Research Methods

1. Research Methods Continued

2. Module Aims • Revisiting design and write-up of studies • Issues in psychological measurement: new procedures • before analysis • types of analysis (linear regression) • Class project using Linear Regression • see report structure h/o & wk by wk project h/o • focus on the introduction • 100% of module mark, due date ? • start thinking ideas

3. Today • Issues in psychological measurement: • standardisation/Z scores • Introduction to Linear Regression

4. Standardisation: Z Scores • Standardising = convert raw scores to Z scores • Z scores = how many sd’s from mean • Z of +2 = 2 sd’s above mean (‘normal’) • Z of -2 = 2 sd’s below mean • Z of 0 = mean • Standard scale invaluable tool for comparing different measures on same scale • Hence Z score referred to as standard score.

5. Raw Score to Z Score: Formula • Subtract mean from raw score (deviation score) • Then divide by sd Z = X – M SD Where X = raw score

6. Raw Score to Z Score: Example • So child who scored 100 on language test shown to have mean 82 and sd 6: • Z = 100 – 82 = 3 6 • = 3 sd’s above mean

7. Z Score to Raw Score: Formula • Just reverse process • Multiply Z score by sd • Then add the mean X = (Z)(SD) + M

8. Z scores to Percentage of Cases • Because normal curve standard, known % of cases above/below particular points • Exactly 50% cases fall below mean (as in any symmetrical distribution) • Approx 34% fall between mean and 1 sd of mean • 14% between 1 and 2 sd of mean • 2% between 2 and 3 sd of mean • So if can remember 34%, 14%, 2%, and know no. sd’s from mean will have good sense of % cases above or below score

9. Percentage of Cases to Z Scores • Possible to reverse this approach • Can figure out no. of sd’s from mean (Z score) from a percentage • E.g if told scored top 2% in test (assuming normal distribution)… • …can see must have score between 2 and 3 sd’s of mean (at least 2).

10. Percentage Cases Between Z scores • In psychology sometimes need to know percentage of cases between two Z scores • Can be computed using formula for normal curve and integrating using calculus • Statisticians computed tables (normal curve) giving % cases between mean and any Z score • What are % cases between mean and Z of .62? • Look up .62 on table, shows 23.24% cases fall between mean and this Z score • Use to find % cases relating to Z score, and to find Z scores for particular % cases

11. Z scores and Linear Regression • Understanding standardisation is important for understanding/using linear regression • So, what is Linear Regression?

12. Linear Regression: Rationale • Psychologists required to make informed, precise estimates, e.g., • how likely parolee commit violence if released • how well maths programme likely to help child • Linear regression uses score on one variable (IQ) to make predictions on another (exam marks) • Variable to make prediction = predictor variable (IV) • Variable you predicting = criterion variable (DV)

13. Regression vs Correlation • Correlation measures strength of relationship/degree of association as indicated by correlation coefficient (r or rs) • from 0 - 1, -ve or +ve, e.g .79 • but correlation not causation • r² = proportion variance in scores accounted for by the association (.79² = 0.62 = 62%) • Regression predicts specific value of one variable based on value of other variable

14. Regression vs ANOVA • Conceptually do same thing, each derived from formula of each other • ANOVA examines whether is difference on DV between means of groups representing different levels of IV • Regression also examines group means but sees this as relationship between DV and these different levels of predictor variables • Similarities lie in calculations which all deal with variance and sums of squares

15. Regression vs ANOVA contd. • SSTin regression and ANOVA both about deviations of each score from mean of all DV scores • Since group means in ANOVA are predicted score for each case in regression, SSE in regression same asSSW in ANOVA. Etc. • Any ANOVA can be set up as regression by making categories that represent different groups into 1 or more dichotomous numerical variables • ANOVA special case of regression • Although used in different research contexts as if different, are conceptually identical procedures

16. Regression vs ANOVA contd.2 • Regression big advantage • direct information on degree of relationship between predictor and criterion variables, and permits significance test • automatic indication of effect size • handles unequal no.s of participants between groups • ANOVA • gives significance only • have to compute effect size • has to make adjustments for unequal no.s participants

17. ‘Types’ of Regression • With 2 variables, where one used to predict value of other = simple or bivariate regression • Here criterion (DV) should be on continuous scale • Predictor (IV) should also be on continuous scale, but nominal predictors legitimate if dichotomous or no more than 2 categories, e.g. gender

18. ‘Types’ of Regression contd. • Using more than 1 predictor variable (IV) to predict value of one criterion variable (DV) = multiple regression • Indeed, in real life often more than one variable that determines performance • Requires large no. observations • no. cases must exceed no. predictor variables • min. = 5X participants than predictor variables (subject-to-variable ratio of 5:1) • 10:1 more acceptable ratio. 40:1 for some methods? • Other way to determine sample size = power analysis

19. ‘Types’ of Regression contd. 2

20. Reading • Standardisation and Z Scores • Aron, A., & Aron, E.N. (1994). ‘Statistics for Psychology’. Prentice Hall International Editions. p48-54 and p137-140. [519 .502 415 ARO] • For recap of correlation see Ch3 Aron & Aron • Linear Regression (prediction) Ch4 Aron & Aron