Variance of a single variable represents the average amount that the data vary from the mean. The cross-product deviation multiplies the deviation for one variable by the corresponding deviation for the second variable. The average value of the cross-product deviation is the covariance. This is an averaged sum of combined deviation. It uses the following formula:A positive covariance indicates that if one variable deviates from the mean, the other variable deviates in the same direction. A negative covariance indicates that if one variable deviates from the mean, the other variable deviates in the opposite direction. Covariance is not standardized and depends on the scale of measurement. The standardized covariance is the correlation coefficient and is calculated using the following formula:A correlation coefficient of values 0.1 represents a small effect. Values of 0.3 represent a medium effect and values of 0.5 represent a large effect. In order to test the null hypothesis of the correlation, namely that the correlation is zero, z-scores can be used. In order to use the z-scores, the distribution must be normal, but the r-sampling distribution is not normal. The following formula adjusts r in order to make the sampling distribution normal:The standard error uses the following formula:This leads to the following formula for z:The null hypothesis of correlations can also be tested using the t-score with degrees of freedom N-2:The confidence intervals for the correlation uses the same formula as all the other confidence intervals. These values have to be converted back to a correlation efficient using the following formula:CORRELATIONNormality in correlation is only important if the sample size is small (1), there is significance testing (2) or there is a confidence interval (3). The assumptions of correlation are normality (1) and linearity (2). The correlation coefficient squared (R2) is a measure of the amount of...