formulate a hypothesis for your thesis, dissertation, or academic paper.
• Market Research: Develop a hypothesis for your market research study to understand consumer behavior or market trends.
• Social Science Research: Create a hypothesis for your social science research to explore societal or behavioral patterns.

Yes, HyperWrite offers a limited trial for users to test the Hypothesis Maker. For additional access, you can choose the Premium Plan at $19.99/mo or Ultra for $44.99/mo. Use the code 'TRYHYPERWRITE' for 50% off your first month.

The Hypothesis Maker is powered by advanced AI models. These models analyze your research question and use their understanding of scientific research and hypothesis formulation to generate a clear, concise, and specific hypothesis that can guide your research process.

Yes, the Hypothesis Maker generates original hypotheses based on your provided research question. It uses advanced AI models to ensure that the generated hypothesis is unique, relevant to your research question, and can guide your research process effectively.

Yes, the Hypothesis Maker is versatile and can be used for a wide range of research types, including scientific, academic, market, and social science research. However, the output should always be reviewed and adjusted as necessary to fit the specific context and objectives of your research.

New & Trending Tools

Brand management tutor, lesson plan maker, marketing research tutor.

Stats Tools

Use Our Free A/B Testing Hypothesis Generator . Never Miss Key Elements From Your Hypotheses. Get Big Conversion Lifts.

Observation, inadvertent impact.

Streamline Your Hypothesis Generation Research with Custom Templates the Pros Use.

Have questions about a/b testing hypotheses, what is a hypothesis.

Many people define a hypothesis as an “educated guess”.

To be more precise, a properly constructed hypothesis predicts a possible outcome to an experiment or a test where one variable (the independent one ) is tweaked and/or modified and the impact is measured by the change in behavior of another variable (generally the dependent one).

A hypothesis should be specific (it should clearly define what is being altered and what is the expected impact), data-driven (the changes being made to the independent variable should be based on historic data or theories that have been proven in the past), and testable (it should be possible to conduct the proposed test in a controlled environment to establish the relationship between the variables involved, and disprove the hypothesis - should it be untrue.)

What is the Cost of a Hastily Assembled Hypothesis?

According to an analysis of over 28,000 tests run using the Convert Experiences platform, only 1 in 5 tests proves to be statistically significant.

While more and more debate is opening up around sticking to the concept of 95% statistical significance, it is still a valid rule of thumb for optimizers who do not want to get into the fray with peeking vs. no peeking, and custom stopping rules for experiments.

There might be a multitude of reasons why a test does not reach statistical significance. But framing a tenable hypothesis that already proves itself logistically feasible on paper is a better starting point than a hastily assembled assumption.

Moreover, the aim of an A/B test may be to extract a learning, but some learnings come with heavy costs. 26% decrease in conversion rates to be specific.

A robust hypothesis may not be the answer to all testing woes, but it does help prioritisation of possible solutions and leads testing teams to pick low hanging fruits.

How is an A/B Testing Hypothesis Different?

An A/B test should be treated with the same rigour as tests conducted in laboratories. That is an easy way to guarantee better hypotheses, more relevant experiments, and ultimately more profitable optimization programs.

The focus of an A/B test should be on first extracting a learning , and then monetizing it in the form of increased registration completions, better cart conversions and more revenue.

If that is true, then an A/B test hypothesis is not very different from a regular scientific hypothesis. With a couple of interesting points to note:

• Most scientific hypotheses proceed with one independent variable and one dependent variable, for the sake of simplicity. But in A/B tests, there might be changes made to several independent variables at the same time. Under such circumstances it is good to explore the relationship between the independent variables to make sure that they do not inadvertently impact one another. For example changing both the value proposition and button copy of a landing page to determine improvement in click through or completion rates is tricky. Reaching a point where the browser is compelled to click the button could easily have been impacted by the value proposition (as in a strong hook and heading). So what caused the improvement in the dependent variable? Was it the change to the first element or the second one?
• The concept of Operational Definition is non-negotiable in most laboratory experiments. And comes baked with the question of ethics or morality. Operation Definition is the specific process that will be used to quantify the change in the value/behavior of the independent variable in the test. As an example, if a test wishes to measure the level of frustration that subjects experience when they are exposed to certain stimuli, researchers must be careful to define exactly how they will measure the output or frustration. Should they allow the test subjects to act out, in which case they may hurt or harm other individuals. Or should they use a non-invasive technique like an fMRI scan to monitor brain activity and collect the needed data. In A/B tests however, since data is collected through relatively inanimate channels like analytics dashboards, generally little thought is spared to Operational Definition and the impact of A/B testing on the human subjects (site traffic in this case).

The 5 Essential Parts of an A/B Testing Hypothesis

A robust A/B testing hypothesis should be assembled in 5 key parts:

1. OBSERVATION

This includes a clear outline of the problem (the unexplained phenomenon) observed and what it entails. This section should be completely free of conjecture and rely solely on good quality data - either qualitative and/or quantitative - to bring a potential area of improvement to light. It also includes a mention of the way in which the data is collected.

Proper observation ensures a credible hypothesis that is easy to “defend” later down the line.

2. EXECUTION

This is the where, what, and the who of the A/B test. It specifies the change(s) you will be making to site element(s) in an attempt to solve the problem that has been outlined under “OBSERVATION”. It serves to also clearly define the segment of site traffic that will be exposed to the experiment.

Proper execution guidelines set the rhythm for the A/B test. They define how easy or difficult it will be to deploy the test and thus aid hypothesis prioritization .

This is where you make your educated guess or informed prediction. Based on a diligently identified OBSERVATION and EXECUTION guidelines that are possible to deploy, your OUTCOME should clearly mention two things:

• The change (increase or decrease) you expect to see to the problem or the symptoms of the problem identified under OBSERVATION.
• The Key Performance Indicators (KPIs) you will be monitoring to gauge whether your prediction has panned out, or not.

In general most A/B tests have one primary KPI and a couple of secondary KPIs or ways to measure impact. This is to ensure that external influences do not skew A/B test results and even if the primary KPI is compromised in some way, the secondary KPIs do a good job of indicating that the change is indeed due to the implementation of the EXECUTION guidelines, and not the result of unmonitored external factors.

