Chi-Square and G-Square Test of Independence, Power and Residual Analysis, Measures of Categorical Association

Provides the facility to perform the chi-square and G-square test of independence, calculates the retrospective power of the traditional chi-square test, compute permutation and Monte Carlo p-value, and provides measures of association for tables of any size such as Phi, Phi corrected, odds ratio with 95 percent CI and p-value, Yule' Q and Y, adjusted contingency coefficient, Cramer's V, V corrected, V standardised, bias-corrected V, W, Cohen's w, Goodman-Kruskal's lambda, and tau. It also calculates standardised, moment-corrected standardised, and adjusted standardised residuals, and their significance, as well as the Quetelet Index, IJ association factor, and adjusted standardised counts. It also computes the chi-square-maximising version of the input table. Different outputs are returned in nicely formatted tables.

chisquare package history

vers 1.1.1:

• Minor changes. Updated DESCRIPTION file formatting: (1) Removed version specifications for base R packages (graphics, stats), (2) Updated R version dependency format.
• No functional changes to the package.

vers 1.1:

• Cramer's V max is now returned and reported in the last rendered table;
• Chi-square max is now reported in the last rendered table;
• 95 percent confidence interval for Yule'Q and Y added;
• Error in the computation of the CI around Yule's Y fixed;
• Haldane-Anscombe correction extended to the computation of Yule's Q and Yule's Y;
• Amended y-axis label for the plot of odds ratios: from Odds Ratios to Odds Ratio;
• Fix to the main label of the odds ratios plot: the confidence interval reported in the title now updates according to the significance level selected via the or.alpha parameter;
• Enhancements to the last rendered table: tests, association measures, and other results are now grouped into sub-sections;
• Returned association measures organised into groups consistent with the grouping featuring the last rendered table;
• Goodman-Kruskal's Gamma and Cohen's k discontinued;
• Updates, fixes, and minor improvement to the help documentation.

vers 1.0:

• Chi-square-maximising table added; it is returned and rendered;
• Ancillary function to compute the Chi-square-maximising table added;
• Chi-squared value computed on the Chi-square-maximising table is returned and reported in the annotation of the rendered chi-square-maximising table; it is also reported in the last rendered table;
• Cramer V corrected added; it is returned and reported in the first and last rendered tables;
• Phi.max in now returned and reported in the last rendered table;
• Changes and fixes to the ancillary function for the computation of phi.max, which was producing a wrong value in some instances;
• Standardised version of the input table added; it is returned and rendered;
• Internal ancillary function for the computation of the standardised tables added (based on Iterative Proportional Fitting);
• New parameters added to allow the user to select the type of target marginals to be used for table standardisation;
• Cramer's V computed on the standardised table added;
• 1-(Cramer's V/Cramer's V standardised) added;
• Verbal articulation of the strength of the association measured by Yule's Q added;
• Yule's Y, its p-value, and the verbal articulation of the strength of the association added;
• Independent odds ratio returned and rendered for tables larger than 2x2;
• Odds ratio, Yule's Q, and Yule's Y added to annotations in the first rendered table;
• Quetelet index and IJ association factor added: they are returned and also rendered in two dedicated tables;
• Table of adjusted standardised counts added: it is returned and rendered in a dedicated table;
• The object "residuals" contained in the returned list has been renamed as "post.hoc";
• In the first rendered table, the report of the symmetric corrected Goodman-Kruskal's lambda replaced by the report of the (uncorrected) lambdas;
• Minor modification in the style of the annotations in the first rendered table: Italics has been dropped to enhance readability. It has been kept in the last part of the annotation, where suggestions as to the "best" chi-squared analysis are given;
• Help documentation updated content-wise, with some layout restructing.

vers 0.9:

• Calculation of the power of the traditional chi-square test added;
• Parameter 'power.alpha' added to allow the user to set the alpha level used for the power calculation;
• First and last rendered table updated to reflect the added power calculation;
• In the first and last rendered table, the report of the (N-1)/N-corrected chi-square test has been moved up and placed right after the traditional chi-square test, and right before the report of the permuted and Monte Carlo version of the test;
• Same as above for the list of results returned by the function;
• The list of the returned results has been updated to report the power of the traditional chi-square test;
• Default value of the 'tfs' parameter reduced to 13;
• Fixes, improvements, and updates to the help documentation.

vers 0.8:

