# Correlations. Captures how the value of one variable changes when the value of the other changes Use it when: Test the relationship between variables.

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Correlations

Captures how the value of one variable changes when the value of the other changes Use it when: Test the relationship between variables Only two variables at a time

Ranges from -1 to +1 A Pearson correlation is based on continuous variables Important to remember this is a relationship for a group, not each person Reflects the amount of variability shared by two variables

r xy = n ΣXY - ΣX ΣY [n ΣX 2 – (ΣX) 2 ][n ΣY 2 - (ΣY) 2 ] r xy = correlation coefficient between x & y n = size of sample X = score on X variable Y = score on Y variable

A study of the relationship between years of post-high school education and income (in 1,000s) ParticipantsYrs EducationIncome 1015 21 3320 4425 5430 6635

1. State hypotheses Null hypothesis: no relationship between years of education and income ρ education*income = 0 Research hypothesis: relationship between years of education and income r education*income 0

r xy = n ΣXY - ΣX ΣY [n ΣX 2 – (ΣX) 2 ][n ΣY 2 - (ΣY) 2 ] r xy = correlation coefficient between x & y n = size of sample X = score on X variable Y = score on Y variable

6. Determine whether the statistic exceeds the critical value.95 >.81 &.92 So it does exceed the critical value 7. If over the critical value, reject the null & conclude that there is a relationship between years of education and income

In results There was a significant positive correlation between years of education and income, such that income increased as years of education increased, r(4) =.95, p <.05 (can say p <.01).

Even though you may suspect theres a causal relationship you can only make causal statements if: X definitely preceded Y X was manipulated so that it was the only probable factor that could cause changes in Y When talking correlations, you can use relationship, relate, associated

Years of Education Income (in 1,000s)

yrsedincome yrsedPearson Correlation 1.95(***) Sig. (2-tailed).000 N 6 6 incomePearson Correlation.95(***)1 Sig. (2-tailed).000 N 66

.80 to 1.0Very strong.60 to.80Strong.40 to.60Moderate.20 to.40Weak.00 to.20Weak/ None

Coefficient of Determination Percentage of variance in one variable that is accounted for by variance in the other Square the correlation coefficient If r =.70 r 2 =.49 49% of variance is shared (or variance in one is explained by variance in other)

Cases/ people will have different scores on measures Correlations reflect the extent to which peoples scores tend to move together Variables are correlated if they share variability So coefficient of determination estimates how much of the differences among people on one measure is associated with differences among people on the other measure

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