Psych 311 1nd Edition Lecture 20 Outline of Last Lecture I Correlation II Pearson Correlation Coefficient r III Formulas Outline of Current Lecture I II III IV Recall Mapping onto Generic Test Stat Formula Coefficient of Determination r 2 HT using r Current Lecture I Recall Covarience the extent to which two variables vary together calculated with SP sum of products of deviation SS the variability of a single variable r SP SSx SSy r the degree to which two variables vary together the degree to which two variables vary separately II Mapping onto Generic Test Stat Formula Test observed or obtained difference due to IV different due to SE r and test have same logic with different wording r test observed or obtained relationship naturally occurring variability in each variable When r 0 then x and y are not related rule smaller closer to 0 the value for r the more likely we are to FTR our Ho if covariance numerator 0 then the numerator 0 and r 0 If r 1 00 strongest relationship then x and y are perfectly related this will never occur in psych research As r approaches 1 00 the more likely it is that we ll reject Ho reject Ho means there is a real and true relationship between x and y 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 FTR Ho means there is no relationship between x and y If every change in x is accompanied by a consistent one to one change in y then the variability in x is completely shared with y numerator the numerator and denominator measure the same thing III Coefficient of Determination r 2 Effect size measure for r Specifies the proportion of variability in one variable that can be determined from its relationship with the second variable degree of overlap between two variables 100 of the variance in x is explained by its relationship with x 100 of the variance in y is explained by its relationship with y r 2 is the percentage of variance shared between x and y Effect size Small 0 01 r 2 0 09 Medium 0 09 r 2 0 25 Large r 2 0 25 IV HT using r A researcher wants to know whether the number of ads for candy brand x is related to the number of packages y for candy x people purchase Possible explanations 1 due to SE two samples that just happen to be related 2 there is a true relationship between x and y Step 1 State hypothesis and set Ho 0 H1 0 0 05 non directional two tailed test Step 2 Set critical level reference comparison distribution Distribution of Covarience n 5 df npairs 2 df 5 2 df 3 Step 3 Collect data and compute r Person Ads Packages 1 5 8 2 4 9 3 4 10 critical level 0 876 4 6 13 5 8 15 Mads 5 4 Mpackages 11 r SP SSx SSy SSads 11 2 r 13 2 11 2 34 SSpackages 34 SP 13 2 r 0 67 Step 4 Make decision We fail to reject our Ho because our r 0 67 which is not within our critical region Therefore we conclude that there is no relationship between the number of ads watched and the number of packages purchased Step 5 Compute effect size r 2 0 67 2 r 2 0 46 Since 0 46 indicates a large effect size and we had failed to reject our Ho we have computed a Type II Error