UW-Madison PSYCH 210 - Correlation and Regression (5 pages)

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Correlation and Regression

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Correlation and Regression


Lecture number:
Lecture Note
University of Wisconsin, Madison
Psych 210 - Basic Statistics for Psychology

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PSYCH 210 Lecture 26 Outline of Last Lecture I Factorial ANOVA a Interpretation of interaction b Assumptions II Correlation Outline of Current Lecture I Finish Correlation a Calculational example Pearson r b Test for significance of r c Assumptions for inferential test d Important aspects of correlation II Regression Current Lecture I Correlation a Pearson r i Calculational formula 1 r SP SSx SSy a SP Sums Products i Def x Mx y My 1 Remember SS def x 2 a x x ii Computational 1 r xy x y n x2 x 2 n y2 y 2 n 2 Precalculations Ex These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute a b c d e f g n 6 x 30 y 498 x y 30 498 xy 2458 x2 168 y2 41406 i Remember Orders of Operation 3 Formula a SP 2458 30 498 6 32 i Ok to have negative numbers here Unlike for SS b SSx 168 30 2 6 18 c SSy 41406 498 2 6 72 4 r 32 18 72 a r 0 88 b Significance test of r i r value is r observed Step 3 of hypothesis test ii Inferential 1 Non directional a Is the r observed value significantly different from 0 2 Directional a Is r obs sig positive Or b Is r obs sig negative iii Other 4 steps of hypothesis test using shyness example still 1 Hypotheses a Non directional i H0 0 ii H1 0 b Directional i Negative 1 H0 0 2 H1 0 2 Critical Value s for r a Using the new table i df n 2 b r crit 0 729 i Because Negative Directional 3 r obs a 0 88 4 Decision Reject H0 5 Conclusion a The correlation between early socialization and shyness is significantly negative c Criteria for Pearson r significance test i Testing for a relationship between 2 DVs measurements d A note on sample size and correlations i The larger the sample size the smaller the correlation you need 1 Correlations for huge data sets easy to get always must be critical of data e Assumptions for Pearson significance test of r i Interval or ratio data 1 Different test for rank data Spearman a Don t need to know this ii Random Samples of x and y iii

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