Calculate bonferroni confidence intervals, Basic Statistics

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The "recoverytime" files record the time (in days) for male blue-collar workers to recover from a common wrist fracture. Each man was given a questionnaire to complete to determine his mental state (whether optimistic or pessimistic) and his physical state (very physically fit, average, or poor condition) at the time of the injury.

The tabular format of the data can be found in the recoverytime.mtp file, while the recoverytime.mtw file restructures the data into three columns, one for the recovery times, the second to indicate the physical condition of the worker, and the third to indicate his mental state. You should know how to convert the tabular format to the 3 column format required by Minitab. (You would start by stacking the two columns of data into a new column called "times", using another column to record the "subscripts" using the names of the original two columns. Finally extend the column for the physical condition to cover all the "times" observations.)

All tests should be done using the .05 level of significance.

(a) Use Minitab to plot the treatment means in an interactions plot. What do you observe about the possibility of interaction, or the possibility of main effects?

(b) Show manually how the MSE can be calculated by pooling the sample variances from the six treatment combinations. Explain why the MSE has 54 degrees of freedom.

(c) Plot the residuals against the fitted values. What key model assumptions can be examined and do these appear to be warranted?

(d) Test for interaction between the physical and mental factors.

(e) Does physical condition affect the average recovery times? Test whether there is a main effect due to physical condition.

(f) Do pessimists and optimists differ in their average recovery times? Test whether there is a main effect due to mental condition.

(g) Calculate Bonferroni confidence intervals to examine all pairwise differences among the K=3 levels of the physical condition. Use an overall 95% confidence level for all the intervals. What do you conclude?

All Bonferroni pairwise comparisons follow the following formula:

Observed difference in means ± t(α/(2J)) * √[MSE*(1/m + 1/m)] where

J is the number of pairwise comparisons, t(α/(2J)) is the critical value (with tail probability α/(2J) from the t distribution based on the number of degrees of freedom in the MSE, and the divisor m is the number of observations that comprises each physical condition mean being compared.


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