1. Postgraduate Course Evidence-Based Management (Some) statistics for managers who hate statistics

2. Postgraduate Course Why do we need statistics? 1.How does my population look like? 2.Is there a difference? 3.Is there a model that ‘fits’?

3. Postgraduate Course Some statistics Some statistic terms 1.Sample vs population 2.Variables 3.Levels of measurement 4.Central tendency 5.Hypothesis Some statistic models 6.Mean 7.Variance, standard deviation 8.Confidence intervals 9.Statistical significance 10.Statistical power 11.Effect sizes 12.Critical appraisal

4. Postgraduate Course 1. Sample vs population

5. Postgraduate Course Sample vs population We want to know about these (population: N) We have to work with these (sample: n) population mean: μ selection sample mean: X _ statistics fit?

6. Postgraduate Course Law of large numbers The larger the sample size (or the number of observations), the more accurate the predictions of the characteristics of the whole population, and smaller the expected deviation in comparisons of outcomes. As a general principle it means that, in the long run, the average (mean) of a large number of observations will be close to (or: may be taken as the best estimate of) the 'true mean’ of the population. Sample vs population

7. Postgraduate Course Sample size: why does it matter?  Law of the large numbers: a reliable and accurate representation of the population  Statistical power: to prevent a type 2 error / false negative Sample vs population

8. Don’t confuse: representativeness and reliability The sample size has no direct relationship with representativeness; even a large random sample can be insufficiently representative. Postgraduate Course Sample vs population

9. Postgraduate Course 2. Variables Postgraduate Course

10. Variables Variable: anything that can be measured and can differ across entities or time Independent variable: predictor variable (value does not depend on any other variables) Dependent variable: outcome variable (value depends on other variables)

11. Postgraduate Course 3. Level of measurement Postgraduate Course

12. Level of measurement Postgraduate Course Relationship between what is being measured and the numbers that represent what is being measured.

13. Postgraduate Course Categorical Continuous NominalOrdinalIntervalRatio Level of measurement

14. Postgraduate Course Nominal scale Classification of categorical data. There is no order to the values, they are just given a name (‘nomen’) or a number. The numbers can’t be used to calculate … (you can’t calculate the mean of fruit).. only frequencies 1 = Apples 2 = Oranges 3 = Pineapples 4 = Banana’s 5 = Pears 6 = Mango’s

15. Postgraduate Course Ordinal scale Classification of categorical data. Values can be rank-ordered, but the distance between the values have no meaning. The numbers can only be used to calculate a modus or a median 1.Full Professor 2.Associate professor 3.Assistant professor 4.PhD 5.Master 6.Bachelor

16. Postgraduate Course Interval scale Classification of continuous data. Values can be rank-ordered, and the distance between the values have meaning. However, there is no natural zero point 1.John (1932) 2.Denise(1945) 3.Mary(1952 4.Marc(1964) 5.Jeffrey(1978) 6.Sarah(1982)

17. Postgraduate Course Ratio scale Classification of continuous data. Values can be rank-ordered, the distance between the values have meaning and there is a natural zero point. 1.Jeffrey (192 cm) 2.John (187 cm) 3.Sarah(180 cm 4.Marc(179 cm) 5.Mary(171 cm) 6.Denise(165 cm)

18. Postgraduate Course NominalOrdinalIntervalRatio ClassificationYes Rank-orderNoYes Fixed and equal intervalsNo Yes Natural 0 pointNo Yes NominalOrdinalIntervalRatio ModeYes MedianNoYes MeanNo Yes Levels of measurement CategoricalContinuous

19. Postgraduate Course Levels of measurement Ordinal or interval? Can I calculate a mean? Q3: Every organization is unique, hence the findings from scientific research are not applicable. Strongly agree ☐ Strongly agree Somewhat agree ☐ Somewhat agree Neither agree or disagree ☐ Neither agree or disagree Somewhat disagree ☐ Somewhat disagree Strongly disagree ☐ Strongly disagree

20. Postgraduate Course 4. Central tendency The aim is to find a single number that characterises the typical value of the variable in the sample. Which one you use depends in part on the level of measurement of the variable.

21. Postgraduate Course Central tendency Central tendency of a set of data / numbers (what number is most representative of the dataset / population?) 7, 9, 9, 9, 10, 11,11, 13, 13  Mean = 10,2  Median= 10  Mode = 9

22. Postgraduate Course Central tendency Central tendency of a set of data / numbers (what number is most representative of the dataset / population?) 3, 3, 3, 3, 3, 3, 100  Mean= 16,9  Median= 3  Mode = 3

23. Postgraduate Course 5. Hypothesis

24. Postgraduate Course “It is easy to obtain evidence in favor of virtually any theory, but such ‘corroboration’ should count scientifically only if it is the positive result of a genuinely ‘risky’ prediction, which might conceivably have been false. … A theory is scientific only if it is refutable by a conceivable event. Every genuine test of a scientific theory, then, is logically an of a scientific theory, then, is logically an attempt to refute or to falsify it.” Hypothesis: falsifiability Carl Popper

25. Postgraduate Course Hypothesis  Null hypothesis (H0): Big Brother contestants and members of the public will not differ in their scores on personality disorder questionnaires  Alternative hypothesis (H1): Big Brother contestants will score higher on personality disorder questionnaires than members of the public.

