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S519: Evaluation of Information Systems

This week's evaluation focuses on measuring the difference in social statistics using range and standard deviation, and how to calculate them using Excel. Explore descriptive statistics, centrality tendency, and variability to describe data characteristics.

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S519: Evaluation of Information Systems

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  1. S519: Evaluation of Information Systems Social Statistics Ch3: Difference

  2. This week • Range • Standard deviation • Variance • Using Excel to calculate them

  3. The whole story • Descriptive statistics • Centrality tendency (average) • Measurement of variability (variability) • Average+Variability = describe the characteristics of a set of data

  4. Measures of variability • Variability • How scores differ from one another • Three sets of data • 7, 6, 3, 3, 1 • 3, 4, 4, 5, 4 • 4, 4, 4, 4, 4 • Variability = the difference from the mean

  5. Measures of variability • Three ways • Range • Standard deviation • Variance

  6. Range • The most general measure of variability • How far apart scores are from one another Range = highest score – lowest score What is the range for 98, 86, 77, 56, 48

  7. Standard deviation • Standard deviation (SD) • Average deviation from the mean (average distance from the mean) • Represents the average amount of variability

  8. Exercise Lab • Calculate standard deviation • 5, 8, 5, 4, 6, 7, 8, 8, 3, 6 • By hand • Using excel (STDEV())

  9. STDEV and STDEVP • STDEV is standard deviation for sample (biased SD) • STDEVP is standard deviation for population (unbiased SD) • If your dataset is the whole population, use STDEVP to calculate standard deviation • If you dataset is the sample of something, use STDEV to calculate standard deviation

  10. STDEV and STDEVP STDEV STDEVP

  11. Why n or n-1? • To be conservative • STDEV • This is the standard deviation for sample • Take n-1 in order to make STDEV a bit larger than it would be. • If we have err, we compensate by overestimating the STDEV

  12. Why n or n-1?

  13. What to remember • Standard Deviation (SD) = the average distance from the mean • The larger SD, the more different data are from one another • Since mean is sensitive to extreme scores, so do SD • If SD=0, this means that there is no variability in the set of scores (they are all identical in value) – this happens very rarely.

  14. Variance • Variance = (Standard Deviation)^2

  15. Exercise Lab • Calculate variance in Excel • 8, 8, 8, 7, 6, 6, 5, 5, 4, 3 • Var()  STDEV • Varp()  STDEVP

  16. SD vs. variance • Often appears in the “Results” sections of journals • They are quite different • Variance is squared SD

  17. SD vs. variance mean Average distance to mean=(2+2+2+1+1+1+2+3)/10=1.4 SD = 1.76 Variance = 3.1

  18. Exercise 1 (S-p78-problem2) Lab • Calculate range, STDEV and STDEVP and variance by hand or calculator • 31, 42, 35, 55, 54, 34, 25, 44, 35 • Use Excel to do that.

  19. Exercise 2 (S-p79-problem4) Lab • Problem 4 in S-p79 • Calculate the variation measures for height and weight

  20. Exercise 3 (S-p79-problem5) Lab

  21. Exercise 3 (S-p79-problem5) Lab • Look at problem 5 • Write a half page summary report to your boss • Form a group to discuss it

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