# Two simple tests for summary data

Here’s two handy scripts for hypothesis testing of summary data. I seem to use these a lot when checking work:

• Chi-squared test of association for categorical data.
• Student’s t-test for difference in means of normally distributed data.

The actual equations are straightforward, but get involved when group sizes and variance are not equal. Why do I use these a lot?!

I wrote about a study from Hungary in which the variability in the results seemed much lower than expected. We wondered whether the authors had made a mistake in saying they were showing the standard deviation (SD), when in fact they had presented the standard error of the mean (SEM).

This is a bit of table 1 from the paper. It shows the differences in baseline characteristics between the treated group (IPC) and the active control group (IP). In it, they report no difference between the groups for these characteristics, p>0.05.

But taking “age” as an example and using the simple script for a Student’s t-test with these figures, the answer we get is different. Mean (SD) for group A vs. group B: 56.5 (2.3) vs. 54.8 (1.8), t=4.12, df=98, p=<0.001.

There are lots of similar examples in the paper.

Using standard error of the mean rather than standard deviation gives a non-significant difference as expected.

$SEM=SD/\sqrt{n}.$

See here for how to get started with R.