Statistical test · BEGINNER LESSON
Paired t-test
A paired t-test is a statistical test used to compare the mean of two dependent measurements taken on the same people or on matched pairs. It asks whether the average difference between the paired values is different from zero.
What it is and what it measures
A paired t-test is used when two measurements are linked to each other, not independent. Common examples are before-and-after measurements on the same participants or two measurements from matched pairs. The test uses the mean difference between the paired values and the spread of those differences, usually summarized with a standard deviation. Its output is often reported with a t value, degrees of freedom, and a p-value, which help judge whether the observed average difference is unlikely to be due to chance alone.
[1] recommendations for reporting statistical methods - PMC - NIH [3] Table 4.
How it works
First, each pair is reduced to a single difference score by subtracting one measurement from the other. Then the test checks whether the average of those difference scores is far enough from zero relative to their variation. If the data follow the normality assumption, this parametric test can be used. In method-comparison contexts, it is important to note that a paired t-test evaluates mean difference, not agreement between methods.
[1] recommendations for reporting statistical methods - PMC - NIH [2] A scoping review of statistical methods for the analysis of ...
When it is appropriate
The paired t-test is intended for dependent, paired data. It is suitable for questions such as whether a pre-test and post-test mean differ in the same group of people. The sources also show it being reported with confidence intervals for the mean difference, which gives a range of plausible values for the average change.
[1] recommendations for reporting statistical methods - PMC - NIH [3] Table 4.
Limitations
The test depends on assumptions, especially normality of the paired differences; the reviewed sources also mention homoscedasticity, meaning roughly similar spread across the data. If the data do not follow a normal distribution, the t-test is considered inappropriate in the cited reporting guidance. Another limitation is that a paired t-test does not tell which method is more accurate and does not measure agreement between two methods. It only addresses mean difference.
[1] recommendations for reporting statistical methods - PMC - NIH [2] A scoping review of statistical methods for the analysis of ...
SEE THE IDEA
How a paired t-test works
Two linked values from the same person or matched pair, such as pre and post.
Subtract one value from the other within each pair.
Compute the mean of all difference scores and compare it with zero.
Summarizes how unusual the observed mean difference is under the test model.
Paired measurements are converted into differences, and the paired t-test evaluates whether their average differs from zero.
The test focuses on within-pair change, not on whether two methods agree perfectly.
TRY IT YOURSELF
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PUT IT TOGETHER
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.