What is a paired t-test?

A paired t-test is a statistical hypothesis test used to compare the means of two related groups. Unlike a two-sample t-test where the groups are independent, a paired t-test focuses on differences within pairs where each data point is paired with another.

What do you use a paired t-test for?

Here are some common applications of a paired t-test:

• Before-and-after studies: Researchers might use a paired t-test to see if a new training program significantly improves participants' test scores compared to their scores before the training.
• Comparing two measurement methods: A study might use a paired t-test to see if blood pressure readings from a new device differ significantly from readings taken with a traditional method.

What to pay attention to while performing a paired t-test?

• Paired data: This is the core requirement. Each data point must have a corresponding pair in the other group.
• Normality of differences: The paired t-test assumes normality of the differences between the paired data points, not necessarily the original data itself.
• Independence of differences: The differences within each pair should be independent of each other.

Statistical Programs for Paired t-Test

Many statistical software programs can perform a paired t-test. Here are a few popular options:

• R: t.test(data1, data2, paired = TRUE) (where data1 and data2 are your paired samples)
• Python (SciPy library): scipy.stats.ttest_paired(data1, data2) (similar to R code)
• SAS: PROC TTEST PAIRED
• SPSS: Analyze > Compare Means > Paired-Samples T Test
• Excel (Data Analysis ToolPak required): =TTEST(data1, data2, 1) (1 indicates a paired test)

These are just a few examples, and most major statistical software packages will have a paired t-test function.