1. Quantitative Methods: Choosing a statistical test Summer School June 2015 Dr. Tracie Afifi

2. Learning Objective How to pick the right statistical test

3. To pick the correct statistical test you need to know… What your research question asking The level of measurement of the variables The distribution of the data

4. Common Statistical Tests T-test ANOVA Pearsons Correlation Linear Regression Logistic Regression Mann Whitney U Kruskal Wallis Test Chi-Square Test Spearmans Correlation

5. What is your research question asking?

6. Choosing a Statistical Test What is your research question asking? Is there a difference? Is there a relationship?

7. Is there a difference? Is there a difference in depression among adolescents who are sexually abused compared to adolescents who are not sexually abused?

8. Is there a difference? T-test ANOVA Mann Whitney U Kruskal Wallis Test Chi-Square Test

9. Is there a difference? T-test ANOVA Mann Whitney U Kruskal Wallis Test Chi-Square Test But how do you know which one to choose?

10. Is there a difference? T-test ANOVA Mann Whitney U Kruskal Wallis Test Chi-Square Test But how do you know which one to choose? What are the variables?

11. Is there a difference? T-test ANOVA Mann Whitney U Kruskal Wallis Test Chi-Square Test But how do you know which one to choose? What are the variables? How are the variables measured?

12. Is there a difference? T-test ANOVA Mann Whitney U Kruskal Wallis Test Chi-Square Test But how do you know which one to choose? What are the variables? How are the variables measured? What is the distribution of the data?

13. What are the Variables? Is there a difference in depression among adolescents who are sexually abused compared to adolescents who are not sexually abused?

14. What are the Variables? Is there a difference in depression among adolescents who are sexually abused compared to adolescents who are not sexually abused? One Variable is Sexual Abuse One Variable is Depression

15. How are the Variables Measured? Categories (yes or no) Categories (none, minor, moderate, severe) Scores (e.g., 0-10) Sexual Abuse Depression

16. How are the Variables Measured? Level of Measurement

17. Nominal – Named categories with no order Ordinal – Categories with a logical order or rank order Interval – Rank order AND distant between intervals of measurement have meaning (zero value is arbitrary). Ratio – Same properties as interval data AND the distance and ratio between two measurements are defined and has an empirical (not arbitrary) zero value. – You can say a score of 20 is “twice as much” as 10. Liamputtong 2013

18. Level of Measurement TypeDescription Nominal Classes or categories without numerical order Male, female Jewish, Catholic, Muslim Ordinal (ranked)Ordered categories Mild pain, moderate pain, and severe pain High school, undergraduate, graduate IntervalThe distance or interval between two measurements have meaning Temperature in Celsius (zero = 273.15 Kelvin) RatioThe distance and ratio between two measurements are defined and zero has a meaning of zero and therefore you can say “twice as much” Weight Age in years Temperature in Kelvin (absolute zero)

19. What is the Distribution of the Data?

20. Central Tendency and Dispersion Central tendency – Where the bulk of the data lie. Mode, Median, Mean, etc Dispersion – How wide or narrow the data are spread out. Number of categories, Range, Standard Deviation, etc Health Research Methods: A Canadian Perspective (2014) Edited by K. Bassil & D. Zabkiewicz; Chapter 7, pp. 119-142

21. Central Tendency Mode – The value that appears most often – (3, 4, 5, 6, 8, 8, 15) Mode = 8 Mean – The arithmetic average of the observations – (3, 4, 5, 6, 8, 8, 15) Mean = 7 Median – Middle value (3, 4, 5, 6, 8, 8, 15) Median = 6

22. Level of Measurement Central TendencyDispersion NominalMode (most frequent category)Number of categories OrdinalMedian (data are ranked, middle value with half above and half below) Range and the Interquartile range (median of upper half and median of lower half IQR is difference between the two) IntervalMean (summed and divided by number)Standard Deviation (how much each data point deviates from the mean) RatioMean (summed and divided by number)Standard Deviation Health Research Methods: A Canadian Perspective (2014) Edited by K. Bassil & D. Zabkiewicz; Chapter 7, pp. 119-142

23. Level of Measurement Central TendencyDispersion NominalMode (most frequent category)Number of categories OrdinalMedian (data are ranked, middle value with half above and half below) Range and the Interquartile range (median of upper half and median of lower half IQR is difference between the two) IntervalMean (summed and divided by number)Standard Deviation (how much each data point deviates from the mean) RatioMean (summed and divided by number)Standard Deviation NON-PARAMETERIC TESTS PARAMETERIC TESTS Health Research Methods: A Canadian Perspective (2014) Edited by K. Bassil & D. Zabkiewicz; Chapter 7, pp. 119-142

24. What is the Distribution of the Data? Normal Distribution Or Non-Normal Distribution

25. Normal Distribution Average Hours of Sleep Mean = 7.92 Std Error = 0.13 95% CI = 7.68 to 8.18

26. Non-Normal Distribution Among respondents with babies Mean = 5.88 Std Error = 0.30 95% CI = 5.27 to 6.49

27. Distribution of the Data Parametric test – Interval or ratio level data with a NORMAL DISTRIBUTION Non-parametric test – Nominal or ordinal level data or interval or ratio with a NON-NORMAL DISTRIBUTION

28. Common Statistical Tests

29. Is there a difference? Parametric T-test ANOVA Non-Parametric Mann Whitney U Kruskal Wallis Test Chi-Square Test

30. T-test To test if two means are statistically different? – One variable is Continuous (interval or ratio level) – One variable is Dichotomous (two categories) – Distribution of continuous variable is NORMAL (bell curve)

