Graphs for Equivalence Test with Paired Data

Find definitions and interpretation guidance for every graph that is provided with the equivalence test with paired data.

Equivalence plot

An equivalence plot displays the equivalence limits, the confidence interval for equivalence, and the decision about whether you can claim equivalence.

Interpretation

Use the equivalence plot to view a graphical summary of the equivalence test results and to determine whether you can claim equivalence.

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.

In these results, the 95% confidence interval is completely within the equivalence 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.

Histogram

A histogram divides sample values into many intervals and represents the frequency of data values in each interval with a bar.

Interpretation

Use histograms to assess the shape and spread of the data. Histograms are best when the sample size is greater than 20.

Skewed data

Determine whether your data appear to be skewed.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.

Right-skewed
Left-skewed

For example, the right-skewed histogram shows salary data. Many employees are paid a relatively small amount, while increasingly few employees are paid large salaries. The left-skewed histogram shows failure rate data. A few items fail earlier while an increasing number of items fail later.

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

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.

On a histogram, isolated bars at the ends suggest possible outliers.

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.

Subject profile plot

Shows the response to the reference treatment and the test treatment for each participant in the study.

Interpretation

Use the subject profile plot to examine the responses of each participant to the test treatment and the reference treatment.

Verify that the overall pattern is consistent with the equivalence test results. Identify any subjects whose response is markedly inconsistent with the other responses, which could affect the overall results.

This subject profile plot shows that most study participants responded similarly to the test treatment and the reference treatment. Neither treatment seems to be consistently associated with a higher or lower response. The results on the plot agree with the test results (not shown), which indicate that the two treatments are equivalent. In addition, no single response differs greatly from the other responses.

Boxplot

The boxplot provides a graphical summary of the distribution of the paired differences that shows their variability and central tendency.

Interpretation

Use a boxplot to examine the spread of the data and identify any potential outliers. Boxplots are best when the sample size is greater than 20.

Skewed data

Determine whether your data appear to be skewed.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.

Right-skewed
Left-skewed

For example, the right-skewed boxplot shows salary data. Many employees are paid a relatively small amount, while increasingly few employees are paid large salaries. The left-skewed boxplot shows failure rate data. A few items fail earlier while an increasing number of items fail later.

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

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.

On a boxplot, outliers are identified by asterisks (*).

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.

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