PSYC 1037: Research Skills II Dr Pam Blundell

1. PSYC 1037: Research Skills IIDr Pam Blundell Lecture Two: Relationships

2. Outline Objectives Answers to last weeks worksheet Covariance and Correlation Theory Practice

3. Objectives At the end of this lecture you should Know how to interpret scatterplots Understand the concepts of covariance and correlation Be able to calculate Covariance Be able to calculate various Correlation coefficients

4. Worksheet A priori power Assuming a=0.05, power of 0.9 gives us a d=3.25 So we need 59 people per group So 118 subjects!

5. Worksheet Post hoc power We have a medium effect size d is less than 1, so power is less than 0.17 � 17% chance of detecting a difference that is really there!

6. Reading Howitt & Cramer Stats book Chapters 6 & 7, 10 SPSS book Chapter 7 Field Chapter 4

7. Correlational method Measures two or more characteristics of the same individual and computes the relationship between those characteristics Studies variance among organisms rather than variance among treatments

8. Relationships Do variables co-vary? Change in one variable results in change in another variable We can look at scattergrams and make observations We need an objective way of calculating the correlation

9. Research questions Is there a relationship between IQ and A Level points? Is there a relationship between IQ and height? Is there a relationship between IQ and the number of children you have?

10. Plotting relationshipsThe Scattergram

11. The Scattergram Each point on the scattergram represents a single individual Each axis is a different variable

12. Scattergrams Enable us to look �at a glance� and see if there are any outliers Can show relationships

13. Positive relationship

14. Negative relationship

15. No relationship

16. Covariance Scattergram illustrates the relationship qualitatively Need to quantify that relationship � how do the variable co-vary.

17. Variance

18. Covariance There is an error in this formula in Howitt & Cramer (p62)

19. Co-variance To calculate how two variables co-vary we Calculate the difference between each data point and the mean Calculate the cross-product value for each data point Add these up, and divide by N-1

21. and is given by the distance between each point and the mean You can see that with this positive correlation, the data points nearly all lie in two quadrants of the scattergram

24. Scattergram

26. Covariance Is not a standardised measure The value will depend upon the units used Doesn�t allow us to compare the magnitude of the covariance between different things Therefore, we need to standardise the covariance

27. Correlation coefficient

29. Correlation r varies between -1 and 1 Can work out probability values(or SPSS tells us)

30. Warning� Correlations tells us about LINEAR relationships

31. Recap Scattergrams Covariance Correlation

32. Do you want a break? Correlations in SPSS Biserial point correlations Non-parametric correlations

33. Correlation in SPSS Enter the data into SPSS � one variable in each column

34. Correlation in SPSS Analyze ? Correlate? Bivariate�

37. SPSS Output

38. Scattergrams in SPSS Graphs ? Scatter

39. Simple - when you have two variables Overlay - examine the effects of two or more variables on another variable Matrix - examine the relationship between all combinations of many different pairs of variables

40. Set the variables for the X-axis and the Y-axis

41. Scattergrams in SPSS

42. Exam performance and anxiety SPSS demonstration -- File ExamAnx.sav First, examine the data using Scattergram Y-Axis (the DV): performance (% of mark) X-Axis (the IV): exam anxiety (/100) Set Markers by: relationship between the variables for different groups (e.g. gender) Overlay Scattergram, to compare effects of revision and anxiety on exam performance Now carry-out statistical test Analyse => Correlation => Bivariate How does exam anxiety affect performance? Does it effect male and females equally? Are there any outliers? What can they be due to? What do you think you should do with them? Could there be another variable that might effect performance? How does exam anxiety affect performance? Does it effect male and females equally? Are there any outliers? What can they be due to? What do you think you should do with them? Could there be another variable that might effect performance?

43. Interpreting the output What does the diagonal represent? How are anxiety and revision time each related to exam performance? 1. Anxiety and performance, (r = -.441, p<.001) 2. Revising and performance, (r = .397, p<.001) 3. Anxiety and Revising, (r = -.709, p<.001) What do 1, 2, and 3 mean? So can we say that anxiety causes poor performance?

44. Causality Correlation does not infer causality Correlation can be caused by a third variable that we have not measured Correlation tells us nothing about the directionality of a relationship We have not manipulated any variables � there is no �independent variable�

45. R2 R2 (Co-efficient of determination) tells you the amount of variability in one variable that is explained by the others How much variability in performance is explained by anxiety? (-.441)� = 0.194 - multiply by 100 = 19.4 19.4% of the variance in performance is accounted by anxiety! 80.6% remains to be accounted by other variables! What about revision time?

46. Correlation Summary Pearsons correlation coefficient (R) Requires parametric data Is extremely robust

47. Non-parametric data There are other tests available to deal with non-parametric data Spearman�s Rho Kendall�s Tau Point-biserial correlations

48. Spearman�s Rho Use when there are violations of parametric assumptions/and or ordinal data (e.g. grades, first, upper second, second, third, and pass)

49. Spearman�s Rho

50. Spearman�s Rho Now, use the ranks instead of the raw numbers, in the same calculation as Pearson�s. Example: Is facial attractiveness associated with ratings of success?

51. Rank the data

53. Spearman�s Rho in SPSS Similar to Pearson�s Correlate�Bivariate� Make sure Spearman�s Rho box is ticked

54. Kendall�s Tau Use when we have a smaller data set with a large number of tied ranks, i.e., if lots of scores have the same rank More sensitive than Spearman�s Rho Used more often because in reality we are more likely to have a large number of tied ranks! See SPSS�

55. Point Biserial correlation When one of the variables is a dichotomous variable (categorical with only two categories) pregnant woman dead or alive male or female DON�T use when there is really a continuum underlying the category (e.g. Pass/Fail).

56. Point Biserial correlation Calculation simple � same as Pearson�s! Example: The relationship between time spent away and gender of cats (file pbcorr.sav) code sexuality (0=female, 1=male) time (mins away) Carry out Pearson�s correlation

57. What about the sign of the correlation? Ignore the sign - depends on your coding! How much of the variance in time spent chatting up is accounted by sexuality? R� = (.378) � = .143, so 14.3% of the variance in time away from home is explained by gender. Do Descriptives - Why?

58. Summary