4. LOGISTICS

An important part of hypothesis formulation, LOGISTICS talk about what it will take to collect enough clean data from which a reliable conclusion can be drawn. How many unique tested visitors, what is the statistical significance desired, how many conversions is enough and what is the duration for which the A/B test should run? Each question on its own merits a blog or a lesson. But for the sake of convenience, Convert has created a Free Sample Size & A/B/N Test Duration Calculator .

Set the right logistical expectations so that you can prioritise your hypotheses for maximum impact and minimum effort .

5. INADVERTENT IMPACT

This is a nod in the direction of ethics in A/B testing and marketing, because experiments involve humans and optimizers should be aware of the possible impact on their behavior.

Often a thorough analysis at this stage can modify the way impact is measured or an experiment is conducted. Or Convert certainly hopes that this will be the case in future. Here’s why ethics do matter in testing.

Now Organize, Prioritise & Learn from Your Hypotheses.

Try convert experiences in free trial & access compass beta - our hypothesis management platform., always working to improve outcomes..

Start Your 15 -Day Free Trial Right Now. No Credit Card Required

Important. Please Read.

• Check your inbox for the password to Convert’s trial account.
• Log in using the link provided in that email.

This sign up flow is built for maximum security. You’re worth it!

Two sample t test

Kruskal wallis

Pearson product moment

Two sample f test

One way anova

Bartlett test

Chi square goodness of fit

Fligner killeen

Hypothesis Test Calculator

Upload your data set below to get started

Or input your data as csv

Sharing helps us build more free tools

• Salary & Income Tax Calculators
• Mortgage Calculators
• Retirement Calculators
• Depreciation Calculators
• Statistics and Analysis Calculators
• Date and Time Calculators
• Contractor Calculators
• Budget & Savings Calculators
• Loan Calculators
• Forex Calculators
• Real Function Calculators
• Engineering Calculators
• Tax Calculators
• Volume Calculators
• 2D Shape Calculators
• 3D Shape Calculators
• Logistics Calculators
• HRM Calculators
• Sales & Investments Calculators
• Grade & GPA Calculators
• Conversion Calculators
• Ratio Calculators
• Sports & Health Calculators
• Other Calculators

Statistics Calculator

Quick Guide to Our Statistics Calculator: After entering the data values, our calculator will provide you with an automated graph and statistics calculation, including the mean, median, and mode.

Using Our Statistics Calculator

Simply enter a variety of values into the "Data Input" box and separate each value with either a comma or a space.

Note that if text or any sort of non-numeric data is entered, then the Total Value, Mean, Median, and Range values will all be ignored.

A pie chart will appear to show you what the top ten values are once the data has been processed by our calculator. Any values that are outside of the top ten will be grouped together as "Others" on the pie chart.

The 3 example buttons are used to demonstrate how results are shown:

• Example A is used for any integer values.
• Example B is used for any text.
• Example C is used for decimal numbers.

Total numbers: 0

Total value of numbers: 0

Median (Middle Value): 0

Mean (Average Value): 0

Range (Max Value - Min Value): 0

Mode (Most Frequent Value): 0

The following algorithms are used by our calculator:

The Mean value, otherwise known as the average, is calculated by simply adding all of the values together and dividing the total number by how many values there were.

The Median value is calculated by sorting the values into the order of smallest to biggest and then picking out whichever value is in the middle of your list.

The Mode value is calculated by simply picking out the number which appears most frequently.

You may also be interested in our Z-Score Calculator or/and Chi-Square Calculator

• Currently 3.89/5

Rating: 3.9 /5 (411 votes)

Hypothesis Maker Online

Looking for a hypothesis maker? This online tool for students will help you formulate a beautiful hypothesis quickly, efficiently, and for free.

Are you looking for an effective hypothesis maker online? Worry no more; try our online tool for students and formulate your hypothesis within no time.

• 🔎 How to Use the Tool?
• ⚗️ What Is a Hypothesis in Science?

👍 What Does a Good Hypothesis Mean?

• 🧭 Steps to Making a Good Hypothesis

🔗 References

📄 hypothesis maker: how to use it.

Our hypothesis maker is a simple and efficient tool you can access online for free.

If you want to create a research hypothesis quickly, you should fill out the research details in the given fields on the hypothesis generator.

Below are the fields you should complete to generate your hypothesis:

• Who or what is your research based on? For instance, the subject can be research group 1.
• What does the subject (research group 1) do?
• What does the subject affect? - This shows the predicted outcome, which is the object.
• Who or what will be compared with research group 1? (research group 2).

Once you fill the in the fields, you can click the ‘Make a hypothesis’ tab and get your results.

⚗️ What Is a Hypothesis in the Scientific Method?

A hypothesis is a statement describing an expectation or prediction of your research through observation.

It is similar to academic speculation and reasoning that discloses the outcome of your scientific test . An effective hypothesis, therefore, should be crafted carefully and with precision.

A good hypothesis should have dependent and independent variables . These variables are the elements you will test in your research method – it can be a concept, an event, or an object as long as it is observable.

You can observe the dependent variables while the independent variables keep changing during the experiment.

In a nutshell, a hypothesis directs and organizes the research methods you will use, forming a large section of research paper writing.

Hypothesis vs. Theory

A hypothesis is a realistic expectation that researchers make before any investigation. It is formulated and tested to prove whether the statement is true. A theory, on the other hand, is a factual principle supported by evidence. Thus, a theory is more fact-backed compared to a hypothesis.

Another difference is that a hypothesis is presented as a single statement , while a theory can be an assortment of things . Hypotheses are based on future possibilities toward a specific projection, but the results are uncertain. Theories are verified with undisputable results because of proper substantiation.

When it comes to data, a hypothesis relies on limited information , while a theory is established on an extensive data set tested on various conditions.

You should observe the stated assumption to prove its accuracy.

Since hypotheses have observable variables, their outcome is usually based on a specific occurrence. Conversely, theories are grounded on a general principle involving multiple experiments and research tests.

This general principle can apply to many specific cases.

The primary purpose of formulating a hypothesis is to present a tentative prediction for researchers to explore further through tests and observations. Theories, in their turn, aim to explain plausible occurrences in the form of a scientific study.

It would help to rely on several criteria to establish a good hypothesis. Below are the parameters you should use to analyze the quality of your hypothesis.

🧭 6 Steps to Making a Good Hypothesis

Writing a hypothesis becomes way simpler if you follow a tried-and-tested algorithm. Let’s explore how you can formulate a good hypothesis in a few steps:

Step #1: Ask Questions

The first step in hypothesis creation is asking real questions about the surrounding reality.

