# Descriptive statistics for Equivalence Test for a 2x2 Crossover Design

Find definitions and interpretation guidance for every descriptive statistic that is provided with the equivalence test for a 2x2 crossover design.

## N

The sample size (N) is the total number of observations in the sample.

### Interpretation

The sample size affects the confidence interval and the power of the test. Usually, a larger sample results in a narrower confidence interval. A larger sample also gives the test more power.

For more information on power in equivalence tests, go to Power for equivalence tests.

## Mean

The mean summarizes the values in each sample with a single value that identifies the center of the data. The mean is calculated as the arithmetic average of the data, which is the sum of all the observations divided by the number of observations.

The equivalence test for a 2x2 crossover design calculates the mean of the treatment response for each period of each sequence in the study.

### Interpretation

Use the mean of each period to estimate the average treatment response for subjects across each treatment sequence. Examine whether each group of participants responded to the two treatments similarly, on average. To determine whether any treatment effects, carryover effects, or period effects are statistically significant, refer to the results in the Effects table.

###### Note

To visually compare the means across each treatment sequence, use the sequence by period mean plot. For more information, go to Graphs for Equivalence Test for a 2x2 Crossover Design and click "Sequence by period mean plot".

## StDev

The standard deviation (StDev) is the most common measure of dispersion, or how much the data vary relative to the mean. Variation that is random or natural to a process is often referred to as noise.

The standard deviation uses the same units as the data. The symbol σ (sigma) is often used to represent the standard deviation of a population. The letter s is used to represent the standard deviation of a sample.

### Interpretation

Use the standard deviation to determine how spread out the data are from the mean.

The standard deviation of the sample data is an estimate of the population standard deviation. Higher values indicate more variation or "noise" in the data. The standard deviation is used to calculate the confidence interval and the p-value. A higher value results in a wider confidence interval and lower statistical power.

## Within-subject standard deviation

The within-subject standard deviation is the standard deviation of multiple response values from the same participant. It estimates the magnitude of the random error in the response measurements from the same participant after eliminating treatment effects, period effects, and other systematic effects. Higher values indicate greater variability in the response values of each participant.

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