• Permutation-based p-value for the chi-squared statistic added;
• The calculation of the p-value for the permutation-based and Monte Carlo method has been modified from (1+sum(chistat.simulated>=chisq.stat)) / (B+1) to sum(chistat.simulated>=chisq.stat)/B;
• The optional plot of the permutation distribution of the chi-square statistic has been added;
• The option of plotting the permutation and the Monte Carlo distribution side-by-side has been added;
• In the plot showing the distribution of the Monte Carlo chi-squared values, the main and sub title have been amended: reference to "permutation" has been changed to "Monte Carlo";
• The minimum and the average expected count are now reported in the last rendered table;
• An annotation has been added to the first rendered table in order to give suggestions as to the selection of the most "reliable" chi-square result on the basis of different criteria (following literature; see help documentation);
• In the first rendered output table, the items featuring the annotation at the bottom of the table have been grouped and separated by an empty line to enhance readability;
• Unlike version 0.7, for determining the magnitude of the association expressed by Cadj, Cramer's V, and V biased-corrected, the coefficients are not internally converted to Cohen's w, but the Cohen's thresholds for small, medium, and large effect are dinamically internally computed on the basis of the table's df;
• For consistency, the indication of the magnitude of the association for the W coefficient is now based on the Cohen's thresholds, using the same procedure employed for Cadj, Cramer's V, and V biased-corrected;
• Scholarly literature about the average expected count added to the help documentation;
• Help documentation updated and improved content-wise.

vers 0.7:

• Indication of effect size added to Phi, Phi signed, Phi corrected, Cadjusted;
• Changes and fix in the method underlying the indication of the effect size for Cramer's V and bias-corrected V; these changes (following Sheskin 2011) allow to provide indication of effect size for tables of any size;
• Wald 95 percent confidence interval around the Monte Carlo (permutation-based) chi-square p-value added;
• The 95 percent CI around the permuted p-value is reported in the annotations at the bottom of the first produced table, and in the Analysis report table;
• Phi-corrected added;
• W coefficient added (including magnitude of effect size and bootstrap 95% CI);
• W is also reported in the annotation at the bottom of the first tables produced by the function;
• Corrected version of Goodman-Kruskal's lambda (both aymmetric and asymmetric) added;
• In the annotations at the bottom of the first table produced by the function, Goodman-Kruskal symmetric lambda has been replaced by its corrected version for its ability to addresses skewed or unbalanced marginal probabilities which create problems to the traditional lambda;
• The magnitude of the effect indicated by the odds ratio (introduced in ver. 0.6) is not returned anymore, but only reported in the Analysis report table for consistency with other effect size magnitude indication;
• Labels used for the magnitude of effect size slightly modified to enhance clarity and consistency;
• The returned results are organised into a nested list format for better clarity and accessibility: input.table, chi.sq.related.results, G.square, residuals, chi.sq.based.assoc.measures, and non.chi.sq.based.assoc.measures;
• Help documentation updated and improved content-wise;
• An error in the help documentation has been amended: the adjusted chi-square statistic was described as produced by "dividing" the chi-square value by (N-1)/N; "dividing" was meant to read "multiplying";
• Relevant scholarly references added.

vers 0.6

• chi-square test adjusted by the (N-1)/N correction added;
• magnitude of the effect size as indicated by the odds ratio added;
• help documentation updated, and improved content-wise;
• relevant scholarly references added.

vers 0.5

• the plot of odds ratios is now returned for cross-tabs featuring 2 rows and at least 2 columns;
• to enhance consistency and clarity, the parameter 'row_category' has been renamed to 'row.level'; the parameter 'reference_level' has been renamed to 'reference.level';
• Haldane-Anscombe correction added in the calculation of odds ratio;
• to improve clarity, minor adjustments have been carried out to the error messages returned when the parameter 'plot.or' is 'TRUE' but the input cross-tab does not meet the needed requirements (2xk, where k >= 2);
• help documentation updated and improved content- and layout-wise.

vers 0.4

• the facility to plot the odds ratios and 95% confidence intervals for table of size 2xk (where k>2) has been added;
• the above added facility rests on a new internal function (visualize_odds_ratios);
• amendments and updates to the help documentation.

vers 0.3

• Moment-corrected standardized residuals added;
• 95% confidence interval for Cramer's V added;
• The output version of the input cross-tabulation now reports some essential analytical results in an annotation at the bottom of the table;
• Fix to the output version of the input cross-tabulation when cells feature a frequency of 0;
• The Goodman-Kruskal's tau reported in previous versions is now indicated as "columns dependent"", and the "row dependent" version of the same coefficent is now calculated and reported.

vers 0.2

• Relative contributions to the chi-square added;
• Contributions to the chi-square previously reported in ver_0.1 are now called absolute contribution;
• Bibliographical reference added for the abovementioned contributions;
• Significance level of the reported standardized and adjusted standardized residuals can be corrected using the Sidak's alpha adjustment method;
• G-square test added;
• Symmetric Goodman-Kruskal's lambda and Goodman-Kruskal's tau added;
• Cohen's k (with 95% CI) added;
• Odds ratio (with p value and 95% CI) added (for 2x2 tables);
• Effect size for Cramer's V and Cramer's V bias-corrected added to the table of the test's results; returned for tables with up to 5 degrees of freedom according to Cohen 1988;
• Degrees of freedom added to the output table reporting the test's result;
• The distribution of the permuted chi-square statistic can be optionally plotted;
• Fix in the calculation of the cells contribution (in percent) to the chi-square;
• Output tables formatted using the 'gt' package instead of 'formattable';
• Option added to customize the font size of the output tables;
• Improvements to the content and layout of the help documentation.

vers 0.1

first release to CRAN