Why do things happen as they do? What are the causes of some occurrences?

Your curiosity will trigger great questions that you can use to formulate a stellar hypothesis. So, ensure you pick a research topic of interest to scrutinize the world’s phenomena, processes, and events.

Step #2: Do Initial Research

Carry out preliminary research and gather essential background information about your topic of choice.

The extent of the information you collect will depend on what you want to prove.

Your initial research can be complete with a few academic books or a simple Internet search for quick answers with relevant statistics.

Still, keep in mind that in this phase, it is too early to prove or disapprove of your hypothesis.

Step #3: Identify Your Variables

Now that you have a basic understanding of the topic, choose the dependent and independent variables.

Take note that independent variables are the ones you can’t control, so understand the limitations of your test before settling on a final hypothesis.

Step #4: Formulate Your Hypothesis

You can write your hypothesis as an ‘if – then’ expression . Presenting any hypothesis in this format is reliable since it describes the cause-and-effect you want to test.

For instance: If I study every day, then I will get good grades.

Step #5: Gather Relevant Data

Once you have identified your variables and formulated the hypothesis, you can start the experiment. Remember, the conclusion you make will be a proof or rebuttal of your initial assumption.

So, gather relevant information, whether for a simple or statistical hypothesis, because you need to back your statement.

Step #6: Record Your Findings

Finally, write down your conclusions in a research paper .

Outline in detail whether the test has proved or disproved your hypothesis.

Edit and proofread your work, using a plagiarism checker to ensure the authenticity of your text.

We hope that the above tips will be useful for you. Note that if you need to conduct business analysis, you can use the free templates we’ve prepared: SWOT , PESTLE , VRIO , SOAR , and Porter’s 5 Forces .

❓ Hypothesis Formulator FAQ

Updated: Oct 25th, 2023

• How to Write a Hypothesis in 6 Steps - Grammarly
• Forming a Good Hypothesis for Scientific Research
• The Hypothesis in Science Writing
• Scientific Method: Step 3: HYPOTHESIS - Subject Guides
• Hypothesis Template & Examples - Video & Lesson Transcript
• Free Essays
• Writing Tools
• Lit. Guides
• Donate a Paper
• Referencing Guides
• Free Textbooks
• Tongue Twisters
• Job Openings
• Expert Application
• Video Contest
• Writing Scholarship
• Discount Codes
• IvyPanda Shop
• Terms and Conditions
• Privacy Policy
• Cookies Policy
• Copyright Principles
• DMCA Request
• Service Notice

Use our hypothesis maker whenever you need to formulate a hypothesis for your study. We offer a very simple tool where you just need to provide basic info about your variables, subjects, and predicted outcomes. The rest is on us. Get a perfect hypothesis in no time!

Student's t-distribution calculator with graph generator

Critical value calculator - student's t-distribution.

This statistical calculator allows you to calculate the critical value corresponding to the Student's t-distribution, you can also see the result in a graph through our online graph generator and if you wish you can download the graph. Just enter the significance value (alpha), degrees of freedom, and left, right, or both tails.

Critical value result

P-value calculator - student's t distribution.

Use our online statistical calculator to calculate the p-value of the Student's t-distribution. You just need to enter the t-value and degrees of freedom and specify the tail. In addition to the p-value, you can get and download the graph created with our graph generator

p-value result

One sample t-test calculator.

The one sample t-test is a statistical hypothesis test calculator, use our calculator to check if you get a statistically significant result or not. To obtain it, fill in the corresponding fields and you will obtain the value of the t-score, p-value, critical value, and the degrees of freedom. You can also download a graph that will display your results in the form of the Student's t-distribution.

T-score result

Two sample t-test calculator.

To determine whether or not the means of two groups are equal, you can use our two-sample t-test calculator that applies the t-test. The results are displayed in a Student's t-distribution plot that you can download. To complete the form, you must include information for both groups, including the mean, standard deviation, sample size, significance level,and whether the test is left, right, or two-tailed.

Common questions related to the Student's t-distribution

In this section, we will try to address the most frequently asked questions about the Student's t-distribution. To give you a fundamental and complementary understanding, we will try to dive into the underlying ideas of the t-distribution. The approach we want to take is to answer the most common questions from students with relevant information. Let's tackle problems simply and offer short and understandable solutions.

Questions related to the student's t-distribution

The formula in relation to the probability density function (pdf) for Student's t-distribution, is given as follows:

Where: π is the pi (approximately 3.14), ν correspond to the degrees of freedom, and Γ is the Euler Gamma function.

A distribution of mean estimates derived from samples taken from a population is what is, by definition, the Student's t-distribution. The t-distribution, commonly known as the Student's t-distribution, is a type of symmetric bell-shaped distribution, it has a lower height but a wider spread than the normal distribution. It is symmetric around 0, but the t-distribution has a wider spread than the typical normal distribution curve, or put another way, the t-distribution has a high standard deviation. The variability of individual observations around their mean is measured by a standard deviation. The degrees of freedom (df) are n - 1. So, df is equal to n – 1, where n is the sample size. The degrees of freedom affect the shape of each t distribution curve.

When the sample size is less than 30 and the population standard deviation is unknown, the t-distribution is utilized in hypothesis testing. It is helpful when the sample size is relatively small or the population standard deviation is unknown. It resembles the normal distribution more closely as sample size grows.

A statistical metric known as the standard deviation is used to quantify the distances between each observation and the mean in a set of data. The standard deviation calculates the degree of dispersion or variability. In other words, it's used to calculate how much a random variable deviates from the mean.

The t-value and t-score have the same meanings. It is one of the relative position measurements. By definition, a value of t defines the location of a continuous random variable, X, in relation to the number of standard deviations from the mean.

The significance level is a point in the normal distribution that must be understood in order to either reject or fail to reject the null hypothesis and to assess whether or not the results are statistically significant. If you decide to make use of our t distribution calculator , you must enter the alpha value corresponding to the significance level. The most common alpha values are 0.1, 0.05 or 0.01. Generally, the most common confidence intervals are: 90%, 95% and 99% (1 − α is the confidence level).

