# Paired t test

Description

Paired T-tests compare the difference in means between two sets of observations which are uniquely coupled e.g. exam scores for an individual before and after a training program. Paired T-tests are used only when you have two categorical ‘related’ groups as your independent variable and a continuous variable for dependent variable. The null hypothesis states that the difference in means is equal to 0, implying that any difference seen is due to chance.

This test produces 3 values, ‘t’ , ‘df’ and ‘p’ for 3 alternative hypotheses - that the true difference is greater than, lesser than, or not equal to 0 . ‘Df’ stands for degrees of freedom, which simply means the number of measurements in the data. ‘T’ is the value calculated in units of standard error which, when compared to a distribution of ‘t’ values, gives a ‘p’ value, which is the probability of obtaining that ‘t’ value or greater (or lesser, depending on the ‘tail’) if it was down to random chance.

Hence, the smaller the p-value, the more evidence there is that the observed difference is less due to chance.

Benefits

Reduces confounding, increase statistical power

Limitations

• Assume continuous dependent variable
• Assume normally distributed dependent variable
• Assume observations are independent

Worked Example:

An example excel file can be downloaded below ‘ Paired T test example’ • There are four columns, ‘before’, ‘after’, ‘RandA’ and ‘Rand B’.
• There are 29 values in each column (these values are randomly generated, but could represent data before and after an intervention)
• A significant difference (i.e. a P-value less than 0.05) should be seen when comparing ‘before’ and ‘after’ columns, and no difference should be seen between ‘RandA’ and ‘RandB’