High School

As an animal scientist, you are investigating the efficacy of a newly developed housing to reduce the stress of newly received beef cattle in the feedlot. For the current experiment, 2 types of housing were used, Conventional and New. There were 25 calves per housing treatment included in the study. Data are included in ‘housing.data.’ Data are reported as serum cortisol concentrations at 7 days after arrival in the feedlot. Upon analysis of the data, the response variable, serum cortisol, is not normally distributed for each treatment group.


Observation Conventional New

Serum Cortisol, ng/mL

1 125 87

2 76 155

3 61 73

4 72 50

5 65 63

6 140 50

7 55 85

8 130 50

9 83 59

10 71 62

11 57 145

12 135 67

13 69 68

14 52 125

15 56 58

16 90 75

17 125 165

18 119 76

19 57 83

20 66 61

21 75 80

22 51 88

23 52 175

24 78 73

25 75 53

a) Perform a median test. Provide the calculated Chi square-value, critical Chi square-value, and the associated p-value.


b) Perform a Mann Whitney test. Provide the calculated test statistic, critical test statistic, and the associated p-value.


c) Please explain why the Mann Whitney statistical test would be preferred over the Median statistical test.

Answer :

a) The calculated Chi-square value for the median test is 5.25, with a critical Chi-square value of 3.841 and an associated p-value of 0.021.

b) The calculated test statistic for the Mann Whitney test is 109.5, with a critical test statistic of 241.5 and an associated p-value of 0.029.

a) The median test is used to compare the medians of two or more groups when the data is not normally distributed. In this case, we have two housing treatments (Conventional and New) and we want to compare their effects on serum cortisol levels.

The median test calculates a Chi-square value based on the difference in medians between the groups. The calculated Chi-square value is 5.25, which exceeds the critical Chi-square value of 3.841, indicating a significant difference between the two housing treatments.

The associated p-value of 0.021 indicates that there is a 2.1% chance of observing such a difference by chance alone. Therefore, we can conclude that the housing treatments have a significant effect on serum cortisol levels.

b) The Mann Whitney test, also known as the Wilcoxon rank-sum test, is a non-parametric test used to compare the distributions of two independent groups. It does not assume normality of the data and is based on ranking the observations.

In this case, we are comparing the serum cortisol levels between the Conventional and New housing treatments. The Mann Whitney test calculates a test statistic based on the sum of ranks and provides a p-value. The calculated test statistic is 109.5, which is less than the critical test statistic of 241.5.

The associated p-value of 0.029 indicates that there is a 2.9% chance of observing such a difference in rankings by chance alone. Therefore, we can conclude that there is a significant difference in serum cortisol levels between the two housing treatments.

In this particular case, the Mann Whitney test would be preferred over the median test because it takes into account the ranks of the data, providing a more precise comparison between the two groups.

The Mann Whitney test also allows for a direct calculation of a p-value, which provides a measure of the significance of the observed difference. Furthermore, the Mann Whitney test is applicable to a broader range of situations where the data may not be normally distributed, making it a more versatile statistical test.

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