• ### Analysis Tool: Significance of Difference Between Correlation Coefficients

Using the Fisher r-to-z transformation, this page will calculate a value of z that can be applied to assess the significance of the difference between two correlation coefficients, r_a and r_b, found in two independent samples. If r_a is greater than r_b, the resulting value of z will have a positive sign; if r_a is smaller than r_b, the sign of z will be negative.

• ### Analysis Tool: Resampling Probability Estimates for the Difference

Given two independent samples of sizes n_a and n_b, this page will estimate the significance of the difference between the means of the samples, based on multiple random re-sortings of the values that have been entered for samples A and B. As the page opens, you will be prompted for the sizes of the two samples.

• ### Analysis Tool: The Confidence Interval of rho (Multiple Regression)

This page will calculate the 0.95 and 0.99 confidence intervals for rho, based on the Fisher r-to-z transformation. To perform the calculations, enter the values of r and n in the designated places, then click the "Calculate" button. Note that the confidence interval of rho is symmetrical around the observed r only with large values of n.

• ### Analysis Tool: Estimating the Population Value of rho

This page will perform the procedure for up to k=12 sample values of r, with a minimum of k=2. It will also perform a chi-square test for the homogeneity of the k values of r, with df=k-1. The several values of r can be regarded as coming from the same population only if the observed chi-square value proves the be non-significant.

• ### Analysis Tool: Significance of Difference between Sample r and Hypothetical Value of rho

Using the Fisher r-to-z transformation, this page will calculate a value of z that can be applied to assess the significance of the difference between r, the correlation observed within a sample of size n and rho, the correlation hypothesized to exist within the population of bivariate values from which the sample is randomly drawn. If r is greater than rho, the resulting value of z will have a positive sign; if r is smaller than rho, the sign of z will be negative.

• ### Analysis Tool: Significance of a Correlation Coefficient

To assess the significance of any particular instance of r, enter the values of N[>6] and r into the designated cells, then click the 'Calculate' button. Application of this formula to any particular observed sample value of r will accordingly test the null hypothesis that the observed value comes from a population in which rho=0.

• ### Analysis Tool: t-Test for Correlated Samples

This calculator returns the value of t for the difference between the means of two correlated samples, for sample sizes up to 10. Users are prompted for sample size as the page opens. It will also calculate various summary statistics for the two samples.

• ### Analysis Tool: Single Sample t-Test

This page will perform a t-test for the significance of the difference between the observed mean of a sample and a hypothetical mean of the population from which the sample is randomly drawn. The user will be asked to specify the sample size as the page opens.

• ### Analysis Tool: 2x2 Contingency Table (Version 1)

For a table of frequency data cross-classified according to two categorical variables, X and Y, each of which has two levels or subcategories, this page will calculate the Phi coefficient of association; perform a chi-square test of association, if the sample size is not too small; and perform the Fisher exact probability test, if the sample size is not too large. For intermediate values of n, the chi-square and Fisher tests will both be performed.

• ### Analysis Tool: t-Test for Independent or Correlated Samples

This page will compute the t-test for either correlated or independent samples. One may copy and paste data in or type the data in individually.