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 Interpreting results: Paired t

## Confidence Interval

The paired t test compares the means of two paired groups, so look first at the difference between the two means. Prism also displays the confidence interval for that difference. If the assumptions of the analysis are true, you can be 95% sure that the 95% confidence interval contains the true difference between means.

P value

The P value is used to ask whether the difference between the mean of two groups is likely to be due to chance. It answers this question:

If the two populations really had the same mean, what is the chance that random sampling would result in means as far apart (or more so) than observed in this experiment?

It is traditional, but not necessary and often not useful, to use the P value to make a simple statement about whether or not the difference is “statistically significant”.

You will interpret the results differently depending on whether the P value is small or large.

## t ratio

The paired t test compares two paired groups. It calculates the difference between each set of pairs and analyzes that list of differences based on the assumption that the differences in the entire population follow a Gaussian distribution.

First, Prism calculates the difference between each set of pairs, keeping track of sign. The t ratio for a paired t test is the mean of these differences divided by the standard error of the differences. If the t ratio is large (or is a large negative number) the P value will be small. The direction of the differences (Column A minus B, or B minus A) is set in the Options tab of the t test dialog.

The number of degrees of freedom equals the number of pairs minus 1. Prism calculates the P value from the t ratio and the number of degrees of freedom.

## Test for adequate pairing

The whole point of using a paired experimental design and a paired test is to control for experimental variability. Some factors you don't control in the experiment will affect the before and the after measurements equally, so they will not affect the difference between before and after. By analyzing only the differences, a paired test corrects for those sources of scatter.

If pairing is effective, you expect the before and after measurements to vary together. Prism quantifies this by calculating the Pearson correlation coefficient, r. From r, Prism calculates a P value that answers this question:

If the two groups really are not correlated at all, what is the chance that randomly selected subjects would have a correlation coefficient as large (or larger) as observed in your experiment? The P value has one-tail, as you are not interested in the possibility of observing a strong negative correlation.

If the pairing was effective, r will be positive and the P value will be small. This means that the two groups are significantly correlated, so it made sense to choose a paired test.

If the 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 on this one P value, but also on the experimental design and the results you have seen in other similar experiments.

If r is negative, it means that the pairing was counterproductive! You expect the values of the pairs to move together – if one is higher, so is the other. Here, the opposite is true – if one has a higher value, the other has a lower value. Most likely this is just a matter of chance. If r is close to -1, you should review your experimental design, as this is a very unusual result.

## 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.