# Analysis Tools

• ### Analysis Tool: The Power of the Chi-Square Goodness of Fit Test (Monte Carlo Simulation)

In the first simulation, random samples of size n are drawn from the population one sample at a time. With df=3, the critical value of chi-square for significance at or beyond the 0.05 level is 7.815; hence, any calculated value of chi-square equal to or greater than 7.815 is recorded as "significant," while any value smaller than that is noted as "non-significant." The second simulation does the same thing, except that it draws random samples 100 at a time. The Power of the Chi-Square "Goodness of Fit" Test pertains to the questionable common practice of accepting the null hypothesis upon failing to find a significant result in a one- dimensional chi-square test.

• ### Analysis Tool: Confidence Interval for the Estimated Mean of a Population

Given a sample of N values of X randomly drawn from a normally distributed population, this page will calculate the .95 and .99 confidence intervals (CI) for the estimated mean of the population.

• ### Analysis Tool: Basic Linear Correlation and Regression (Data-Import Version)

The following pages calculate r, r-squared, regression constants, Y residuals, and standard error of estimate for a set of N bivariate values of X and Y, and perform a t-test for the significance of the obtained value of r. Allows for import of raw data from a spreadsheet; for samples of any size, large or small.

• ### Analysis Tool: Spearman Rank Order Correlation Coefficient

This page will calculate r_s , the Spearman rank- order correlation coefficient, for a bivariate set of paired XY rankings. As the page opens, you will be prompted to enter the number of items for which there are paired rankings. If you are starting out with raw (unranked) data, the necessary rank-ordering will be performed automatically.

• ### Analysis Tool: Basic Linear Correlation and Regression (Direct-Entry Version)

The following pages calculate r, r-squared, regression constants, Y residuals, and standard error of estimate for a set of N bivariate values of X and Y, and perform a t-test for the significance of the obtained value of r. Values of X and Y are entered directly into individual data cells. This page will also work with samples of any size, though it will be rather unwieldy with samples larger than about N=50. As the page opens, you will be prompted to enter the value of N.

• ### Analysis Tool: Friedman Test for k = 3

Nonparametric test for the significance of the difference among the distributions of k correlated samples (A, B, etc., each of size n) involving repeated measures or matched sets. As the page opens, you will be prompted to enter the value of n. The necessary rank- ordering of your raw data will be performed automatically.

• ### Analysis Tool: Friedman Test for k = 4

Nonparametric test for the significance of the difference among the distributions of k correlated samples (A, B, etc., each of size n) involving repeated measures or matched sets. As the page opens, you will be prompted to enter the value of n. The necessary rank- ordering of your raw data will be performed automatically.

• ### Analysis Tool: Kruskal-Wallis Test for K = 3

As the page opens, you will be prompted to enter the sizes of your several samples. If you are starting out with raw (unranked) data, the necessary rank- ordering will be performed automatically.

• ### Analysis Tool: Kruskal-Wallis Test for K = 4

As the page opens, you will be prompted to enter the sizes of your several samples. If you are starting out with raw (unranked) data, the necessary rank- ordering will be performed automatically.

• ### Analysis Tool: 4x4 Orthogonal Latin Square with Restricted Full Rank Model (One Measure per Cell)

In the Latin Square computational pages on this site, the third IV, with levels designated as A, B, C, etc., is listed as the "treatment" variable. The analysis of variance within an orthogonal Latin Square results in three F-ratios: one for the row variable, one for the column variable, and one for the third IV whose j levels are distributed orthogonally among the cells of the rows x columns matrix.