Pearson Product-Moment Correlation ..

The Pearson correlation is appropriate only when bothvariables lie on an ordinal scale.
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the Pearson correlation, the null hypothesis states Choose ..

The polychoric correlationcoefficient is the maximum likelihood estimate of the product-momentcorrelation between the normal variables, estimating thresholds fromthe observed table frequencies.

The Spearman correlation coefficient is computed using rank scores  and , defined in the section .
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Tests on Many Correlation Coefficients ..

PROC FREQ also computes the exact test for the hypothesisthat the Spearman rank correlation equals zero when you specify the SCORR option in the EXACT statement.

It has the range .The Spearman correlation coefficient is computed aswith
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where ej is the j error. D-W takes values within [0, 4]. For no serial correlation, a value close to 2 is expected. With positive serial correlation, adjacent deviates tend to have the same sign, therefore D-W becomes less than 2; whereas, with negative serial correlation, alternating signs of error, D-W takes values larger than 2. For a least-squares fit where the value of D-W is significantly different from 2, the estimates of the variances and covariances of the parameters (i.e., coefficients) can be in error, being either too large or too small. The serial correlation of the deviates arise also time series analysis and forecasting. You may use the JavaScript to check this condition.

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Type I and type II errors - Wikipedia

There are two points to be made with the above numbers: (1) the correlation coefficient is invariant under a linear transformation of either X and/or Y, and (2) the slope of the regression line when both X and Y have been transformed to z-scores is the correlation coefficient.

CORRELATION - Missouri State University

The Pearson correlation describes the strength of the linearassociation between the row and column variables, and it is computedusing the row and column scores specified by the SCORES= option inthe TABLES statement.

An introductory statistics text for the social sciences

The scatterplots presented below perhaps best illustrate how the correlation coefficient changes as the linear relationship between the two variables is altered. When r=0.0 the points scatter widely about the plot, the majority falling roughly in the shape of a circle. As the linear relationship increases, the circle becomes more and more elliptical in shape until the limiting case is reached (r=1.00 or r=-1.00) and all the points fall on a straight line.

Significance Tests / Hypothesis Testing - Jerry Dallal

The two-sided -value is computed asExact tests are available for two measures of association, thePearson correlation coefficient and the Spearman rank correlationcoefficient.

Significance Tests / Hypothesis Testing

PROC FREQ also computes the exact test for the hypothesisthat the Pearson correlation equals zero when you specify the PCORR option in the EXACT statement.