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PSYC 221: Statistics

PSYC 221: Statistics. Correlation: PEARSON r. What is Correlation?. It’s all about the relationship. Correlation. Contrast with hypothesis testing Sig diff between groups Sig relationship between 2 sets of scores Always within 2 DV, no IV Graphing Scatterplots x and y scores

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PSYC 221: Statistics

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  1. PSYC 221: Statistics Correlation: PEARSON r

  2. What is Correlation? It’s all about the relationship

  3. Correlation Contrast with hypothesis testing Sig diff between groups Sig relationship between 2 sets of scores Always within 2 DV, no IV Graphing Scatterplots x and y scores Examples of correlations Height and weight ACT and GPA Hours of sleep and depression

  4. IV. Graphic representations

  5. II. Computation A. Conceptual 1. deviation score (x-M) subtract each score from mean highs go with highs; lows go with lows cross products: (x-M)(y-M) if strong positive big positive number if strong negativebig negative number if no relationship pos and neg cancel 2. remaining scaling matters n more scores  higher number greater variation in scores  higher number correction? Divide by variability similarity to z 3. computational and conceptual formuli page 449 – blue box page 485 – chapter notes SPSS

  6. Sleep and Mood example (pg 449) Number hours slept happy mood 7 4 5 2 8 7 6 2 6 3 10 6 __________ _____________ Sx = 42 Sy = 24 Sxy = 184 Sx2 = 310 Sy2 = 118 n = 6

  7. III. Interpretation of the output A. -1 -------- 0 --------- +1 1. strength 2. direction B. Correlation and Causation C. Limitations 1. nonlinear relationships 2. truncated range

  8. IV. Common Uses A. Correlational survey research - correlation tables (pg 468) - SPSS correlation output B. Testing - reliability - test/retest - split half - parallel forms - validity - convergent - divergent - predictive C. As measure of effect size r2 = proportion of variance in x accounted for by y

  9. V. Significance? A. Null hypothesis r = 0 B. Logic - same logic as other hypothesis tests - alpha level C. Formula (pg 453) - df = (N-2) - SPSS

  10. Regression • Prediction • Real example: student selection at CSB/SJU • Want to select students who will succeed Linear regression • Y(hat) = a + bx Y(hat) = predicted criterion score (unknown) a = regression constant (y intercept) b = regression coefficient (slope) x = score on predictor variable (known)

  11. Least squared error principle • Smallest sum of squared errors • Smallest deviation from a straight fitting line

  12. Do you find this disturbing? No, I prefer a melon that can fit in the glove compartment of my car No, genetically modified food always tastes better No, isn’t your watermelon shaped that way? Huh?

  13. Standardized regression coefficient - B • Difficulty comparing across studies with different scales of measurement with least squares rule • slope relative to scale of measurement • Sleep study 1 – mood scaled 0-8 (increase of 1 for each additional hour of sleep) • Sleep study 2 – mood scale 0-20 (increase of 2 for each additional hour of sleep) • Solution is make a z-like conversion • Standardized regression coefficient (slope) • Regression in standard deviation units • With only one predictor variable B=r • Allows equivalent interpretation across different scales • Can be expanded to 1+ predictor variables

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