BPK 304W Correlation Correlation Coefficient r Limitations of r

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BPK 304W Correlation Correlation Coefficient r Limitations of r Significance of r Coefficient of Determination

Correlation Coefficient (r) Correlation Coefficient (r) is a measure of association between two variables Varies from -1 to +1 r is a ratio of variability in X to that of Y. 0 = no relationship; 1 = perfect relationship Correlation

Correlation

Linear Fit High Correlation Coefficient does not mean a linear fit

Correlation does not mean causation Spurious Correlations – coincidental correlation between two unrelated variables A study of boys aged 6 to 18 years produced correlations of standing broad jump with other measures. Which had the highest correlation? Correlation

Range of the Data affects the Correlation Coefficient

Correlation coefficient depends upon the orientation of the two groups

Significance of the Correlation Coefficient The critical value of the correlation coefficient is determined by the sample size Bigger sample size = lower critical value of r Statistical significance of r does not infer “practical significance” Correlation

Degrees Probability of Freedom 0.05 0.01 1 .997 1.000 24 .388 .496 2 .950 .990 25 .381 .487 3 .878 .959 26 .374 .478 4 .811 .917 27 .367 .470 5 .754 .874 28 .361 .463 6 .707 .834 29 .355 .456 7 .666 .798 30 .349 .449 8 .632 .765 35 .325 .418 9 .602 .735 40 .304 .393 10 .576 .708 45 .288 .372 11 .553 .684 50 .273 .354 12 .532 .661 60 .250 13 .514 .641 70 .232 .302 14 .497 .623 80 .217 .283 15 .482 .606 90 .205 .267 16 .468 .590 100 .195 .254 17 .575 125 .174 .228 18 .444 .561 150 .159 .208 19 .433 .549 200 .138 .181 20 .423 .537 300 .113 .148 21 .413 .526 400 .098 .128 22 .404 .515 500 .088 .115 23 .396 .505 1,000 .062 .081 Table 2-4.2: Critical Values of the Correlation Coefficient

Coefficient of Determination R squared (r2) The circle represents the total variance in the measure Weight 75% unexplained Correlation of Weight with Arm Girth r = 0.5, r2 = 0.25 Therefore 25% of the variance in weight is explained by arm girth 25% Arm Girth

Correlations between all variables Correlation Matrix Correlations between all variables Weight vs Arm Girth r = 0.5, r2 = 0.25 Weight vs Calf Girth r = 0.6 , r2 = 0 .36 Arm Girth vs Calf Girth r = 0.4 , r2 = 0 .16 Weight Arm Girth Calf Girth