Example

You measure the Km of a kidney enzyme (in nM) before and after a treatment. Each experiment was done with renal tissue from a different animal.

Using a conventional paired t test, the 95% confidence interval for the mean difference between control and treated Km value is -0.72 to 9.72, which includes zero. The P value 0.07. The difference between control and treated is not consistent enough to be statistically significant. This makes sense because the paired t test looks at differences, and the differences are not very consistent.

The ratios are much more consistent, so it makes sense to perform the ratio t test. The  geometric mean of the ratio treated/control is 2.02, with a 95% confidence interval ranging from 1.88 to 2.16. The data clearly show that the treatment approximately doubles the Km of the enzyme.

Analyzed with a paired t test, the results were ambiguous. But when the data are analyzed with a ratio t test, the results are very persuasive – the treatment doubled the Km of the enzyme.

The P value is 0.0005, so the effect of the treatment is highly statistically significant.

The P value answers this question:

If there really were no differences between control and treated values, what is the chance of obtaining a ratio as far from 1.0 as was observed? If the P value is small, you have evidence that the ratio between the paired values is not 1.0.

Descriptive statistics

The analysis tab of descriptive statistics summarizes only the data that was used for the paired t test. If you had any data in one column, but not the other, those values are not included in the descriptive statistics results that are included with the paired t test. But of course, the general descriptive statistics analysis analyzes all the data.