Equivalence Testing:  It is well known that in null hypothesis testing, one can never accept the null hypothesis.  This means that you can never state that two or more groups are equivalent on some outcome.  Yet investigators often desire to assert equivalence.

Meta-Analysis:  ZumaStat provides for meta analyses of percentage differences and of odds ratios.  It applies both fixed effects and random effects models for averaging these statistics. In addition, a test of effect size homogeneity is provided.  In addition, it provides programs for conducting contrast analyses of different study groupings to determine if the average effect size for one group of studies differs from the average effect size for another group of studies.  ZumaStat also provides utilities for weighted least squares regression models predicting effect sizes from study characteristics that are continuous or categorical in nature.  Finally, ZumaStat offers an extensive set of programs for conducting power analysis in meta-analysis (see the complete list of programs in the 'List of Programs' section). These include power analysis for the test of average odds ratios and percent differences, power analysis for contrasts between groups of studies on average odds ratios and percent differences, power analysis of WLS regression analyses of percent differences and power analysis for the Q test of homogeneity for odds ratios and percent differences for a fixed effects model. The programs are easy to use.

Power Analysis: ZumaStat offers power analysis for several common statistical tests. Importantly, it permits you to conduct a power analysis on a coefficient in a multiple logistic regression model, both for the case of a binary predictor and a continuous predictor. Many researchers conduct power analysis on the omnibus effects for an equation. But interest usually is focused on what happens at the level of the coefficients within the model. ZumaStat helps to ensure that you will have adequate statistical power for such tests. You can also do power analysis on the difference between percentages. The utilities allow you to either specify a desired level of power and an effect size and determine the sample size you will need, or you can specify a sample size and an effect size and obtain the statistical power associated with it.

Analysis of Precision: Some researchers focus not on hypothesis testing but rather on magnitude estimation. The focus in this approach is estimating the magnitude of a difference rather than whether that difference is zero or not. When designing a study, you want to make sure that your magnitude estimates will be sufficiently precise and not subject to too much random error. ZumaStat offers utilities for determining sample sizes you should use to minimize sampling error. You provide a confidence interval width that you want to achieve and ZumaStat suggests a sample size for you.

Bonferroni Based Significance Tests:  The classic Bonferroni method for controlling alpha levels across a set of analyses is overly conservative.  Numerous modifications of the procedure have been suggested that maintain the overall alpha level at the desired magnitude but that are statistically more powerful than the traditional Bonferroni method.  ZumaStat describes three such procedures, the Holm method, the Hochberg method and the  False Discovery Rate method and provides the critical p values you need to implement each.

Excel Graphs for Frequency Data:  ZumaStat will create Excel graphs for one way frequency data as well as two way contingency tables based on frequency data that you provide.  The creation of the charts is quick and painless, ready to be cut and pasted into a Word document or some other word processor.  Editing the graphs is easy.  All you need is Excel.

Excel Graphs for Logistic Regression:  ZumaStat also creates Excel graphs to illustrate the shape of a curve for predicted probabilities, predicted odds or predicted log odds for a logistic regression equation.  You can plot up to five equations on a single graph.  Construction of the graphs is simple and this is a great tool for illustrating interaction effects and curve differences.  ZumaStat also includes a plotting strategy for logistic regression equations with quadratic terms. 

Confidence Interval for a Percentage:  ZumaStat calculates the confidence interval for a percentage using the percentage and the sample size as input.  In addition to the method based on traditional asymptotic theory, ZumaStat reports confidence intervals based on the more accurate score method.  ZumStat also performs a significance test against a hypothesized population value (e.g., 50%).

Confidence Interval for a Percentage Difference:  ZumaStat calculates both a significance test and a confidence interval for testing the difference between two percentages.  Both the case of independent and dependent percentages are covered.  For the former, input is the percentages in the two groups and the sample sizes.  For the latter, additional information is required focused on the correlation between the two percentages.

Interaction Analysis of Percentages:  ZumaStat calculates both significance tests and confidence intervals for group differences in percentage differences.  To illustrate a two way interaction, suppose that there are gender differences in the percent of males versus the percent of females who obtain a college degree for African Americans.  Suppose there also is a gender difference in these two percentages for Latinos.  if a researcher wants to test if the gender difference in percentages for African Americans is the same as that for Latinos, then ZumaStat conducts such a test using the sample percentages and sample sizes as input.  ZumaStat also analyzes a three way interaction for percentage differences and provides confidence intervals for all parameter estimates.

Percentage Contrasts:  ZumaStat offers a general routine for conducting single degree of freedom contrasts for percentages from multiple groups, analogous to single degree of freedom contrasts for one way analysis of variance.  Input is the sample percentages and sample sizes.

R x C Contingency Table:  You enter the observed frequencies into a contingency table and ZumaStat will conduct a test of independence for you in addition to many supplementary statistics. 

Confidence Interval for Cramer's V: A common measure of effect size in contingency table analyses is Cramer's V. ZumaStat calculates confidence intervals for this statistic.

Odds Calculator:  ZumaStat offers a simple to use odds calculator that quickly and easily converts between probabilities, odds and log odds.

Confidence Intervals for Odds:  ZumaStat calculates the confidence interval for an odds, using the group odds and sample size as input.

Confidence Intervals for Odds Ratios:  ZumaStat calculates the confidence interval for an odds ratio comparing the odds for two groups.  It also provides a significance test that the ratio of the two odds is 1.0.   ZumaStat uses the odds and the sample sizes for the two groups as input.

Confidence Intervals for Relative Risks:  ZumaStat calculates the confidence intervals  for a relative risk comparing risk probabilities for two groups.  It also provides a significance test that the ratio of the probabilities is 1.0.   ZumaStat uses the risk probabilities and the sample sizes for the two groups as input.

Interaction Analysis of Odds Ratios:  ZumaStat uses commonly reported summary statistics to compare odds ratios for two groups and to conduct three way interaction analysis of odds ratios.  For example if you have calculated an odds ratio for males versus females for African Americans and a similar odds ratio for Latinos, ZumaStat will conduct an analysis of the null hypothesis of equal odds ratios in the two ethnic groups.

Hosmer-Lemeshow Fit Analysis:  A useful procedure for evaluating goodness of fit of a logistic regression model is the Hosmer-Lemeshow test.  This  test is provided in all standard computer packages.  ZumaStat uses output from the test to calculate predicted and observed probabilities for groups divided into deciles based on the predicted log odds scores and generates an Excel scatterplot of them.  The result is a more intuitive sense of the fit of the model, both algebraically and graphically.  The input data are easily "cut and pasted" from the output of an SPSS logistic analysis.

Pseudo R Squared:  A wide number of pseudo R squared indices have been suggested for logistic regression.  ZumaStat calculates some of the better behaved indices that are omitted from many statistical packages.  Input is simple summary statistics from a traditional logistic regression analysis.

Alternatives to the Wald Test: The SPSS logistic regression program tests the significance of a logistic coefficient using the Wald test. This test has been found to behave badly under some circumstances. ZumaStat offers a utility that tricks SPSS into printing a likelihood ratio test and an exact conditional scores test for each coefficient in addition to the Wald test. You must have SPSS for this utility to work.

Predicted Values in Logistic and Probit Regression:  Enter a logistic or probit equation once and then calculate predicted log odds, predicted odds, and/or predicted probabilities for a wide range of predictor profiles.  ZumaStat will accommodate equations with up to 1,000 predictors.