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Research Methods & Design in Psychology. Lecture 4 Correlation Lecturer: James Neill. Readings. Howell (Fundamentals) Ch9 (Correlation) Howell (Methods) Ch6 (Categorical Data and Chi-Square) Ch 9 (Correlation and Regression). Overview. Correlational analyses Types of answers
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Research Methods & Design in Psychology Lecture 4 Correlation Lecturer: James Neill
Readings • Howell (Fundamentals) • Ch9 (Correlation) • Howell (Methods) • Ch6 (Categorical Data and Chi-Square) • Ch 9 (Correlation and Regression)
Overview • Correlational analyses • Types of answers • Types of correlation • Interpretation • Assumptions / Limitations
Correlational Research Questions Are two variables related? Interesting questions tend to: • test a novel relationship, e.g. • “is time spent studying for exams associated with increased incidence of brain cancer?” • avoid simply showing an expected relationship, e.g. • “is time spent studying studying for exams associated with higher exam marks?”
Correlational analyses 1 Correlational analyses are used to examine the extent to which two variables have a simple linear relationship. Correlations provide the building blocks for: • Factor analysis • Reliability • Regression • Etc.
Correlational analyses 2 Linear relationship between 2 variables: • direction and • strength • ranges from -1 to +1 • Sign indicates direction • Size indicates strength
Correlational analyses 3 Measures the extent to which: • differences in one variable can be predicted from differences in the other variable • one variable varies with another variable A correlation is also an effect size.
Types of Answers • No relationship (independence) • Linear relationship: • As one variable increases, so does the other (+ve) • As one variable increases, the other decreases (-ve) • Non-linear • Restricted range • Heterogeneous samples
Types of Correlation • Phi / Cramer’s V • Spearman’s rank / Kendall’s Tau b • Point bi-serial rpb • Product-moment or Pearson’s r
Contingency Tables 1 • Bivariate frequency tables • Marginal totals • Can include %
Clustered Bar Graph • Bar graph of frequencies or percentages with the category axis clustered by coloured bars to indicate the two variable’s categories
Phi (f) & Cramer’s V Phi () • Two dichotomous variables (2x2, 2x3, 3x2) • E.g., Gender & Pass/Fail Cramer’s V • Two dichotomous variables (3x3 or greater) • E.g., Favourite Season x Favourite Sense
Spearman’s rho (rs) • For ranked (or recoded to ordinal) data • Uses product-moment correlation, but interpretations must be adjusted to consider the underlying ranked scales • e.g. Olympic Placing vs. World Ranking
Kendall’s Tau-b • Kendall’s tau-b • for ordinal/ranked data • takes joint ranks into account • Ranges -1 to +1, but only for square tables
Point-biserial correlation • Point-biserial correlation (rpb) • one dichotomous & one continuous variable • calculate as for Pearson’s r, but interpretations must be adjusted to consider the underlying ranked scales • e.g., gender and self-esteem
Product-moment correlation (r) • For two interval and/or ratio variables • r = covxy sxsy
Scatterplots • Plot each pair of observations (X, Y) • x = predictor variable (independent) • y = criterion variable (dependent) • Check for: • outliers • linearity • ‘Line of best fit’ y = a + bx
The correlation between 2 variables is a measure of the degree to which: • Pairs of numbers (points) cluster together around a best-fitting straight line
Correlation Estimation Indicate level (high, med., or low) and sign of the correlation for: • number of guns in community and number firearm deaths • robberies and incidence of drug abuse • protected sex and incidence of AIDS • community education level and crime rate • solar flares and suicide
Covariance • Variance shared by 2 variables • Covariance reflects the direction of the relationship: +ve cov indicates + relationship -ve cov indicates - relationship. Cross products
-ve dev. products +ve dev. products -ve dev. products +ve dev. products Covariance – Cross-products -ve cross products