# Resource Library

#### Statistical Topic

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• ### 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: 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: 2x2 Contingency Table (Version 2)

This page will calculate standard measures for Rates, Risk Ratio, Odds, Odds Ratio, and Log Odds. It will also 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.

• ### Analysis Tool: Analysis of Covariance (one-way)

These pages will perform an analysis of covariance for k independent samples, where the individual samples, A, B, etc., represent k quantitative or categorical levels of the independent variable; DV = the dependent variable of interest; and CV = the concomitant variable whose effects one wishes to bring under statistical control. The pages in this first batch require the direct entry of data, item by item, and as they open you will be prompted to enter the size of the largest of your several samples. The pages in this second batch allow for the import of data from a spreadsheet via copy and paste procedures.

• ### Analysis Tool: Analysis of Covariance Model (two-way)

These pages will perform a factorial analysis of covariance for RxC independent samples, cross-tabulated according to two independent variables, A and B, where A is the row variable and B the column variable; DV = the dependent variable of interest; and CV = the concomitant variable whose effects one wishes to bring under statistical control. As the pages open, you will be prompted to enter the size of the largest of your several samples.

• ### Analysis Tool: Normal Distribution

Generate a graphic and numerical display of the properties of the Normal Distribution. For a unit normal distribution, with M=0 and SD=Œ±1, enter 0 and 1 at the prompt. For a distribution with M=100 and SD=Œ±15, enter 100 and 15. And so forth

• ### Analysis Tool: Chi-Square, Cramer's V, and Lambda for an RxC Contingency Table

This calculator performs the following for a contingency table up to 5x5: chi-square analysis; Cramer's V; two asymmetrical versions of lambda; the Goodman-Kruskal index of predictive association; other measures relevant to categorical prediction. Key Word: Categorical Analysis.