Below are resuits of two studies, each using box plots to compare three groups.

Question

Below are resuits of two studies, each using box plots to compare three groups. E based on a random sample of size 40. Use the information to answer the questions that follow Each box plot is 1. Judging from the box plots, which study will more likely lead to a rejection of the ANDOVA null hypothesis of equal population mean? Explain. 2. Which study will have the large value for the F test statistic? Why? 3. Assuming the P-value for the ANOVA F test for the second study equals 0.001. Does this necessarily imply that all three population means are different from each other. If not, what does it imply? ? ?? ympodium

Explanation / Answer

1.) Second study is more likely to reject the NULL hypotheses. Reason being if we consider the range of data for all 3 groups, its clearly visible that they all 3 groups have different range.

Also if we consider the data between 1st and 3rd quartile, it's clearly visible that all the groups have different range for points in these quartiles.

In first study, the data between 1st and 3rd quartile, it's clearly visible that all the groups have almost same range for points in these quartiles. Since box plot shows that most data is always between these quartiles, so the mean for all these groups look similar. Although this study has more variablity which can affect the mean but there will be very few points which will be out of 1st and 3 quartile. So impact will be less.

Hence, i think 2nd study has more chance to reject Null Hypotheses.

2.) The second study will have have mpre F value.

Since we are checking for equal population mean and study 2 is more likely to difference in population mean, hence it will be having large F value. Corresponding p-value willl become less indicating that we can reject Null Hypothese with a certain level of confidence,

3.) p = 0.001 signifires that we can reject NULL Hypotheses with 99.999% of confidence.

This means that we are 99.999% sure that popuktion mean of 3 groups is not similar.

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