The p-value is a probability with a value ranging from 0 to 1. It is used to test a hypothesis. As an example, in some experiment, we choose the significance level value as 0.05, in this case, the alternative hypothesis is more likely to be supported by stronger evidence when the p-value is less than 0.05 (p-value < 0.05), in case the p-value is high (p-value > 0.05), the probability of accepting the null hypothesis is also high.

The z and t distributions are symmetric and bell-shaped. However, what most characterizes the t distribution are its tails, since they are heavier than in the normal distribution. Furthermore, it can be seen that there are more values in the t-distribution located at the ends of the tail instead of the center of the distribution. You must have the population standard deviation to use the standard normal or z distribution. On the other hand, one of the important conditions for adopting the t distribution is that the population variance is unknown

The t-test , it is a parametric comparison test, is used if the means of two samples are compared using a hypothesis test, if they are independent, from two separate samples, or dependent, a sample evaluated at two different times. The procedure is carried out to evaluate if the differences between the means are significant, determining that they are not due to chance.

To interpret the results of a t-test, you can compare the t-score to the critical value and consider the p-value. A high t-score and low p-value indicate that there is a statistically significant difference between the two means, while a low t-score and high p-value indicate that the difference is not statistically significant. The degrees of freedom and the significance level (alpha) also play a role in determining the critical value and the p-value.

A one sample t-test is a statistical procedure used to test whether the mean of a single sample is significantly different from a hypothesized mean. It is used to determine whether the sample comes from a population with a mean that is different from the hypothesized mean. To perform a one sample t-test using a calculator, you need to input the following information: The sample data, including the mean and standard deviation. The hypothesized mean. The significance level (alpha). The type of tail (left, right, or two-tailed). The calculator will then calculate the t-score and p-value based on this information, and will also provide the critical value and degrees of freedom. To interpret the results, you can compare the t-score to the critical value and consider the p-value. If the t-score is greater than the critical value and the p-value is less than the significance level, you can reject the null hypothesis and conclude that the sample mean is significantly different from the hypothesized mean. If the t-score is less than the critical value or the p-value is greater than the significance level, you cannot reject the null hypothesis and must conclude that the sample mean is not significantly different from the hypothesized mean.

A two-sample t-test is a statistical procedure used to determine whether there is a significant difference between the means of two groups. It is often used to compare the means of two groups in order to determine whether a difference exists between them. For example, a researcher might use a two-sample t-test to determine whether there is a significant difference in the average scores on a test between males and females, or between two different treatment groups in a medical study. The t-test is based on the t-statistic , which is calculated from the sample data and represents the difference between the two groups in relation to the variation within the groups. The t-test is used to determine whether this difference is statistically significant, meaning that it is unlikely to have occurred by chance.

Creating a Hypothesis Test Graph with Minitab

Follow the instructions for creating your graph for the mathematical notation with the following exceptions.

Making a Normal Distribution Graph

Instead of a normal distribution, you will be using a Student's t distribution.

• Create a column called t instead of one called z . Change all references throughout the document from z to t .
• IF your test statistic is smaller than -3.5 or larger than 3.5, you will need to adjust the values when you make the patterned data for t . Change it so that the test statistic (and a little bit more) is included.
• Instead of going to Calc / Probability Distributions / Normal, go to Calc / Probability Distributions / T
• You will need the degrees of freedom from the hypothesis test

Customizing the Graph

You still need to read this section.

Empirical Rule Graph (Chapters 5 - 6)

This was for Chapters 5 and 6 and you can skip that section for this graph.

Hypothesis Test Graph (Chapters 7 - 8)

Follow the instructions given with the following changes.

• Change all references to z to t . This includes labels on critical values (instead of z= , you'll write t= )
• The critical values are not z=±1.96. You will need to determine the critical values based on the degrees of freedom and use those values. Label them with t= instead of z=
• Add an additional reference line for the test statistic (wherever it is) and label it.
• Draw an additional ray (a line with an arrow at the end) to the side of the test statistic. If the test statistic is negative, draw the ray to the left of the test statistic and if the test statistic is positive, draw the ray to the right of the test statistic. The area that you label this branch with is the p-value if it is a one tail test of p-value/2 if it is a two tail test. Minitab gives you the the full p-value, but the line gets labeled with either that value (for a one tail test) or 1/2 that value (for a two tail test).

Go to Math 113 Technology Exercises page.

Go to Math 113 homepage

Last updated October 20, 2005 2:52 PM

Normal Probability Plot Maker

Instructions: Use this Normal Probability Plot maker by entering the sample data below and this statistics calculator will provide step-by-step calculation of the required elements to construct the required probability plot.

More About the Normal Probability Plot

A normal probability plot is a plot that is typically used to assess the normality of the distribution to which the passed sample data belongs to.

There are different types of normality plots (P-P, Q-Q and other varieties), but they all operate based on the same idea. The theoretical quantiles of a standard normal distribution are graphed against the observed quantiles.

Therefore, if the sample data comes from a normality distributed population , then the normal probability plot should look like a 45 o line, with random variations about it. If that is not the case, and the pattern of the normal probability plot departs significantly/systematically from the normal probability plot, then one should suspect that the distribution is not normal.

How do you compute a normal probability plot?

There are several concrete steps you need to take, in a specific order to construct a normal probability plot

• In this concrete case, the data are ordered in ascending order, and we call such data as \(X_1, X_2, ...., X_i , ...., X_n\).
• For each \(X_i\) in this sequence of ordered data, we compute the theoretical frequencies \(f_i\), which are approximated using the following formula:
• We then we also compute \(z_i\), is corresponding associated z-score as
• Then, the normal probability plot is obtained by plotting the ordered X-values (your sample data) on the horizontal axis, and the corresponding \(z_i\) values on your vertical axis.

Normal probability plot Excel

You can plot a normal probability graph in Excel, but it takes some time. Yo

Calculators for the normal distribution and others

Other chart makers you can use are our normal distribution grapher , scatter plot maker or our Pareto chart maker .

Example: Calculation of a normal probability plot

Question : You are provided with the following sample data: 2, 3, 4, 3, 3, 2, 3, 4, 5, 3, 2, 3, 1, 2, 3, 4, 5, 6, 3, 2, 4, 5, 6 10 10 10 12 12 1 2 3 3 and 23. Construct a normal probability plot.

