Using graphs to understand the results of a hypothesis test

When you perform a hypothesis test in Minitab, you can choose to display an individual value plot, a boxplot, and a histogram with your results. These and other graphs can help you summarize your results and more fully interpret the statistical results of a hypothesis test.


The scales used for a graph can dramatically affect how the results look. Therefore, when possible, use the calculated numeric results in the output to confirm what the graphs show.

Examining test results and confidence intervals

You can use a graph to illustrate the results of the hypothesis test.

The plot illustrates the difference in means for the two samples, A and B. Using a 2-sample t-test, this difference was found to be statistically significant.

Examining measures of center

You can use a graph to show the center of the data, such as the mean and median.

The line in the middle of the boxplot shows the median of the data. The point in the middle of the interval bar shows the mean.

Multi-modal distribution

Sometimes a set of data may have more than one cluster of data and thus more than one central value. To identify and show these multi-modal distributions, use an individual value plot, histogram, or dotplot. Data that has a multi-modal distribution can indicate that the data represent two different populations. Consider performing a separate analysis on each population.

The two peaks in this histogram show that there are two centers in the data.


A boxplot cannot show a multi-modal distribution because there are two centers in the data.

Examining the spread of the data

Use graphs to show the show the range of the data and to see how far the data are from their center. If the data have a large spread, their variability may make the estimate of the central value less precise.

Histograms, boxplots, and individual value plots can help you easily see the spread in your data. To evaluate the spread more, boxplots display quartiles that let you easily estimate the interquartile ranges.

The range of the data is from approximately 62 to 98. Approximately 50% of the data lies between 71 and 84, which is the region defined by the colored region of the box.

You can also use graphs to explore data and assess the validity of statistical assumptions for the test.

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