26. Postgraduate Course Hypothesis: type I vs type II error null hypothesis is true & was rejected (type I error) α null hypothesis is false & was rejected (correct conclusion) null hypothesis is true & was accepted (correct conclusion) null hypothesis is false & was accepted (type II error) β H0 is true H0 is false reject H0 accept H0

27. Postgraduate Course Statistic models

28. Postgraduate Course Statistic models: prediction likely not likely

29. Postgraduate Course 6. The mean The most widely used statistic model μ X_or samplepopulation

30. Postgraduate Course The mean EBMgt Lecturer Number of Friends

31. Postgraduate Course The mean Assessing the fit of the mean  Sum of squared errors (SS): (- 1,6) + (-0,6) + (0,4) + (0,4) + (1,4) = 5,2  Variance (s ): = = 1,3  Standard deviation (s): √s = 1,14 2 2 2 2 2 2 SS N-1 5,2 4 2

32. Postgraduate Course The second most widely used statistic model σ s or sample population 7. Standard Deviation

33. Postgraduate Course Standard Deviation

34. Postgraduate Course 110 IQ Postgraduate Course Standard Deviation Which class would you prefer to teach? 130 170

35. Postgraduate Course 110130 IQ S=10 S=20 S=60 170 Postgraduate Course Standard Deviation

36. Postgraduate Course Standard Deviation

37. Postgraduate Course So, what does “two standard deviations of the mean” mean? Standard Deviation

38. Postgraduate Course 8. Confidence intervals Postgraduate Course

39. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter (e.g. the mean). Confidence intervals are usually calculated so that this percentage is 95% (95% CI) Confidence intervals

40. Postgraduate Course When you see a 95% confidence interval for a mean, think of it like this: if we’d collected 100 samples and calculated the mean for each sample, than for 95 of these samples the mean would fall within the confidence interval. Confidence intervals

41. Postgraduate Course 1,96! Confidence intervals

42. Postgraduate Course Confidence intervals

43. Postgraduate Course 2008 2009 4,5 4,0 3,5 5,0 3,0 “According to the federal government, the unemployment rate has dropped from 4.3% to 3.8%.” 95% CI= 4,1 - 3,5. This means the unemployment rate could have increased from 4.0 to 4,1 ! Confidence intervals

44. Postgraduate Course When a point estimate (e.g. mean, percentage) is given, always check:  standard deviation or  confidence interval Confidence intervals

45. Postgraduate Course 9. Statistical significance

46. Postgraduate Course Statistical significance Sir Ronald A. Fisher 1890 - 1962

47. Significant = the probability of incorrectly rejecting the null hypothesis (= Type I error, α) p = 0,05 / p = 0,01 Postgraduate Course Statistical significance (1 in 20 / 1 in 100)

48. Postgraduate Course Statistical significance

49. 110130 Postgraduate Course 1.Is there a difference / an effect? 2.How certain is it that the difference / effect found is not a chance finding? X _ 0 X _ 1 Statistical significance

50. Testing multiple hypothesis When you test 20 different hypotheses (or independent variables), there is a high chance that at least one will be statistically significant. example: Does apples, bacon, cheese, eggs, fish, garlic, hazelnuts, ice cream, ketchup, lamb, melons, nuts, oranges, peanut butter, roasted food, salt, tofu, vinegar, wine or yoghurt cause cancer? Postgraduate Course Statistical significance

51. Significance testing: always prospective, never retrospective Postgraduate Course Statistical significance

52. Statistical significant ≠ practical relevant Postgraduate Course Effect size Statistical significance

53. Postgraduate Course 10. Statistical power

54. Sample size Effect size (Significant increase in IQ) 410 25 4 100 2 10.0000,2 Postgraduate Course Statistical power The statistical power: the power to detect a meaningful effect, given sample size, significance level, and effect size.

55. Postgraduate Course Overpowered: sample size too large, high probability of making a Type I error Underpowered: sample size too small, high probability of making a Type II error. Statistical power

56. Postgraduate Course 11. Effect size

57. Postgraduate Course Effect size Effect size: a standardized measure of the magnitude of effect, independent of sample size standardized > makes it possible to compare effect sizes across different studies that have measured different variables, or have used different scales of measurement

58. Postgraduate Course Effect sizes  Cohen’s d  Pearson’s r  other - Hedges’ g - Glass’ Δ - odds ratio OR - relative risk RR

59. Postgraduate Course Effect sizes  Cohen’s d Effect size based on means or distances between/among means Interpretation <.10 = small.30 = moderate.30 = moderate >.50 = large

60. Postgraduate Course Effect sizes  Pearson’s r Effect size based on ‘variance explained’ Interpretation <.10 = small (explains 1% of the total variance).30 = moderate (explains 9% of the total variance).30 = moderate (explains 9% of the total variance) >.50 = large (explains 25% of the total variance)

61. Postgraduate Course 12. Critical appraisal When you critically appraise a study, what characteristics of the findings will you consider to determine its statistical significance and magnitude?

62. Postgraduate Course Critical appraisal When you critically appraise a study, what characteristics of the findings will you consider to determine its statistical significance and magnitude?  p-value  confidence interval  sample size / power  effect size  practical relevance