Social Statistics: Difference

# Social Statistics: Difference

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## Social Statistics: Difference

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1. Social Statistics: Difference

2. Review • Social statistics • Descriptive statistics • Inferential statistics • Mean, median and mode S519

3. Outline • Range • Standard deviation • Variance • Using Excel and SPSS to calculate them S519

4. The whole story • Descriptive statistics • Centrality tendency (average) • Measurement of variability (variability) • Average+Variability = describe the characteristics of a set of data S519

5. 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 S519

6. Measures of variability • Three ways • Range • Standard deviation • Variance S519

7. 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 S519

8. Standard deviation • Standard deviation (SD) • Average deviation from the mean (average distance from the mean) • Represents the average amount of variability S519

9. Exercise • Calculate standard deviation • 5, 8, 5, 4, 6, 7, 8, 8, 3, 6 • By hand • Using excel (STDEV()) S519

10. 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 S519

11. STDEV and STDEVP STDEV STDEVP S519

12. 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 S519

13. Why n or n-1? S519

14. 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. S519

15. Variance • Variance = (Standard Deviation)^2 S519

16. Exercise • Calculate variance in Excel • 8, 8, 8, 7, 6, 6, 5, 5, 4, 3 • Var()  STDEV • Varp()  STDEVP S519

17. SD vs. variance • Often appears in the “Results” sections of journals • They are quite different • Variance is squared SD S519

18. 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 S519

19. Exercise 1 (S-p78-problem2) • 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. S519

20. Exercise 2 (S-p79-problem4) • Problem 4 in S-p79 • Calculate the variation measures for height and weight S519

21. Exercise 3 (S-p79-problem5) • Look at problem 5 • Write a half page summary report to your boss • Form a group to discuss it S519