When data is organized in the form of a contingency table where the two categorical independent variables (corresponding to the row and columns) are ordered, then we can calculate a polychoric correlation coefficient. This coefficient is an approximation to what the Pearson’s correlation coefficient would be if we had continuous data. For a 2 × … Read More
I am pleased to announce Release 4.14 of the Real Statistics Resource Pack. The new release is now available for free download at Download Resource Pack for Excel 2007, 2010, 2013 and 2016 (Windows version) environments. Note that now there are three versions of the software: one for Excel 2013/2016, another for Excel 2010 and a third … Read More
I am pleased to announce Release 4.6 of the Real Statistics Resource Pack. The new release is now available for free download (Download Resource Pack) for Excel 2010, 2013 and 2016 (Windows version) environments. It will be available tomorrow for Excel 2007 users. The spreadsheets for all the examples used on the Real Statistics website, including … Read More
Introduction We now show how to perform post-hoc testing using Tukey’s HSD for two-factor ANOVA. This means that we will assume that we are dealing with a balanced model. As described in Tukey HSD for One-way ANOVA (see Unplanned Comparisons) two means are significantly different if where the critical values qcrit are presented in the Studentized Range q Table based … Read More
I am pleased to announce Release 4.0 of the Real Statistics Resource Pack. The new release is now available for free download (Download Resource Pack) for Excel 2007, 2010 and 2013 environments. The Real Statistics Examples Workbook and Real Statistics Multivariate Examples Workbook have both been updated for capability with the new release and can be downloaded for free. The Real Statistics website … Read More
Basic Concepts The same approach used to calculate a confidence interval for the effect size of a t test (see Confidence Intervals for Power and Effect Size of t Test) can be employed to create a confidence interval for a noncentrality parameter, and in turn Cohen’s effect size and statistical power, for a chi-square goodness … Read More
Introduction For completeness, we now present another non-parametric replacement for one-way ANOVA, namely Mood’s Median Test. This test is essentially an extension of the Sign Test to two or more variables. We have already described this test for two independent variables in Mood’s Median Test for Two Samples. The Kruskal-Wallis test has more power and … Read More
Basic Concepts The Mood’s Median Test, essentially a two-sample version of the Sign Test, is used to determine whether the medians of two independent samples are equal (the null hypothesis). To perform this test, you need to execute the following steps: Calculate the median m of the combination of the two samples. Create a 2 × 2 … Read More
Basic Concepts The power of the goodness of fit or chi-square independence test is given by where F is the cumulative distribution function (cdf) for the noncentral chi-square distribution χ2(df), xcrit is the χ2(df) critical value for the given value of α and λ = w2n = χ2 is the noncentrality parameter where w is the φ effect … Read More
The following is a summary of all the multivariate functions provided in the Real Statistics Resource Pack. These functions are organized into the following categories: Multivariate normal distribution Mahalanobis Distance and Outliers Hotelling T2 One-way MANOVA Two-way MANOVA Permutational MANOVA Box’s Test Extraction Factor Analysis Cluster Analysis Jenks Natural Breaks Discriminant Analysis Correspondence Analysis Gaussian … Read More