Aug 30 2012

# Related Samples T-Test

**When to use it**

Use a Related (paired)-samples t-test if you have a continuous measurement on 2 groups in which the observations are paired (e.g. measuring the same person twice or mothers and daughters) and you want to know if there is a difference between the 2 groups.

e.g. Are daughters taller than their mothers?

e.g.Does running raise the heart rate?

To decide whether your samples are independent or related you need to ask the question ”If I take any particular observation in group 1, does it matter which observation I match it to in group 2?” If the answer is yes then your samples are related.

For instance, if you’re comparing the heights of mothers and daughters, If you pick a mother, you need to match her to her own daughter.

If you’re asking whether a drug reduces blood pressure and you measure people before and after the drug, then once you’ve picked a before observation, it matters that the after observation comes from the same person.

**Assumptions **

The distribution of the sample statistic is normal within each group. In practice, as long as the measurement is scalar, this can be assumed for samples bigger than about 30 (by the Central Limit Theorem). For smaller samples you need the DV to be approximately normal within each group.

* Note that doesn’t mean that the DV is normal for the whole sample, you need to split the sample into groups first.

There are exactly 2 samples – the IV (explanatory variable) is nominal with exactly 2 categories

Each observation in group 1 has a natural pairing with another observation in group 2.

**What to do if you don’t meet the assumptions**

If your DV doesn’t appear to be normal then consider using Wilcoxon’s Signed Rank test or increasing the sample size because for large samples, the sample statistic will be approximately normal no matter what how the DV is distributed.

If your DV is ordinal, consider using Wilcoxon’s Signed Rank test or the Sign test.

If there is 1 sample (no IV) consider using a 1 sample t-test

If the observations in group 1 are independent of those in group 2 consider using an independent 2 samples t-test.

If there are 3 or more samples (a categorical IV with 3 or more values) consider using a repeated measures ANOVA.

To run a related samples t-test in SPSS go to *Analyze->Compare Means->Paired Samples T-Test*