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Interpreting the paired t test
How a paired t test works
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. If thevalue in column B is larger, then the difference is positive. If the value in column A is larger, then the difference is negative. 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 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. Byanalyzing only the differences, therefore, 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. (See Correlation.) 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 itmade 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 wascounterproductive! 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.
How to think about results of a paired t test
The paired t test comparestwo paired groups so you can make inferences about the size of the average treatment effect (average difference between the paired measurements). The most important results are the P value and the confidence interval.
The P value answers this question: If the treatment really had no effect, what is the chance that random sampling would result in an average effect as far from zero (or more so) asobserved in this experiment?
"Statistically significant" is not the same as "scientifically important". Before interpreting the P value or confidence interval, you should think about the size of the treatment effect you are looking for. How large a difference would you consider to be scientifically important? How small a difference would you consider to be scientifically trivial? Use scientificjudgment and common sense to answer these questions. Statistical calculations cannot help, as the answers depend on the context of the experiment.
You will interpret the results differently depending on whether the P value is small or large.
If the P value is small (paired t test)
If the P value is small, then it is unlikely that the treatment effect you observed is due to a coincidence of...
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