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

# Hypothesis Testing

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

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

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

## P values and Statistical Significance

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 P values and Statistical Significance

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

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

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

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

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

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

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

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?

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.

[Read more…] about Hypothesis Testing and the Mythbusters: Are Yawns Contagious?