Bonferroni Test Shown below are weights (kg) of poplar trees o...

Question

Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data.

a. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight.

c. Use the Bonferroni test procedure with a 0.05 significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and either the P-value or critical values. What do the results indicate?

Table showing Bonferroni test results comparing treatments with mean differences, standard errors, significance, and confidence intervals.

Accepted Answer

Hello. In this video we are told that researchers studied the heights of sunflowers grown under 4 different light conditions natural light, artificial light, mixed light, and no light. They wish to perform pairwise comparisons of the mean heights between all the like conditions using the Bonfroni correction at a 0.05 significance level. The partial results show the test statistics for the comparison between natural light and mixed group lights is T is equal to 2.85 with a p value of 0.007. There are 4 groups in total. What is the Bonfroni adjustment or adjusted significance level for this comparison, and what do the results indicate? So the the Bonferoni correction is used when multiple comparisons are made to reduce the risk of Type one errors, and the adjusted significance level is calculated by dividing the original significance level by the comparison or by the number of comparisons, so. The adjustment. Is defined as our original significance level divided by the number of comparisons. Now, in this video, or in this problem here, we are given that there are 4 groups, and the number of pairwise comparisons is going to be 4 choose 2, which is equal to 6. So what this means is that for our adjusted significance level. We are going to divide the original significance level 0.05 by 6, and with the help of a calculator, this is going to give us a Bonfroni adjusted significance level of 0.00833. So this is going to be the adjusted significance level. Now what we want to do is we want to go ahead and compare this with the P value. Now the P value given to us is 0.007. And if we were going to compare this to the adjusted significance level, this value is less than the adjusted significance level. So what does this tell us? Well, what this tells us is that we are going to reject the null hype hypothesis, and the interpretation is that the results indicate that the mean height of the sunflowers under natural light is significantly different from the mean height of sunflowers under mixed light after adjusting for multiple comparisons. So the correct solution to this problem is going to be option A. So I hope this video helps you in understanding on how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Bonferroni Test

Test Statistic and P-value

Confidence Intervals in Multiple Comparisons

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