Evidence -Based Management (Some) statistics for managers who hate statistics

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

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

3. Some statistics Some statistic terms Sample vspopulation Variables Levels of measurement Central tendency Hypothesis Some statistic models Mean Variance, standard deviation Confidence intervals Statistical significance Statistical power Effect sizes Critical appraisal

4. 1. Sample vs population

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

6. Sample vs population 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.

7. Sample vs population 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

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

9. 2. Variables Postgraduate Course

10. Variables Postgraduate Course 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. 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. Level of measurement Nominal Ordinal Interval Ratio Categorical Continuous

14. 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 Nominal scale 1 = Apples 2 = Oranges 3 = Pineapples 4 = Banana’s 5 = Pears 6 = Mango’s

15. 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 Ordinal scale Full Professor Associate professor Assistant professor PhD Master Bachelor

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

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

18. Levels of measurement Categorical Continuous

19. 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 ☐ Somewhat agree ☐ Neither agree or disagree ☐ Somewhat disagree ☐ Strongly disagree

20. 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. 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. 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. 5. Hypothesis

24. Hypothesis: falsifiability “It is easyto 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. … Atheory is scientific only if it is refutable by a conceivable event. Every genuine test of a scientific theory, then, is logically an attempt to refute or to falsify it.” Carl Popper

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

27. Statistic models

28. Statistic models: prediction not likely likely

29. 6. The mean _ The most widely used statistic model μ X or sample population

30. The mean Number of Friends EBMgt Lecturer

31. 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 5,2 SS 2 4 N-1 2

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

33. Standard Deviation

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

35. Standard Deviation Postgraduate Course S=10 S=20 S=60 IQ 170 110 130

36. Standard Deviation Postgraduate Course

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

38. 8. Confidence intervals Postgraduate Course

39. Confidence intervals 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)

40. Confidence intervals 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.

41. Confidence intervals 1,96!

42. Confidence intervals

43. Confidence intervals “According to the federalgovernment, the unemploymentrate has droppedfrom 4.3% to3.8%.” 95% CI= 4,1 - 3,5. This means the unemploymentratecouldhave increasedfrom 4.0 to 4,1 ! 5,0 4,5 4,0 3,5 3,0 2008 2009

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

45. 9. Statistical significance

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

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

48. Statistical significance Postgraduate Course

49. Statistical significance Postgraduate Course Is there a difference / an effect? How certain is it that the difference / effect found is not a chance finding? _ _ X X 0 1 110 130

50. Statistical significance Postgraduate Course 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?