Hypothesis Testing

What is the Relationship Between the Reproducibility of Experimental Results and P Values?

The ability to reproduce experimental results should be related to P values. After all, both of these statistical concepts have similar foundations.

P values help you separate the signal of population level effects from the noise in sample data.
Reproducible results support the notion that the findings can be generalized to the population rather than applying only to a specific sample.

So, P values are related to reproducibility in theory. But, does this relationship exist in the real world? In this blog post, I present the findings of an exciting study that answers this question! [Read more…] about What is the Relationship Between the Reproducibility of Experimental Results and P Values?

Why Are P Values Misinterpreted So Frequently?

By Jim Frost 2 Comments

P values are commonly misinterpreted. It’s a very slippery concept that requires a lot of background knowledge to understand. Not surprisingly, I’ve received many questions about P values in statistical hypothesis testing over the years. However, one question stands out. Why are P value misinterpretations so prevalent? I answer that question in this blog post, and help you avoid making the same mistakes. [Read more…] about Why Are P Values Misinterpreted So Frequently?

Confidence Intervals vs Prediction Intervals vs Tolerance Intervals

By Jim Frost 27 Comments

Intervals are estimation methods in statistics that use sample data to produce ranges of values that are likely to contain the population value of interest. In contrast, point estimates are single value estimates of a population value. Of the different types of statistical intervals, confidence intervals are the most well-known. However, certain kinds of analyses and situations call for other types of ranges that provide different information. [Read more…] about Confidence Intervals vs Prediction Intervals vs Tolerance Intervals

Five P Value Tips to Avoid Being Fooled by False Positives and other Misleading Hypothesis Test Results

By Jim Frost 6 Comments

Despite the popular notion to the contrary, understanding the results of your statistical hypothesis test is not as simple as determining only whether your P value is less than your significance level. In this post, I present additional considerations that help you assess and minimize the possibility of being fooled by false positives and other misleading results. [Read more…] about Five P Value Tips to Avoid Being Fooled by False Positives and other Misleading Hypothesis Test Results

Goodness-of-Fit Tests for Discrete Distributions

By Jim Frost 15 Comments

Discrete probability distributions are based on discrete variables, which have a finite or countable number of values. In this post, I show you how to perform goodness-of-fit tests to determine how well your data fit various discrete probability distributions. [Read more…] about Goodness-of-Fit Tests for Discrete Distributions

Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes

By Jim Frost 7 Comments

In my house, we love the Mythbusters TV show on the Discovery Channel. The Mythbusters conduct scientific investigations in their quest to test myths and urban legends. In the process, the show provides some fun examples of when and how you should use statistical hypothesis tests to analyze data. [Read more…] about Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes

How to Identify the Distribution of Your Data

By Jim Frost 56 Comments

You’re probably familiar with data that follow the normal distribution. The normal distribution is that nice, familiar bell-shaped curve. Unfortunately, not all data are normally distributed or as intuitive to understand. You can picture the symmetric normal distribution, but what about the Weibull or Gamma distributions? This uncertainty might leave you feeling unsettled. In this post, I show you how to identify the probability distribution of your data. [Read more…] about How to Identify the Distribution of Your Data

Interpreting P values

By Jim Frost 41 Comments

P values determine whether your hypothesis test results are statistically significant. Statistics use them all over the place. You’ll find P values in t-tests, distribution tests, ANOVA, and regression analysis. P values have become so important that they’ve taken on a life of their own. They can determine which studies are published, which projects receive funding, and which university faculty members become tenured!

Ironically, despite being so influential, P values are misinterpreted very frequently. What is the correct interpretation of P values? What do P values really mean? That’s the topic of this post! [Read more…] about Interpreting P values

How Hypothesis Tests Work: Significance Levels (Alpha) and P values

By Jim Frost 18 Comments

Hypothesis testing is a vital process in inferential statistics where the goal is to use sample data to draw conclusions about an entire population. In the testing process, you use significance levels and p-values to determine whether the test results are statistically significant.

You hear about results being statistically significant all of the time. But, what do significance levels, P values, and statistical significance actually represent? Why do we even need to use hypothesis tests in statistics? [Read more…] about How Hypothesis Tests Work: Significance Levels (Alpha) and P values

Nonparametric Tests vs. Parametric Tests

By Jim Frost 63 Comments

Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.

You’ve probably heard it’s best to use nonparametric tests if your data are not normally distributed—or something along these lines. That seems like an easy way to choose, but there’s more to the decision than that. [Read more…] about Nonparametric Tests vs. Parametric Tests

How Hypothesis Tests Work: Confidence Intervals and Confidence Levels

By Jim Frost 8 Comments

A confidence interval is calculated from a sample and provides a range of values that likely contains the unknown value of a population parameter. In this post, I demonstrate how confidence intervals and confidence levels work using graphs and concepts instead of formulas. In the process, you’ll see how confidence intervals are very similar to P values and significance levels. [Read more…] about How Hypothesis Tests Work: Confidence Intervals and Confidence Levels

How t-Tests Work: t-Values, t-Distributions, and Probabilities

By Jim Frost 8 Comments

T-tests are statistical hypothesis tests that you use to analyze one or two sample means. Depending on the t-test that you use, you can compare a sample mean to a hypothesized value, the means of two independent samples, or the difference between paired samples. In this post, I show you how t-tests use t-values and t-distributions to calculate probabilities and test hypotheses.

As usual, I’ll provide clear explanations of t-values and t-distributions using concepts and graphs rather than formulas! If you need a primer on the basics, read my hypothesis testing overview. [Read more…] about How t-Tests Work: t-Values, t-Distributions, and Probabilities

How t-Tests Work: 1-sample, 2-sample, and Paired t-Tests

By Jim Frost 11 Comments

T-tests are statistical hypothesis tests that analyze one or two sample means. When you analyze your data with any t-test, the procedure reduces your entire sample to a single value, the t-value. In this post, I describe how each type of t-test calculates the t-value. I don’t explain this just so you can understand the calculation, but I describe it in a way that really helps you grasp how t-tests work. [Read more…] about How t-Tests Work: 1-sample, 2-sample, and Paired t-Tests

How to Analyze Likert Scale Data

By Jim Frost 41 Comments

How do you analyze Likert scale data? Likert scales are the most broadly used method for scaling responses in survey studies. Survey questions that ask you to indicate your level of agreement, from strongly agree to strongly disagree, use the Likert scale. The data in the worksheet are five-point Likert scale data for two groups. [Read more…] about How to Analyze Likert Scale Data

Chi-Square Test of Independence and an Example

By Jim Frost 28 Comments

The Chi-square test of independence determines whether there is a statistically significant relationship between categorical variables. It is a hypothesis test that answers the question—do the values of one categorical variable depend on the value of other categorical variables? [Read more…] about Chi-Square Test of Independence and an Example

Hypothesis Testing and the Mythbusters: Are Yawns Contagious?

By Jim Frost 1 Comment

When it comes to hypothesis testing, statistics help you avoid opinions about when an effect is large and how many samples you need to collect. Opinions about these things can be way off—even among those who regularly perform experiments and collect data! This can lead you to draw the incorrect conclusions. Always perform the correct hypothesis tests so you understand the strength of your evidence.