Complete the following steps to interpret the equivalence test with paired data. Key output includes the estimate of the difference (or ratio), the confidence interval, the equivalence plot, and other graphs.

Compare the confidence interval with the equivalence limits. If the confidence interval is completely within the equivalence limits, you can claim that the mean of the test population is equivalent to the mean of the reference population. If part of the confidence interval is outside the equivalence limits, you cannot claim equivalence.

Difference | StDev | SE | 95% CI for Equivalence | Equivalence Interval |
---|---|---|---|---|

-0.11929 | 0.42324 | 0.11312 | (-0.319605, 0.0810335) | (-0.5, 0.5) |

In these results, the 95% confidence interval is completely within the interval defined by the lower equivalence limit (LEL) and the upper equivalence limit (UEL). Therefore, you can conclude that the test mean is equivalent to the reference mean.

You can also use the p-values to evaluate the results of the equivalence test. To demonstrate equivalence, the p-values for both null hypotheses must be less than alpha.

Problems with your data, such as skewness or outliers, can adversely affect your results. Use graphs to look for skewness (by examining the spread of the data) and to identify potential outliers.

When data are skewed, the majority of the data is toward the high or low side of the graph. Often, skewness is easiest to identify with a boxplot or histogram.

Data that are severely skewed can affect the validity of the test results if your sample is small (< 20 values). If your data are severely skewed and you have a small sample, consider increasing your sample size.

Outliers, which are data points that are far away from most of the other data, can strongly affect your results. Outliers are easiest to identify on a boxplot.

You should try to identify the cause of any outliers. Correct any data entry or measurement errors. Consider removing data that are associated with special causes and repeating the analysis. For more information on special causes, go to Using control charts to detect common-cause variation and special-cause variation.