We need to construct a normal probability plot. These are the sample data that have been provided:

The theoretical frequencies \(f_i\) need to be computed as well as the associated z-scores \(z_i\), for \(i = 1, 2, ..., 33\):

Observe that the theoretical frequencies \(f_i\) are approximated using the following formula:

where \(i\) corresponds to the position in the ordered dataset, and \(z_i\) is corresponding associated z-score. This iscomputed as

The following table is obtained

The normal probability plot is obtained by plotting the X-values (your sample data) on the horizontal axis, and the corresponding \(z_i\) values on your vertical axis. The following normality plot is obtained:

Related Calculators

log in to your account

Reset password.

• App Downloads

Hypothesis z-test

New resources.

• Addition of Vectors
• Exploring the Area of a Triangle
• alg2_05_05_01_slider_practice_flvs
• Parallelograms: Quick Investigation
• Tutorial: Create lists of numbers and objects

Discover Resources

• NUMERI: UNO, DUE, TRE
• Rajveer's Inverse Graph
• EDUC_Lesson3
• MODUL 12_EKSPONEN_PRI HASTUTI SURYANINGRUM_SMPN 57
• เกมส์คณิตคิดเร็ว

Discover Topics

• Percentages
• Quadrilaterals
• Hypergeometric Distribution

( Photo-illustration by Realtor.com; Source: Getty Images (3) )

Local Home Prices in Swing States Could Result in ‘Vote-Switching’ in 2024 Race

Home prices could play a subtle but important role in the 2024 presidential election, according to a recent first-of-its kind study.

The academic study, Housing Performance and the Electorate , analyzed home prices and election results at the county level for each of the six presidential elections from 2000 to 2020.

The authors found that local home price performance significantly affects voting in presidential elections at the county level. Counties with superior gains in home prices in the four years preceding an election were more likely to “vote-switch” to the incumbent party’s presidential candidate.

Conversely, counties with relatively inferior home price performance leading up to an election were more likely to flip their vote to support the candidate challenging the incumbent party.

In other words, quickly rising home prices tend to favor the incumbent president’s party, whether it be the Democrats or Republicans. The study found that the relationship is strongest in the years closest to an election, and that home prices were most influential in the small group of “swing counties” with a history of switching party preference.

University of Alabama Associate Professor of Finance Alan Tidwell , one of the study’s co-authors, explains that the logic driving this trend is simple: For most voters, their home represents their single largest asset.

“People feel more financially wealthy if they have a lot of housing equity, relative to lower housing equity,” he says. “How financially wealthy they feel really impacts their sense of financial and economic well-being.”

For the upcoming presidential election, the new finding suggests the outcome could be partly influenced by home prices in swing counties of the seven battleground states: Arizona, Georgia, Michigan, Nevada, North Carolina, Pennsylvania, and Wisconsin.

“In the swing counties, they care about this economic factor most, and real estate is one of the main drivers of household wealth,” says lead author Eren Cifci , an assistant professor of finance at Austin Peay State University in Tennessee. “So there may be many other factors that affect how people vote, but this definitely appears to be one of the factors influencing voters when they make their decisions.”

Explaining the 'homevoter hypothesis'

The study’s finding is an extension of the “homevoter hypothesis,” which holds that homeowners tend to vote in support of policies and candidates they believe will boost their home values.

While that phenomenon is well documented in local politics, where government policies have the clearest impact on home values, the new study is the first to show evidence of homevoter behavior in national elections.

The term “homevoter” was coined in 2001 by William A. Fischel , a now-retired economics professor at Dartmouth College and expert in local government and land use regulation.

Fischel conceived the homevoter hypothesis while serving on the local zoning board in Hannover, NH. Regularly, he would hear objections and concerns about zoning changes that seemed esoteric, and noticed that the complaints were always from homeowners.

Fischel says he came to realize that homeowners are essentially shareholders in their community, similar to owners of stock in a company—but that unlike corporate shareholders, they cannot easily diversify their portfolio or liquidate their holdings.

“It's people who are voting their homes, and that's actually an old concept in economics,” says Fischel. “But also, they're very risk-averse, because so much of their assets are stuck in one stock, in one place.”

Fischel says he was surprised by the recent study linking home prices and voting in national elections, since he had always viewed homevoting as primarily a local phenomenon.

“​​I can see, a little bit, what a presidential election might mean for home values. But it's so indirect, I was really quite surprised at the strength of the evidence,” he says. “How did they find such a strong mechanism? But I have no reason to doubt their evidence.”

For his part, Tidwell argues that the economy plays a major role in most presidential elections, and that rising home equity has a significant impact on how voters perceive the strength of the economy.

Even if local policies, such as zoning laws and public school funding, have a bigger direct impact on local home prices, national elections are where more voters take the opportunity to weigh in with their concern or satisfaction, he says.

“Local elections don't have big turnout, and they don't have big visibility, whereas the national election has a whole bunch more turnout and a whole lot more national media exposure, especially with talk of the economy,” says Tidwell.

Home prices play the biggest role in swing counties

To conduct their study, Cifci and Tidwell, with co-authors Sherwood Clements  and Andres Jauregui , looked at the voting results for every county in the continental U.S. over the past six presidential elections.

Of those counties, 77% never changed their party preference, voting for either the Democrat or the Republican in every election since 2000, which was used as the base year for analyzing the 2004 election.

But 641 counties across the country–or 23%–switched their party vote at least once across the survey period, some as many as four times. In that subset of swing counties, home prices appeared to have the biggest impact on election results, according to the study.

In swing counties, for every 1% increase in home values over the four years preceding an election, the county was 0.36% more likely to vote for the incumbent party in the next election, the study found.

As well, the data showed that each 1% increase in home prices made the county 0.19% more likely to “flip” its vote to the incumbent party’s candidate. Those figures are after the study controlled for a variety of other factors that could sway elections, such as changes in demographics, the economy, and government benefits.

“The larger the return [on home values], the more likely you are to vote for the incumbent, or to flip for the incumbent,” explains Tidwell. “For every percent of positive return, there is a percentage increase in voting for the incumbent.”

What does it mean for 2024?

Home prices have risen rapidly across the country over the past four years, including in the seven swing states.

From March 2020 to March 2024, national home values rose 46.4%, according to the Freddie Mac Home Price Index. Of the swing states, North Carolina, Arizona, Georgia, and Wisconsin all outperformed the national average, with four-year price gains greater than 50%.

