Descriptive Statistics


An overall measure of performance was computed by computed by summing scores over three test problems. Descriptive statistics for the HAL and 1-2-3 conditions are shown below.

Descriptive Statistics for Performance Scores
Boxplots for Performance Scores

The descriptive statistics above show that
The HAL group performed higher overall and had more spread than the 1-2-3 group
The HAL group scored lower overall and had less spread than the 1-2-3 group
The HAL group scored higher overall and had less spread than the 1-2-3 group
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The following scatterplots show the relationship between the performance scores and the Wonderlic test scores.
HAL
1-2-3

The relationship between Wonderlic scores and Performance scores
is clearly nonlinear
appears to be approximately linear
is negligible
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Pearson's correlations for the HAL and 1-2-3 groups are 0.443 and 0.447 respectively.

Descriptive Statistics for the Wonderlic Test Scores


These data indicate that
Group differences in Performance scores were due mostly to differences in Wonderlic scores
Group differences in Performance scores occurred in spite of differences in Wonderlic scores
Group differences in Performance scores account partially for differences in Wonderlic scores
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The purpose of including the Wonderlic test was to control for individual differences in cognitive ability. To obtain scores controlling or adjusting for Wonderlic scores, find the residuals for a model in which the performance scores are predicted by Group and Wonderlic. Since the residuals for each group will always have means of 0.0, they cannot be used to compare groups. To compare groups, it is necessary to compute the least squares means (sometimes called adjusted means) and add the least squares mean of the HAL group to the score of each subject in the HAL group and add the least squares mean of the 1-2-3 group to the score of each subject in the 1-2-3 group. The resulting scores represent performance controlling for Wonderlic.



Descriptive Statistics for Adjusted Performance Scores
Boxplots for Adjusted Performance Scores

Controlling for Wonderlic scores
Reduced the within-group variation
Increased the differences between group means
Reduced the number of outliers
All of the above
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