LibGuides: Maths and Stats Support: Paired t-test

Differences between two paired measurements

Paired measurements occur when you collect the same variable twice either at different time points or under different conditions such as each person trying two different biscuits and giving them both a taste rating or weights before and after a diet.

Parametric: Paired T-Test

Use: Comparing the mean difference of two measurements of the same continuous variable. You should have measurements in different columns with each row representing one subject.

Dependent (outcome) variable: Continuous
Independent (predictor) variable: Two categories e.g. before/after a diet or type of biscuit

Example: testing for a change in weight before and after a diet or comparing taste scores for two different biscuits

Summary statistics/graphs: Summarise the paired difference e.g. weight loss using mean, standard deviation and a boxplot

Wilcoxon signed rank

Non-parametric: Wilcoxon signed rank

Use: Testing for a difference between two measurements of the same variable when the variable of interest is ordinal or the paired differences are very skewed.

Dependent (Outcome): Ordinal or skewed paired differences
Independent (predictor): Two time points or conditions

Example: Each person tries two different biscuits and gives a taste rating from disgusting to delicious or weight loss on a diet is very skewed

Summary statistics/graphs: Use medians, Interquartile range and boxplot for ordinal or skewed data.

Note: If you have taken the mean or sum of several ordered questions (scale mean), use parametric tests such as t-tests. Some disciplines use parametric tests for individual ordinal questions but a wider range of responses (ideally 7+) is needed

Resources by software

The following resources show you how to carry out, interpret and report tests using SPSS.

SPSS: Summarising continuous data
Producing appropriate summary statistics and charts for continuous variables
SPSS: Paired t-test
How to carry out, interpret and check assumptions for the paired t-test in SPSS
SPSS:Wilcoxon signed rank
How to carry out, interpret and check assumptions for the Wilcoxon signed rank test in SPSS

There are a set of videos taking you through all the steps including discussing key concepts, data summary and choosing between t-tests and non-parametric equivalents. There are also quick guides.

Jamovi: Summary statistics for continuous data
Video discussing the different types of chart and summary statistics for continuous data
Jamovi: Independent t-test preparation
This video helps you check that your data is in the right format, choosing the right t-test and summary statistics

Jamovi:Paired t-test and Wilcoxon signed rank quick resource

The resources guide you through the r code and interpretation of the relevant summary statistics and test for comparing two different groups of subjects. The script files with all the code can be adapted to run each technique on your own data.

These resources contain the SAS code needed for the paired t-test, the non-parametric equivalent, the Wilcoxon signed rank test, if the assumptions have not been met and a one sample t-test