The study suggests that trend would tend broadly to favor the incumbent, President Joe Biden , as he seeks reelection, particularly in the areas that have seen the strongest home price gains. But the authors caution that their finding only demonstrates a statistical nudge in one direction or the other. They warn that there are many other variables at play in an election.

“It's just one of many factors,” Tidwell says of home price performance. “It's not really a forecast on its own.”

As well, voter turnout in counties that are reliably Democratic or Republican can be just as important to the state-level results in swing states as the marginal shifts in counties that flip from one party to another.

But in an election that is increasingly focused on the housing market, the new findings provide an interesting twist on the role of home prices in voter decision making.

Donald Trump , the presumptive Republican nominee, and his allies have recently levied attacks against Biden over rising home prices, pointing to the challenges raised for prospective first-time homebuyers.

“Under President Biden, home prices have risen almost 50%, making it nearly impossible for millennials to buy their first home and driving the American Dream further and further out of reach,” wrote Sen. Tim Scott , a South Carolina Republican and staunch Trump supporter, on the social media platform X.

On his own Truth Social platform, Trump himself recently wrote: “Crooked Joe has made it impossible for millions of Americans, especially YOUNG Americans, to buy a home.” (Conversely, Trump has also accused Biden of trying to “destroy your property values” by abolishing single-family zoning in the suburbs. The two arguments seem difficult to reconcile.)

It’s true that rising home prices, along with high mortgage rates, are key factors in a national housing crisis that has pushed ownership out of reach for many prospective homebuyers. But on the flip side, most voters are already homeowners. The U.S. homeownership rate is about 66%, and homeowners are significantly more likely to vote than renters.

For existing homeowners, rising home prices mean more equity and higher household net worth, the same as what rising stock prices mean for shareholders.

It suggests that for Republicans, attacking Biden over rising home prices might not carry the same weight with voters as criticism over inflation for goods such as gasoline and groceries.

“When you go to the grocery store or restaurant or the gas pump, I think maybe people feel a little bit different pain than if they own a house and they see their house price going up,” says Tidwell.

On the other hand, the study found evidence that, for swing counties, the economically rational choice might be to always flip to the non-incumbent party, which in 2024 would be the Republicans.

The study found that counties that flipped their vote to an incumbent party candidate were not rewarded with superior home price returns in the four years after the election.

However, counties that flipped to vote for the non-incumbent did experience “positive and significant post-election housing returns” if that candidate won. The authors speculate that this might be due to the winning party rewarding new supporters by increasing investment in those areas after regaining the White House.

“The counties that make the national results flip parties, they do well,” says Clements, a collegiate assistant professor of real estate at Virginia Tech. “Whatever counties voted for Biden last time and vote for Trump this time, if you believe our research, they’re going to have home prices rising if Trump wins.”

Editor's note: This article is part of a special Realtor.com series on the housing market and the swing states in the 2024 presidential election. For additional coverage in this series,  click here .

Keith Griffith is a journalist at Realtor.com. He covers the housing market and real estate trends.

• Related Articles

Share this Article

The state of tourism and hospitality 2024

Tourism and hospitality are on a journey of disruption. Shifting source markets and destinations, growing demand for experiential and luxury travel, and innovative business strategies are all combining to dramatically alter the industry landscape. Given this momentous change, it’s important for stakeholders to consider and strategize on four major themes:

• The bulk of travel is close to home. Although international travel might draw headlines, stakeholders shouldn’t neglect the big opportunities in their backyards. Domestic travel still represents the bulk of travel spending, and intraregional tourism is on the rise.
• Consumers increasingly prioritize travel—when it’s on their own terms. Interest in travel is booming, but travelers are no longer content with a one-size-fits-all experience. Individual personalization might not always be practical, but savvy industry players can use segmentation and hypothesis-driven testing to improve their value propositions. Those that fail to articulate target customer segments and adapt their offerings accordingly risk getting left behind.
• The face of luxury travel is changing. Demand for luxury tourism and hospitality is expected to grow faster than any other travel segment today—particularly in Asia. It’s crucial to understand that luxury travelers don’t make up a monolith. Segmenting by age, nationality, and net worth can reveal varied and evolving preferences and behaviors.
• As tourism grows, destinations will need to prepare to mitigate overcrowding. Destinations need to be ready to handle the large tourist flows of tomorrow. Now is the time for stakeholders to plan, develop, and invest in mitigation strategies. Equipped with accurate assessments of carrying capacities and enhanced abilities to gather and analyze data, destinations can improve their transportation and infrastructure, build tourism-ready workforces, and preserve their natural and cultural heritages.

Now boarding: Faces, places, and trends shaping tourism in 2024

Global travel is back and buzzing. The amount of travel fell by 75 percent in 2020; however, travel is on its way to a full recovery by the end of 2024. More regional trips, an emerging population of new travelers, and a fresh set of destinations are powering steady spending in tourism.

There’s no doubt that people still love to travel and will continue to seek new experiences in new places. But where will travelers come from, and where will they go?

We share a snapshot of current traveler flows, along with estimates for growth through 2030.

The way we travel now

Which trends are shaping traveler sentiment now? What sorts of journeys do today’s travelers dream about? How much are they willing to spend on their trips? And what should industry stakeholders do to adapt to the traveler psychology of the moment?

To gauge what’s on the minds of present-day travelers, we surveyed more than 5,000 of them. The findings reveal disparate desires, generational divides, and a newly emerging set of traveler archetypes.

Updating perceptions about today’s luxury traveler

Demand for luxury tourism and hospitality is expected to grow faster than for any other segment. This growth is being powered in part by a large and expanding base of aspiring luxury travelers with net worths between $100,000 and $1 million, many of whom are younger and increasingly willing to spend larger shares of their wealth on upscale travel options. The increase is also a result of rising wealth levels in Asia.

We dug deeper into this ongoing evolution by surveying luxury travelers around the globe about their preferences, plans, and expectations. Some widely held notions about luxury travelers—such as how much money they have, how old they are, and where they come from—could be due for reexamination.

Destination readiness: Preparing for the tourist flows of tomorrow

As global tourism grows, it will be crucial for destinations to be ready. How can the tourism ecosystem prepare to host unprecedented volumes of visitors while managing the challenges that can accompany this success? A large flow of tourists, if not carefully channeled, can encumber infrastructure, harm natural and cultural attractions, and frustrate locals and visitors alike.

