A t-test helps you discover if a survey you conducted has results that matter. Let’s say that you are a pollster in the Phoenix-area, and you want to gauge how voters feel about the president’s job performance. You survey 600 people and ask them to rank the president’s job performance on a scale of 1 to 5, with 1 being the lowest. After reviewing the results and doing some quick math, you learn that the president’s average approval in your poll was 2.7. What can you learn from this?

This is where a t-test comes in. There are three types of t-tests that people can use: one-sample t-tests, two-sample t-tests, and paired t-tests. To perform a t-test we:

- Calculate the t-statistic - Based on whether you are using a one-sample, two-sample, or paired t-test.
- Calculate the degrees of freedom - Broadly speaking, the number of ways that your sample can change. Larger sample sizes have more degrees of freedom because they have more data points that can change the overall mean. Again, based on what type of t-test you are performing.

- Calculate the critical value - the threshold at which the difference in your means can be considered “statistically significant.”
- Compare the absolute value of the t-statistic to the critical value. If your t-statistic is greater than your critical value, there is a statistically significant difference between the two numbers. If your t-statistic is less than your critical value, you cannot say that the two numbers you are comparing are statistically different.

Between these three types of t-tests, you can discover statistical differences and similarities between groups, statistical changes of a group over time, and any statistical differences before/after implementing a dependent variable for a group, such as a political ad.

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