Specifically, the Posttest mean is greater than the Pretest mean. Our sample data support the notion that the average paired difference does not equal zero. If the p-value is less than your significance level, the difference does not equal zero.īecause our p-value (0.002) for the paired sample t-test is less than the standard significance level of 0.05, we can reject the null hypothesis. The average difference between the paired pretest and posttest scores is -10.77. The output indicates that the mean for the Pretest is 97.06, and for the Posttest it is 107.83. Here’s how to read and report the results for a paired t test. In that case, we’d need to perform an independent samples t test. The change between the pretest for one subject and the posttest for another does not provide meaningful information. The paired t-test is the correct choice.Ĭonversely, if each row had contained different subjects, it would not make sense to subtract them. Because we have paired samples, each difference in a row represents how much a subject’s score changed after the training program. Consequently, it makes sense to find the difference between the pairs of values. Does it make sense to assess the difference within a row? In other words, does each row correspond to one person or item? Are the samples paired with each other?įor our dataset, each row in the dataset contains the same subject in the two measurement columns. Here’s the deciding characteristic for when you should use paired t tests versus an independent samples t test. Note that the analysis does not use the subject’s ID number. Here is what the data look like in the datasheet. We need to determine whether the average change for the pairs of scores is different from zero. Consequently, each student has a pair of test scores. Related post: Central Limit Theorem and Skewed Distributions Paired T Test Exampleįor example, imagine we have a training program and administer a pretest and posttest to the same sample of students. However, when you have a smaller sample size, nonnormal data can cause the test results to be unreliable. However, you can waive this assumption when your sample size is large enough thanks to the central limit theorem.įor a paired sample t test, if you have at least 20 subjects, your test results will be reliable even when your data are skewed. For a paired t test, the normality assumption applies to the distribution of paired differences rather than raw test scores. Data should follow a normal distribution or have a sample size larger than 20Īll t-tests assume that your data follow the normal distribution. To learn more, read my post, Comparing Hypothesis Tests for Continuous, Binary, and Count Data. If you don’t have continuous data, you’ll need to use a different type of hypothesis test. For example, weight, temperature, and height are continuous data. Typically, you measure continuous variables on a scale. Values can be meaningfully divided into smaller increments, including fractional and decimal values. Continuous variables can take on any numeric value. If the two groups contain different subjects, use an independent samples t test instead.
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