This document explains how WinCross handles significance testing for both unweighted and weighted data. It provides guidance on using the built-in Significance Testing Tool—originally developed for unweighted data—and outlines how different statistical programs, such as WinCross and SPSS, approach the treatment of weights in testing means and percentages. The paper emphasizes that the WinCross method yields more accurate results, detailing how to input weighted means, standard deviations, and effective sample sizes correctly for reliable analysis.

Authored by Dr. Albert Madansky, this paper compares how WinCross, Quantum, and SPSS compute the standard error of a weighted mean. It explains the theoretical foundation behind each method and demonstrates why WinCross’s approach—using the unweighted variance and effective sample size (b)—provides an unbiased estimate of the variance of a weighted mean. In contrast, SPSS employs a “weighted variance” and the sum of the weights as its sample size, leading to biased results. Through formulas and a practical example, the document shows how these differing methodologies impact hypothesis testing and underscores the statistical rigor of the WinCross approach.

Written by Dr. Albert Madansky, this paper compares how WinCross, SPSS, and Mentor (CfMC) handle significance testing with weighted means. It breaks down the mathematical foundations behind each system’s computation of the standard error and variance, highlighting how these differences affect test accuracy. The document concludes that WinCross’s method—using the unweighted variance and effective sample size—provides the most statistically reliable results, as it produces an unbiased and lower-variance estimate of the true population variance. The paper also demonstrates how to replicate each software’s method using T-Test templates, showing why the WinCross approach is preferred for precise and defensible hypothesis testing.

In this simulation study by Dr. Albert Madansky, 1,000 random samples were generated to compare how WinCross, SPSS, and Mentor estimate the variance of a weighted mean. The results show that both WinCross and Mentor provide unbiased estimates, while SPSS tends to overestimate due to its weighting method. However, WinCross demonstrates a smaller standard deviation in its estimates, meaning its results are consistently closer to the true variance. The paper concludes that the WinCross approach is statistically superior, producing more stable and accurate estimates of weighted variance across repeated samples.

This paper by Dr. Albert Madansky provides a detailed theoretical comparison of how WinCross, SPSS, and Mentor (CfMC) calculate the variance of a weighted mean. It breaks down each program’s mathematical method, explaining the role of effective sample size and weighting bias in determining the accuracy of statistical results. The analysis shows that WinCross and Mentor both produce unbiased estimates, but the WinCross estimator (s²/f) has a smaller variance—making it the more efficient and reliable choice. SPSS, by contrast, applies a biased weighting formula that inflates variance estimates and reduces test precision. The paper mathematically demonstrates why WinCross yields more stable and consistent significance testing outcomes.

This paper by Dr. Albert Madansky examines how to test whether the mean of a subgroup (“part”) differs significantly from that of the total group (“whole”). It compares the WinCross t-test approach with the National Assessment of Educational Progress (NAEP) method. WinCross calculates the variance of the part–whole difference using a formulation that provides greater sensitivity and accuracy, while the NAEP approach produces a larger standard error, leading to fewer detected differences. The analysis shows that the WinCross method more precisely identifies real differences between a subset and its parent population, particularly when the subset is a substantial portion of the total sample.

This paper addresses situations where statistical tests can misleadingly indicate “significant” differences due to overlapping or disproportionate samples. Dr. Albert Madansky explains how comparisons involving shared respondents—or cases where a subset (“part”) makes up almost all or very little of a dataset (“whole”)—can distort test results. The document details both mean and proportion comparisons, showing how variance approaches zero as overlap increases, falsely inflating t or z statistics. To prevent such errors, WinCross automatically flags and suppresses results where overlap exceeds 95% or is below 5%, ensuring that only meaningful differences are reported.

In this paper, Dr. Albert Madansky outlines the correct statistical approach for testing differences between Net Promoter Scores (NPS) across samples. It explains that NPS, derived from “promoters,” “passives,” and “detractors,” follows a multinomial distribution, and that treating these proportions as independent—as many analyses mistakenly do—underestimates the true variance, leading to false significance. The document provides the correct formulas for both unweighted and weighted NPS comparisons, incorporating effective sample size adjustments for accurate variance estimation. It also discusses complex scenarios such as overlapping samples or correlated responses, ensuring researchers apply valid inference techniques when comparing NPS across groups or time periods.