Chapter 11 Multiple choice questions

. Download the data file for the multiple-choice questions for Chapter 11 , and open it in R. Conduct a one-sample Hotelling's T² test on the data stored in the matrix xydata, comparing to the point x = 0, y = 0. What is the T² statistic and p-value?

T² = 8.51, p = 0.6

T² = 17.62, p = 0.001

T² = 0.23, p = 0.002

T² = 6.89, p = 0.001

. Repeat the test from the previous question, but this time comparing to the point x = 0.5, y = 0. How does the outcome change?

The previously significant test is no longer significant

The previously non-significant test is now significant

There is no change in the outcome because both tests were non-significant

There is no change in the outcome because both tests were significant

. Use the mahalanobis function to calculate the Mahalanobis distance (D) for the data in xydata, comparing it to x=0, y=0 and also to x=0.5, y=0. What are the two effect sizes?

0.59 and 0.18

0.59 and 0.43

0.77 and 0.43

0.77 and 0.18

. To check for outliers, you can also calculate the Mahalanobis distance for each pair of points in the data set, comparing to the group mean. What is the largest Mahalanobis distance (D)?

2.37

2.22

4.93

5.62

. Run the condition index test on the data in xydata. Are the conditions for T²_circ met, and what outcome leads you to that conclusion?

No, because the condition index test is significant

No, because the condition index test is non-significant

Yes, because the condition index test is significant

Yes, because the condition index test is non-significant

. The data frames stimulusabsent and stimuluspresent contain data from a human SSVEP experiment similar to that described in Figure 11.4. Conduct a paired Hotelling's T² test on these data. What is the outcome?

F(2,48) = 4.37, p = 0.02

F(2,47) = 4.21, p = 0.02

F(2,96) = 4.22, p = 0.02

F(2,23) = 4.43, p = 0.02

. Are we justified in conducting a T²_circ test instead?

No, because condition index tests for both data sets are significant

Yes, because condition index tests for both data sets are non-significant

Yes, because condition index tests for both data sets are significant

No, because the condition index test for the stimulus present condition is significant

. What is the pairwise Mahalanobis distance between the two condition means, assuming repeated measures (paired) data?

0.37

0.61

0.83

0.91

. What is the pairwise Mahalanobis distance between the two condition means, assuming independent samples?

0.37

0.61

0.83

0.91

. Do any data points in the stimuluspresent matrix exceed a Mahalanobis distance of 3, identifying them as possible outliers?

No, all data points are within a distance of 3

Yes, one data point exceeds the distance

Yes, two data points exceed the distance

Yes, several data points exceed the distance

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