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Home Store JC Whitney. Submit JC Whitney Coupon. Submit a new coupon and help others save! Store Website. Select an Offer Type Online Code. Side-by-side boxplots are provided by ggplot2. The boxplots below seem to indicate one outlier in each treatment group. This indicates that the data is highly skewed by the effects of the outlier s. Prior to performing the Mann-Whitney U, it is important to evaluate our assumptions to ensure that we are performing an appropriate and reliable comparison.

If normality is present, an independent samples t-test would be a more appropriate test. Many times, histograms can also be helpful. However, this data set is so small that histograms did not add value. In this example, we will use the shapiro. However, for spray D, a small deviation from normality can be observed which supports our Shapiro-Wilk normality test conclusion. So far, we have determined that the data for each treatment group is not normally distributed, and we have major influential outliers.

As a result, a Mann-Whitney U test would be more appropriate than an independent samples t-test to test for significant differences between treatment groups. Our next step is to officially perform a Mann-Whitney U test to determine which bug spray is more effective.

We have concluded that the number of bugs in each treatment group is not normally distributed. In addition, outliers exist in each group. As a result, a Mann-Whitney U test is more appropriate than a traditional independent samples t-test to compare the effectiveness of two separate insecticide treatments.

This indicates that we should reject the null hypothesis that distributions are equal and conclude that there is a significant difference in insecticide effectiveness.

Descriptive statistics indicate that the median value for spray C is 1. That is to say, the difference between the median values of each treatment is about 3. The Hodges-Lehmann estimate more precisely indicates that we can expect a median of about 3 more bugs will survive when spray D is used instead of spray C.