31. T-test Is the mean depression score different for adolescents who are sexually abused compared to adolescents who are non-sexually abused? Sexual abuse = Yes or No (nominal or Dichotomous) Depression = 1 to 10 (interval with higher scores worse depression) Depression (mean) Total Sample4 No Sexual abuse2 Sexual abuse8

32. What if the Distribution was NON-NORMAL? – One variable is Continuous (interval or ratio level) with a NON-NORMAL DISTRIBUTION – One variable is Dichotomous (two categories)

33. Mann-Whitney U test A non-parametric test for comparing ordinal, or non-normal continuous level data for two independent groups Non-normal distribution – One Variable Ordinal or non-normal continuous level – One Variable Two-level-categorical, dichotomous Bruce, 2008 Quantitative Methods for Health Research, pp. 491-495

34. Is there a difference? Parametric T-test – Difference in means in two groups Non-Parametric Mann Whitney U – Difference in medians in two groups

35. Is there a difference? What if you have three groups or more? – No sexual abuse, minor sexual abuse, moderate sexual abuse, severe sexual abuse?

36. ANOVA Analysis of Variance Used to compare statistical difference between three or more group means ANOVA compares differences across all means at the same time Distribution of the sample means are normal (Parametric) – Dependent Variable Continuous (one variable) – Independent Variable Categorical (One variable with more than two levels or groups) Bruce, (2008); Tabachnick & Fidell (2007); Winston (1999); Liamputtong, 2013

37. ANOVA Are the mean depression score different for adolescents who experience mild sexual abuse, moderate sexual abuse, or severe sexual abuse? – Distribution of depression scores is NORMAL Sexual abuse (Ordinal as none, minor, moderate, severe) Depression (interval ranging 0 to 10) Depression (mean) Total Sample4 No Sexual Abuse2 Minor Sexual Abuse4 Moderate Sexual Abuse7 Severe Sexual Abuse9

38. ANOVA To test if three or means are statistically different? – One variable is continuous (interval or ratio level) with a NORMAL DISTRIBUTION – One variable is categorical (three or more categories)

39. What if the Distribution was NON-NORMAL? – One variable is ordinal OR continuous (interval or ratio level) with a NON-NORMAL DISTRIBUTION – One variable is Categorical (three or more categories)

40. Kruskal Wallis Test Median scores from three or more groups – One variable = continuous (non-normal) or ordinal – One variable = categorical with 3 levels or more – An extension of the Mann Whitney U test and the non-parametric equivalent to ANOVA. Liamputtong, 2013

41. Chi-Square Test of Significance (X 2 ) Non-parametric test (Non-normal distribution) – One Variable Categorical with 2 or more levels – One Variable Categorical with 2 or more levels Bruce (2007); Tabachnick & Fidell (2007); Winston (1999)

42. Is there a difference? Parametric T-test ANOVA Non-Parametric Mann Whitney U Kruskal Wallis Test Chi-Square Test

43. Is there a relationship? Is there a positive correlation between sexual abuse and depression? Is sexual abuse severity associated with increased severity of depression? Is sexual abuse associated with increased odds of depression?

44. Is there a relationship? Is there a positive correlation between sexual abuse and depression? Is sexual abuse severity associated with increased severity of depression? Is sexual abuse associated with increased odds of depression? Correlation Logistic Regression Linear Regression

45. Is there a relationship? Parametric Pearsons Correlation Linear Regression Logistic Regression Non-Parametric Spearmans Correlation

46. Correlation Strength of a linear relationship Pearson Distribution of the variables are normal (parametric test) – One Variable Continuous – One Variable Continuous Spearman Distribution of the variables are non-normal (non- parametric test) OR one or more variables are ordinal – One Variable Continuous/Categorical – One Variable Continuous/Categorical Bruce, 2008 Quantitative Methods for Health Research, pp. 74-78

47. Linear Regression Describes how one variable (DV) depends on the other variable (IV) Regression estimates the relationship between two variables – One Dependent Variable Continuous – One or more Independent Variables Any level of measurement Bruce, 2008 Quantitative Methods for Health Research, pp. 232-255

48. Logistic Regression Predicts a dichotomous outcome from one or more Independent variables (Odds Ratio) Parametric test (some distribution assumptions apply) – One Dependent Variable Dichotomous (two categories) – One or More Independent Variables Any level

49. Is there a relationship? Parametric Test (Normal Distribution)Non-Parametric Test (Non-Normal Distribution) Pearsons Correlation One variable = continuous Spearmans Correlation One variable = continuous or categorical Linear Regression Dependent variable = continuous (1 variable) Independent variable = any level (1 or more) Logistic Regression Dependent variable = Dichotomous (1 variable) Independent variable = any level (1 or more)

50. Is there a difference? Parametric Test (Normal Distribution)Non-Parametric Test (Non-Normal Distribution) T-test (difference in means) One variable = continuous One variable = Dichotomous Mann Whitney U (difference in Medians) One variable = Continuous or ordinal One variable = dichotomous ANOVA One variable = continuous One variable = 3 or more categories Kruskal Wallis Test One variable = continuous or ordinal One variable = categories or more Chi-Square Test One variable = 2 or more categories

51. To pick the correct statistical test you need to know… What your research question asking The level of measurement of the variables The distribution of the data