Chapter 11 Correlation Pt 1: Nov. 6, 2014

Correlation Association between scores on two variables –Use scatterplots to see the relationship –Rule of thumb – if 1 var is a “predictor”, put it on the x axis

Patterns of Correlation Linear correlation – straight line relationship (appropriate to compute corr) Curvilinear correlation – U or S shaped curves No correlation – no trend to points in scatterplot Positive correlation – points move from lower left to upper right (pos slope) Negative correlation – points move from upper left to lower right (neg slope)

Degree of Linear Correlation The Correlation Coefficient Figure correlation using products of deviation scores Multiply pos x pos  get positive results Multiply negative x negative  get positive results, which we want Multiply pos x neg  get negative results 1) Find means of x variable (Mx) and y variable (My) 2) Find deviation scores for each person for x variable (x-Mx) and y variable (y-My) 3) Sum these up across the sample 4) divide by sqrt of (SSx)(SSy) – where SSx=sum of squared deviations for x variable and SSy=sum of squared deviations for y variable

Formula for the correlation coefficient: r = Σ [(x – Mx)(y – My)] sqrt [(SSx)(SSy)] where SSx = Σ (x-Mx) 2 where SSy = Σ (y-My) 2 Positive perfect correlation: r = +1 No correlation: r = 0 Negative perfect correlation: r = –1 Example on board…

Correlation and Causality Three possible directions of causality: 1.X Y 2. X Y 3. Z X Y Can only determine causality w/longitudinal study or a true experiment (w/random assignment) to rule out 3 rd variables (z) Examples of 3 rd variable explaining the correlation between x & y?

Issues in Interpreting the Correlation Coefficient Statistical significance – for correlation, test is whether true corr in pop = 0. –If corr is statistically signif, means it is highly unlikely that we’d get this corr if true pop corr = 0. Restriction in range –With limited range, corr is different than what it would be with full range (more variability) –Ex) Correlate job perf with hiring test score – may have range restriction

Size of r: Cohen’s Guidelines What is a large corr? –Cohen’s guidelines: >.5 or -.5 = large,.3 or -.3 = moderate,.1 or -.1 = small Unusual to have corr above.5 or -.5 Consider average r =.19 for job satisfaction & job perf… –Interpretation?

Correlation in Research Articles Scatter diagrams occasionally shown Correlation matrix presented in table. Notice only lower triangle completed & corr of variable w/itself represented with dash. –In text: “The correlation between acculturation and assimilation was significant (r =.56, p <.05).