Correlations and Regressions
Can use correlation/regression with either manipulated predictor variables or natural variation.
Correlational statistics can be applied to any type of design (including experimental) but a correlational design occurs when we do not randomly assign participants to the level of either variable - i.e., levels of variables are not manipulated.
Quasi-analytic experiments: Steps in conducting correlational designs
1) select population and subjects of interest;
2) measure variables of interest;
3) calculate the extent to which the variables are systematically related
Pearson's product moment correlation coefficient (for Interval or ratio data) measures the direction and degree of association. r is the mean of z-score cross-products: r=
S (ZxZy)/N, the extent to which deviations from the average on each measure are similar for each subject sampled.r2 (coefficient of determination) = estimate of the proportion of variance shared by the two variables; extent to which they co-vary. (Can be used as a measure of effect size.)
1-r2: coefficient of nondetermination (also called coefficient of alienation or error variance)
Statistical inference: for a given sample size: larger the absolute value of r, the less likely it is to have occurred by chance, similarly, for a given value of r, the larger the sample, the less likely it was to have occurred by chance. The power of a correlational design is increased by minimizing error variance, avoiding restricting the range of scores, and increasing the sample.
Pearson's r (based on means) is very sensitive to the presence of outliers, heteroscedasticity (rXY relationship may vary across levels of X), and can be biased by having a restricted range. Combining group data can also influence the size of the correlation (in either direction). So: examine scatterplots to detect these potential problems!!
Visual inspection of data
Graph data (scatterplot): predictor (assumed causal or IV) variable on abscissa (X-axis) and criterion or DV on ordinate (Y-axis)