Discussion: Mean variance and Z scores Discussion: Mean variance and Z scores
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Discussion: Mean variance and Z scores
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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.
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