Basic Concepts Given n subjects, each of whom is given two treatments where the result of each treatment is assigned one of k categories (including the case where there is only one treatment but each subject is in one of k categories prior to treatment and one of the same categories after the treatment). This … Read More
I am pleased to announce Release 6.3 of the Real Statistics Resource Pack. The new release is now available for free download at Download Resource Pack for Excel 2010, 2013, 2016, 2019, 365 in Windows and Mac environments. The Basics, Distribution, Non-parametric, Regression 1, Multivariate and Time Series examples workbooks have also been revised for compatibility with … Read More
After a significant result from the Chi-square independence test, as described at Independence Testing Follow-up, you can perform follow-up tests to pinpoint the source of the significant result. The approaches used are somewhat similar to the use of contrasts after ANOVA. Post-hoc worksheet functions The following Real Statistics array function is available to assist in … Read More
Basic Concepts When the chi-square test of independence produces a significant result, indicating that it is unlikely that the two variables are independent, it is often desirable to pinpoint which components of the two variables are responsible for the significant result. This can often be done by using additional chi-square tests of independence based on … Read More
I am pleased to announce Release 6.2 of the Real Statistics Resource Pack. The new release is now available for free download at Download Resource Pack for Excel 2010, 2013, 2016 Windows users The version for Excel 2013, 2019 and 365 Mac users will be available shortly. The Basic, Distribution, Non-parameter and Time Series examples workbooks have … Read More
Data Analysis Tool Real Statistics Data Analysis Tool: The two types of independence tests for contingency tables with ordered row an column categories can be performed using the Chi-square Test for Independence data analysis tool. To use this tool for Example 1 of Ordered Independence Testing, press Ctrl-m and select Chi-square Test for Independence from … Read More
The chi-square test of independence described in Independence Testing uses categorical data. If the rows and columns in the contingency table are ordered, this ordering is not taken into account. We now show how to take this order into account. Example Example 1: 127 people who attended a training course were asked to rate their … Read More
On this webpage, we describe Real Statistics’ support for chi-square independence testing with missing data. Worksheet Functions Real Statistics Functions: The Real Statistics Resource Pack provides the following array functions. Here R1 is an m+1 × n+1 array, the last row and last column of which contains counts of missing elements. EM_CHISQ(R1, iter, prec): outputs … Read More
Basic Concepts We now show how to conduct the chi-square test for independence even when there is missing data by using the EM approach described in Contingency Tables with Missing Data. If the row and column variables of a contingency table are assumed to be independent, then we can apportion the missing data using an … Read More
The EM algorithm can be used when a data set has missing data elements. The missing data is estimated using an iterative process where each iteration consists of two steps: (1) an M step (maximization) where parameters are calculated based on the missing data results from the previous E step (or via a guess in … Read More