Now is the time for tourism stakeholders to combine their thinking and resources to look for better ways to handle the visitor flows of today while properly preparing themselves for the visitor flows of tomorrow. We offer a diagnostic that destinations can use to spot early-warning signs about tourism concentration, along with suggestions for funding mechanisms and strategies to help maximize the benefits of tourism while minimizing its negative impacts.

Six trends shaping new business models in tourism and hospitality

As destinations and source markets have transformed over the past decade, tourism and hospitality companies have evolved, too. Accommodation, home sharing, cruises, and theme parks are among the sectors in which new approaches could present new opportunities. Stakeholders gearing up for new challenges should look for business model innovations that will help sustain their hard-won growth—and profits.

Unbundling offerings, cross-selling distinctive experiences, and embracing data-powered strategies can all be winning moves. A series of insight-driven charts reveal significant trends and an outlook on the future.

RELATED ARTICLES

The future of tourism: Bridging the labor gap, enhancing customer experience

The promise of travel in the age of AI

From India to the world: Unleashing the potential of India’s tourists

• Skip to main content
• Skip to FDA Search
• Skip to in this section menu
• Skip to footer links

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

U.S. Food and Drug Administration

•   Search
•   Menu
• Inspections, Compliance, Enforcement, and Criminal Investigations
• Compliance Actions and Activities
• Warning Letters
• AstraZeneca Pharmaceuticals LP - 664789 - 08/04/2023

WARNING LETTER

AstraZeneca Pharmaceuticals LP MARCS-CMS 664789 — August 04, 2023

1800 Concord Pike Wilmington , DE 19850 United States

United States

RE: NDA 212122 BREZTRI AEROSPHERE™ (budesonide, glycopyrrolate, and formoterol fumarate) inhalation aerosol, for oral inhalation use MA 385

Dear Pascal Soriot:

The Office of Prescription Drug Promotion (OPDP) of the U.S. Food and Drug Administration (FDA) has reviewed a promotional communication, a professional sales aid (US-68433), for BREZTRI AEROSPHERE™ (budesonide, glycopyrrolate, and formoterol fumarate) inhalation aerosol, for oral inhalation use (Breztri) submitted by AstraZeneca under cover of Form FDA 2253. The sales aid makes false or misleading claims and/or representations about the efficacy of Breztri. Thus, the sales aid misbrands Breztri within the meaning of the Federal Food, Drug, and Cosmetic Act (FD&C Act), and makes its distribution violative. 21 U.S.C. 352(a); 331(a). Cf. 21 CFR 202.1(e)(5). These violations are concerning from a public health perspective because the promotional communication creates a misleading impression regarding the overall benefits a patient may expect as a result of Breztri treatment.

Below are the indication and summary of the most serious and most common risks associated with the use of Breztri. 1 According to the FDA-approved Prescribing Information (PI):

BREZTRI AEROSPHERE is indicated for the maintenance treatment of patients with chronic obstructive pulmonary disease (COPD).

Limitations of Use:

BREZTRI AEROSPHERE is not indicated for the relief of acute bronchospasm or for the treatment of asthma.

Breztri is contraindicated in patients who have demonstrated hypersensitivity to budesonide, glycopyrrolate, formoterol fumarate, or any of the excipients. The PI for Breztri includes the following Warnings and Precautions: serious asthma-related events—hospitalizations, intubations, and death; deterioration of disease and acute episodes; avoid excessive use of Breztri and avoid use with other long-acting beta2-agonists; oropharyngeal candidiasis; pneumonia; immunosuppression and risk of infections; transferring patients from systemic corticosteroid therapy; hypercorticism and adrenal suppression; drug interactions with strong cytochrome P450 3A4 inhibitors; paradoxical bronchospasm; hypersensitivity reactions including anaphylaxis; cardiovascular effects; reduction in bone mineral density; glaucoma and cataracts, worsening of narrow-angle glaucoma; worsening of urinary retention; coexisting conditions; and hypokalemia and hyperglycemia. The most common adverse reactions reported with use of Breztri are upper respiratory tract infection, pneumonia, back pain, oral candidiasis, influenza, muscle spasm, urinary tract infection, cough, sinusitis, and diarrhea.

False or Misleading Claims about Efficacy

Prescription drug advertisements and labeling (promotional communications) misbrand a drug if they are false or misleading with respect to efficacy. The determination of whether a promotional communication is misleading includes, among other things, not only representations made or suggested in the promotional communication, but also the extent to which the promotional communication fails to reveal facts material in light of the representations made or with respect to consequences that may result from the use of the drug as recommended or suggested in the promotional communication.

The sales aid includes the prominent headline claim (emphasis original), “ DIFFERENCE OBSERVED IN TIME TO ALL-CAUSE MORTALITY (OVER 52 WEEKS) ,” in conjunction with a graph titled, “ SECONDARY ENDPOINT STUDY 1: Time to all-cause mortality in the ITT

population ,” and the following claims (emphasis original):

• “ An observed relative difference with BREZTRI vs LAMA/LABA was shown in data published in 2020/2021, including in the New England Journal of Medicine ”
• “ 49% Observed relative difference with BREZTRI vs LAMA/LABA ”

These claims and presentation, in the context of a promotional communication describing the safety and efficacy of Breztri, are misleading because they suggest that Breztri treatment has been shown to have a positive impact on all-cause mortality (ACM) and reduce the risk of death in COPD patients. These suggestions are not supported by the cited references 2,3 that analyzed data from the Efficacy and Safety of Triple Therapy in Obstructive Lung Disease (ETHOS) trial. The ETHOS trial was designed with ACM as one of multiple secondary endpoints, and due to the failure of the study to show statistically significant results on endpoints higher in the analysis hierarchy, the trial does not allow for any conclusions to be drawn from the ACM data. In addition, as the ETHOS study design required removing patients from inhaled corticosteroids (ICS) prior to entering a treatment arm, abrupt withdrawal of ICS may have been a confounding factor when analyzing any positive effect on ACM. Due to the statistical testing hierarchy failure and to the fact that abrupt withdrawal of ICS may have been a confounding factor, no conclusions about the effect of Breztri on ACM can be drawn from the ETHOS trial. We note the statement below the graph, “These results are observational in nature, and any comparisons between treatment arms should be interpreted with caution.” However, this does not mitigate the misleading impression. To date, no drug has been shown to improve ACM in COPD. 4 The results of the ETHOS trial do not exclude the possibility that the benefits in ACM claimed above may be attributable to chance or to the withdrawal of ICS and not due to Breztri. These claims and presentation are concerning from a public health perspective because they overstate the efficacy of the drug and misleadingly suggest that Breztri will have a positive impact on ACM and reduce the risk of death in COPD patients.

