Discuss Mean, variance, and Z scores

Discussion: Mean, variance, and Z scores

The table below shows ratings of various aspects of work and home life of 100 middle-class men in India who were fathers. Pick three rows of interest to you and explain the results to someone who is familiar with the mean, variance, and Z scores, but knows nothing else about statistics.

Comparison of Fathers’ Mean Psychological States in the Job and Home Spheres (N = 100)
Sphere
Scale Range Work Home Work vs. home
Important 0-9 5.98 5.06 6.86***
Attention 0-9 6.15 5.13 7.96***
Challenge 0-9 4.11 2.41 11.49***
Choice 0-9 4.28 4.74 -3.38***
Wish doing else 0-9 1.5 1.44 0.61
Hurried 0-3 1.8 1.39 3.21**
Social Anxiety 0-3 0.81 0.64 3.17**
Affect 1-7 4.84 4.98 -2.64**
Social Climate 1-7 5.64 5.95 4.17***
Note: Values for column 3 are t scores; df = 90 for all t tests.
**p < .01 ***p < .001 They give you the location of a score in a distribution of scores in relation to themean in standard deviation units. — The mean of a set of Z–scores is always 0. — The standard deviation (and variance) of a set of Z–scores is always 1. … (This is themean squared difference from the mean or variance.) A Z–score is a numerical measurement used in statistics of a value’s relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. If a Z–score is 0, it indicates that the data point’s score is identical to the mean score.