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Introductory Psychology: Statistics

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lecture 2 from a college level introduction to psychology course taught Fall 2011 by Brian J. Piper, Ph.D. ([email protected]) at Willamette University, crash course in descriptive and inferential statistics, includes scatterplots, correlation, mean, SD/SEM, effect size

Text of Introductory Psychology: Statistics

  • 1. StatisticsBrian J. Piper, Ph.D.

2. Mark Twain (?) There are three types of lies, lies, damn lies, and statistics.http://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics 3. Goals Levels of measurement Group comparisons (t) Association (scatterplot/r) Effect-size (d) 4. ) Levels of Measurement Nominal: categorical, example: sex Ratio: quantitative, example: age Ordinal: ranking, example: self-report Strongly disagree = 1 Disagree = 2 Neutral = 3 Agree = 4 Strongly agree = 5 S.D.-------------------------------------------------------------------------------------------S.A. 5. What do these countries have in common? Liberia Burma United States 6. Metric SystemUnit Symbol Factortera T1 x 1012giga G1 x 109kilo K1 x 103----- 1centic1 x 10-2millim1 x 10-3micro1 x 10-6 7. DataSexHeight Weight SexHeight Weight (m)(kg)(m)(kg)Female 2.060 Male 2.580Female 1.958 Male 2.376Female 1.856 Male 2.174Female 1.754 Male 2.073Female 1.652 Male 1.872Female 1.550 Male 1.770Female 1.448 Male 1.668Female 1.346 Male 1.565Female 1.657 Male 250 8. Sex Height Weight Sex Height Weight(m)(kg) (m)(kg)Female2.060 Male2.580Female1.958 Male2.376Female1.856 Male2.174Female1.754 Male2.073Female1.652 Male1.872Female1.550 Male1.770Female1.448 Male1.668Female1.346 Male1.565Female1.657 Male250 Average1.64 53.4 1.94 69.8Mean (or average) = Sum (X) /N where N is the # of scores 9. Variability Variability: how much scores differ, onaverage, from mean Variance = Sum (X Mean)2 /N Standard Deviation (SD) = Variance Standard Error of Mean (SEM) = SD / N 10. Group Comparisons I Are women lighter then men? P = probability valueif p < .05 therefore statistically significant t test = (MeanMales - MeanFemales) / SEM t = 4.97, p = .0001908070 WEIGHT6050SEX_ female40 male9876543210123456789 CountCount 11. Group Comparisons II Do men have a higher IQ then women? T is the measure of variability (e.g. S.E.M.) A. Sample Size = 40 B. Sample Size = 4,000 C. Sample Size = 4,000 ( * p < .05). 125 125105 100 100100 7575*IQIQ IQ 505095 25250 0 90Men (N = 20) Women (N=20)Men (N = 2000) Women (N=2000) Men (N = 2000) Women (N=2000)A finding with a * refers to a statistically significant finding, e.g. men > women 12. Error Bars Example 2Batterham et al. New England Journal of Medicine, 349, 941-948. 13. Scatterplots 6490 6080 WEIGHT_MALEOutlier? ->WEIGHT_F 5670 5260 4850 Outlier? -> 44401.3 1.4 1.51.6 1.7 1.8 1.9 2.01.4 1.6 1.8 2.0 2.2 2.4 2.6HEIGHT_FHEIGHT_M 14. Study Hours Score Positive3 80Association5 902 756 807 901 502 657 851 407 100 15. Negative AssociationVariable B Variable A 16. 3.1Standardized Z Scores Z is a # Z = 0 therefore average Z > 0 therefore above average Z < 0 therefore below average Z = (X Mean) / SD Z = (600 500) / 100= 1.0 17. B C A3.6 r = Sum(Zx * Zy)/ N D E r: quantifies relationship between two variables (e.g. x & y) No association: r = 0.00 (C) Positive association: r > 0.00 (A B) Negative association: r < 0.00 (DE) Strong association: A E, Weak association: B D 18. ProbabilityEyesEyesProbability Frequency BlueBrownBlueBrown.000002 .000010 + 2 10 +BrainCancer.999998 .99999 - 999,998 999,990- 19. 3.2 Risk Absolute Risk: Rate of condition/totalpopulation studied, e.g. .000002 or .000010 .0002% or .0010% Relative Risk: Rate of condition among groupA divided by rate of condition among group B .000010 = 5.0 ________.0000002 20. 4.3Effect-Size Procedure used to summarize the magnitudeof group differences. Cohens d = (MeanA MeanB) / SD d = 0.20 small effect size d = 0.50 medium effect size d = 0.80 large effect sizeCan be averaged for multiple studies (meta-analysis). 21. SummaryGoalIntuitionTestDifference in Bar Graphs with t-testmeans SEMRelationship betweenvariables (ratio x ratio)ScatterplotCorrelation rSummarize Read papersEffect sizemany studies Cohens d