The ratio t test compares the means of two matched groups, assuming that the distribution of the logarithms of the before/after ratios follows a Gaussian distribution.
The ratio t test assumes that you have sampled your pairs of values from a population of pairs where the log of the ratios follows a Gaussian distribution.
While this assumption is not too important with large samples, it is important with small sample sizes. Test this assumption with Prism.
The pairing should be part of the experimental design and not something you do after collecting data. Prism tests the effectiveness of pairing by calculating the Pearson correlation coefficient, r, between the logarithms of the two columns of data. If the corresponding P value. If the P value is small, the two groups are significantly correlated. This justifies the use of a paired test.
If this P value is large (say larger than 0.05), you should question whether it made sense to use a paired test. Your choice of whether to use a paired test or not should not be based solely on this one P value, but also on the experimental design and the results of other similar experiments.
The results of a ratio t test only make sense when the pairs are independent – that whatever factor caused a rato (of paired values) to be too high or too low affects only that one pair. Prism cannot test this assumption. You must think about the experimental design. For example, the errors are not independent if you have six pairs of values, but these were obtained from three animals, with duplicate measurements in each animal. In this case, some factor may cause the after-before differences from one animal to be high or low. This factor would affect two of the pairs, so they are not independent.
Use the t test only to compare two groups. To compare three or more matched groups, transform the values to their logarithms, and then use repeated measures one-way ANOVA followed by post tests. It is not appropriate to perform several t tests, comparing two groups at a time.
If you chose a one-tail P value, you should have predicted which group would have the larger mean before collecting data. Prism does not ask you to record this prediction, but assumes that it is correct. If your prediction was wrong, then ignore the reported P value and state that P>0.50.
The ratio t test analyzes the logarithm of the ratios of paired values. The assumption is that the ratio is a consistent measure of experimental effect. With many experiments, you may observe that the difference between pairs is a consistent measure of effect, and the ratio is not. In these cases, use a paired t test, not the ratio t test.