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Measures of Dispersion

Measures of Dispersion. CJ 526 Statistical Analysis in Criminal Justice. Introduction. Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together

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Measures of Dispersion

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  1. Measures of Dispersion CJ 526 Statistical Analysis in Criminal Justice

  2. Introduction Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together All measurements vary. If there were no variation, one unit could be measured, and there would be no need for other measurement or statistics

  3. Six Measures of Variability • Variation Ratio • Range • Interquartile Range • Variance • Standard Deviation • Coefficient of Variation

  4. 2. Range Distance between the largest and smallest scores Not very stable—depends on only two scores

  5. 3. Interquartile Range The distance between the first quartile and third quartile The score at the 75th percentile minus the score at the 25th percentile 50% of the scores fall in this range, 25% above this range and 25% below this range

  6. 4. Variance Based on mean squared deviations Deviation = mean minus the score Sum the deviations Squared to eliminate the negative sign

  7. Population and SampleVariance • Population variance represented by sigma squared: 2 • Sample variance represented by: s2

  8. 5. Standard Deviation Standard deviation is the square root of variance More easily interpreted than the variance, more meaningful Standard deviation for a sample represented by the symbol SD

  9. 6. Coefficient of Variation • Used to compare SD’s of variables that have different units of measurement (different units of measurement: Height—inches, ACT, 1-36, etc.

  10. Interpretation of SD • SD used with the mean, must be interval level • Add and subtract SD from the Mean • i.e., if the Mean is 10 and the SD is 2, add it to the mean (12) and subtract it from the mean (8) • If the mean is 10 and the SD is 2, the majority of the scores fall in the range between 8 and 12 • If the SD is 4, most of the scores are between 6 and 14

  11. Interpretation of SD • Generally speaking, the larger the SD, the more variability in that sample for that variable • The smaller the SD, the less variability • If one sample had a SD of 2 and another of 4, for a particular variable, the one with an SD of 2 had less variability

  12. Interpretation of SD • A particular variable can be compared from sample to sample in terms of variability • However, if the variables are on different scales, samples cannot be compared in terms of variability using SD (z scores would be needed, which will be covered later) • Example: the SAT has a SD of 100, IQ has an SD of 15. Variability cannot be compared, as they are different scales

  13. Report Writing - Text • Children who viewed the violent cartoon displayed more aggressive responses (M = 12.45, SD = 3.7) than those who viewed the control cartoon (M = 4.22, SD = 1.04).

  14. SPSS Frequencies Procedure • Frequencies • Statistics • Central tendency • Mean • Median • Mode

  15. SPSS Frequencies Procedure -- continued • Dispersion • Standard Deviation • Variance • Range • Minimum • Maximum • Standard Error of the Mean

  16. SPSS Descriptives Procedure • Descriptives • Minimum • Maximum • Mean • Standard Deviation

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