The sales aid also includes the following claims (bolded emphasis original, underlined emphasis added):

• “In a 52-week study where patients had a history of exacerbations within the last year, BREZTRI was the ONLY triple therapy vs ICS/LABA to show a significant reduction in severe exacerbations ”
• “ 20% EXACERBATION REDUCTION VS ICS/LABA [;] rate ratio: 0.80[;] P=0.02 ”

The presentation of these claims with the associated p-value creates a misleading impression regarding the benefit of the drug by suggesting that Breztri will have a statistically significant reduction in severe exacerbations. This suggestion is not supported by the ETHOS trial data analyzed in the cited reference 5 because the reduction in severe exacerbations was not statistically significant for patients treated with Breztri relative to comparator groups. A pvalue is generally understood to indicate statistical significance if it is less than 0.05. Therefore, the inclusion of a p-value of 0.02 in conjunction with the above presentation creates the impression that the reduction in severe exacerbations was statistically significant. However, for the Breztri to inhaled corticosteroid/long-acting beta agonist (ICS/LABA) comparison (i.e., “20% REDUCTION VS ICS/LABA”), the result was not statistically significant due to the p-value being greater than the significance threshold (critical value) established in the testing strategy. In the ETHOS trial 6 testing strategy the raw p-value of each hypothesis test was compared to the corresponding critical value to determine whether the test was statistically significant. As the p-value for the Breztri to ICS/LABA comparison (p=0.02) was greater than the critical value (0.008) for that hypothesis test, the result, per the threshold set by the testing strategy, is not statistically significant. Therefore, the presentation of these claims (i.e., with a p-value of 0.02) creates the misleading impression that Breztri provides a statistically significant reduction in severe exacerbations compared to ICS/LABA by 20% when this has not been demonstrated. We acknowledge the footnote, “*Based on predefined Type-1 error control plan” is included following these claims and related presentations. However, this does not mitigate the misleading impression. The presentation is concerning from a public health perspective because it overstates the efficacy of the drug and misleadingly represents that Breztri significantly reduces severe exacerbations.

Conclusion and Requested Action

For the reasons discussed above, the detail aid misbrands Breztri within the meaning of the FD&C Act and makes its distribution violative. 21 U.S.C. 352(a); 331(a). Cf. 21 CFR 202.1(e)(5).

This letter notifies you of our concerns and provides you with an opportunity to address them. OPDP requests that AstraZeneca cease any violations of the FD&C Act. Please submit a written response to this letter within 15 working days from the date of receipt, addressing the concerns described in this letter, listing all other promotional communications (with the 2253 submission date) for Breztri that contain representations such as those described above, and explaining any plan for discontinuing use of such communications, or for ceasing distribution of Breztri.

Failure to adequately address this matter may lead to regulatory action. If you believe that your products are not in violation of the FD&C Act, please include in your submission to us your reasoning and any supporting information for our consideration within 15 working days from the date of receipt of this letter.

Additionally, we request that your submission include a comprehensive plan of action to disseminate truthful, non-misleading, and complete corrective communication(s) about the concern(s) discussed in this letter. The corrective communication(s) should be disseminated to the audience(s) that received the promotional communication(s) identified in the opening paragraph of this letter. OPDP recommends that corrective communication(s) include a description of the promotional communication(s) identified in this letter, which misbrand Breztri; include a summary of the concern(s) described in this letter; and provide information to correct each of these concern(s). Corrective communication(s) should be free of promotional claims and presentations. To the extent possible, corrective communication(s) should be distributed using the same media, and generally for the same duration of time and with the same frequency as the promotional communication(s) identified in the opening paragraph of this letter.

The concerns discussed in this letter do not necessarily constitute an exhaustive list of potential violations. It is your responsibility to ensure compliance with each applicable requirement of the FD&C Act and FDA implementing regulations.

Please direct your response to the undersigned at the Food and Drug Administration, Center for Drug Evaluation and Research, Office of Prescription Drug Promotion, 5901-B Ammendale Road, Beltsville, Maryland 20705-1266 . A courtesy copy can be sent by facsimile to (301) 847-8444. Please refer to MA 385 in addition to the NDA number in all future correspondence relating to this particular matter. All correspondence should include a subject line that clearly identifies the submission as a Response to Warning Letter. You are encouraged, but not required, to submit your response in eCTD format. All correspondence submitted in response to this letter should be placed under eCTD Heading 1.15.1.6. Additionally, the response submission should be coded as an Amendment to eCTD Sequence 0454 under NDA 212122. Questions related to the submission of your response letter should be emailed to the OPDP RPM at [email protected].

Sincerely, {See appended electronic signature page} Twyla Mosey, Pharm.D. Director Division of Advertising & Promotion Review 2 Office of Prescription Drug Promotion -------------------------------------------------------------------------------------------- This is a representation of an electronic record that was signed electronically. Following this are manifestations of any and all electronic signatures for this electronic record. -------------------------------------------------------------------------------------------- /s/ ------------------------------------------------------------ MATTHEW J FALTER on behalf of TWYLA N MOSEY 08/04/2023 10:20:52 AM

_____________________

1 This information is for background purposes only and does not necessarily represent the risk information that should be included in the promotional communications cited in this letter.

2 Martinez FJ, Rabe KF, Ferguson GT, et al. Reduced all-cause mortality in the ETHOS trial of budesonide/glycopyrrolate/formoterol for COPD: a randomized, double-blind, multi-center, parallel-group study. Am J Respir Crit Care Med. 2021;203(5):553-564.

3 Rabe KF, Martinez FJ, Ferguson GT, et al. Triple inhaled therapy at two glucocorticoid doses in moderate-to-very severe COPD. N Engl J Med. 2020;383(1):35-48.

4 Through the issuance of this letter, FDA does not intend to convey any views on whether data that did show that Breztri improved ACM in COPD would support a change to the FDA-approved labeling for Breztri.

6 The ETHOS trial used a combination of hierarchical and Hochberg test procedures to control the overall Type I error among different endpoints and different doses.

PROMOTIONAL MATERIAL