Psychology Practical (Year 2) PS2001

1. Psychology Practical (Year 2) PS2001 Correlation and other topics

2. Correlation A brief review • It is a level of analysis between description and explanation • It can allow prediction • Examination of relationships between two variables (for same individual) • If a relationship (association) exists then this should allow us to predict the behaviour on one variable from the measure of behaviour on another variable (regression) • A measure of consistency of relationship

3. Correlation Key points • No manipulation or control –not an experiment • Can control when and where measured and sample, but no 'direct' control exercised • Variables measured 'in situ' • Statistically you may find a relationship is indicated between two variables, but you cannot determine ‘cause and effect’– • There may be a number of other, unmeasured variables that could be interrelated and responsible for the relationship found • There may be an effect, but a correlation will not prove this - need an experimental design

4. Techniques • For interval data: • Pearson's Product-Moment Correlation – this is the best known correlation and the most used. • For categorical data: • Spearman's Rank Correlation Coefficient • Kendall's tau statistics • In general: • Correlation examines the degree to which the two variables change together: covary • Partial correlation: • Uses Pearson’s • Allow examination of a relationship between two variables while at the same time controlling for another variable

5. Characteristics of a Relationship • Direction • Positive (+) or negative (-) • Form • Linear or non-linear • Degree • How well data fit the form (consistency or strength) • From 0 (no fit) to 1 (perfect fit)

6. Visual Characteristics: an example • 2 variables - X & Y • X on horizontal axis • Y on vertical axis • Look for a 'form' made by the points representing the scores • Rising to right is + • Falling left to right is -

7. Positive linear correlations – these are based on 1000 pairs of numbers. Each square with a number corresponds to its mirror graphical representation.

8. Strength of a correlation Cohen (1988) suggested the following interpretations of correlations: But this depends on context. If this is in the context of a very highly controlled physics experiment one would expect high correlations, but not in the context of testing a general population’s attitudes. So judgements about the extent or strength of a correlation should if possible be made in the context of similar studies.

9. Why Use Correlations? • Prediction • A relationship allows predictions to be made of one behaviour from another • Validity • To demonstrate a test scale is valid by showing a significant relationship between it and another accepted scale for a related construct • Reliability • To show consistency of measurement on two occasions (indirectly for internal consistency) • Theory verification • Use to support hypotheses that predict relationships between variables

10. Spearman's Correlation rS • A non-parametric version of Pearson's correlation coefficient • Uses ordinal data that is given a ranking to create numerical values • Same general comments apply to this form of correlation as to Pearson's • Can be used for ordinal data as can identify non-linear relationships - a measure of consistency independent of its specific form

12. Correlation Matrix • SPSS produces a matrix to present correlation coefficients between variables, if you are reporting a number of correlations, you should use a table in the form of a matrix

13. Partial Correlation • Similar to Pearson’s • Allows control of an additional variable • Usually one thought to influence the two other variables of interest • Removal of this confounding variable permits better examination of relationship between two variables of interest

14. Two Correlation Coefficients • Separate for two groups • Use Split File procedure • Comparing • Use separate coefficients (and n) to determine if two r values differ significantly • Convert r values to z values (table) • Calculate Zobs from formula • Is Zobs value equal to or greater than 1.96 - at either end of the distribution? • If yes then two coefficients differ significantly

15. Cronbach's Coefficient Alpha • Measures internal consistency • Estimate of reliability of a scale • How well the items measure the same underlying construct • Examines average correlation between all items in the scale • Value from 0 to 1 (highest reliability) • Expect a minimum value of .70 for a moderate to large scale

16. SPSS Output - Alpha Value

17. SPSS Output - Item Total Statistics

18. SPSS Output - Item Total Statistics • Corrected item-total correlation • Correlation of item to overall scale score • Low or ‘opposite direction’ item correlations suggest ambiguous statement, statement that poorly reflects construct, or possibly failure to correctly score item • Alpha if item deleted • Overall alpha value of scale if that item is deleted • Items that if omitted would improve alpha should be examined - will be same items indicated by previous column output