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 Distributions of x and y must be normal iv The x y relationship must be linear f Important concepts on Correlation i Pearson only for Linear relationships 1 Make a scatterplot first If appears curvilinear use different test ii Restriction of range 1 Performance and Motivation a Researchers only getting part of the picture leads to incorrect conclusion from data observed iii Effects of outliers 1 Could give you significantly positive or negative data even if there is no correlation a Skew the data b Make scatter plot first i Run test with outliers included ii Run test with outliers excluded 1 If vastly different use excluded version iv Correlation and Causation 1 Violent Video Games and Aggression a 3 possible scenarios we don t know which i x causes y ii y causes x iii z causes x and y b It s not that causation doesn t exist we just cannot determine which one is occurring v Coefficient of determination 1 r squared a Amount of variability in y that can be explained by variability in x i Shyness Ex 1 0 88 2 0 774 2 77 of the variance in Shyness y can be explained by the variability in Early Socialization x a Think Pie Graph i 33 unexplained variance II Regression a Scatterplots and regression lines i Scatterplots tell us about direction and degree of relationship 1 Summarize this relationship using a regression line ii Line of best fit minimizes distance between actual y and predicted y yhat 1 Linear equation y hat bx a a b slope b a y intercept iii What will regression line be able to tell us 1 Direction of relationship 2 Degree of relationship a Amount of scatter around line 3 Prediction predict y for a given x 4 Measure of central tendency average degree of relationship iv Finding the regression line 1 Best fir minimize distance between y and y hat least squared error solution 2 Thing ok y y hat as a deviation score a Find average deviation but square so deviations don t sum v Regression equation does NOT tell us about the accuracy of predictions 1 The same regression line could be linked to different levels of prediction accuracy a Ex Varying degree of amounts of scatter but same line used i Standard error of estimate SEE is related to correlation value 1 Measures amount of scatter between line and points a The lower SEE the more accurate the regression line smaller amount of distance between point and line 2 Higher r lower SEE better fitting regression line

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