Chi-square test of independence
Categorical × categorical
Pearson chi-square on a contingency table, with Cramér’s V as the effect size. With a weight column, the test uses weighted cell totals and the p-value is approximate for frequency weights.
Statistical methods
The tests, models, scores, and survey measures in the product, in one list. Each entry names the method, where it is used, and what the result contains.
Showing 47 of 47
13 methods
Banner tables and pivots test the cut in front of you. Categorical cells use chi-square and proportion tests. Numeric groups use a mean comparison. The family of tests in one table is Holm-adjusted.
Significance in tables →Categorical × categorical
Pearson chi-square on a contingency table, with Cramér’s V as the effect size. With a weight column, the test uses weighted cell totals and the p-value is approximate for frequency weights.
One category against the others
Each category is collapsed against all remaining categories and tested on its own. This shows which levels carry a categorical association, beyond the omnibus chi-square.
A cell versus a reference
A cell proportion is compared with the total, with its complement, or with another column or row. Pairwise column and row contrasts use a two-proportion z-test. Cohen’s h is the effect size for a difference in proportions.
Each cell of a crosstab
The standardized residual shows how far a cell sits from the count expected under independence. Shading in a banner uses these residuals together with the adjusted p-values.
Pairwise category contrasts
Categories that differ after Holm adjustment are marked with letters, so a stakeholder table can show which columns differ without a matrix of p-values.
Many tests in one table
Cell tests and pairwise contrasts in a banner or crosstab are adjusted with Holm’s step-down procedure. That is the multiple-comparison correction used on these tables.
Two groups, numeric outcome
Compares two group means without assuming equal variance. The effect size is Cohen’s d, using the pooled sample standard deviation.
Three or more groups, numeric outcome
An F test for a difference among group means. Weighted runs use Kish effective sample size for the within-group variance and the error degrees of freedom, and are marked approximate. The effect size is eta-squared.
Small groups, unweighted
A rank-based omnibus test. On unweighted data it is used when at least two groups have fewer than four observations and the raw samples are available. The reported effect size is an eta-squared derived from the H statistic.
After unweighted ANOVA
Pairwise comparisons of group means after a one-way ANOVA, using the studentized range. These pairs are produced for unweighted ANOVA.
Numeric means in a pivot
Pairwise letters for group means inside a numeric pivot, using Fisher’s LSD with Holm adjustment.
Alongside the p-value
Results carry an effect size with the test: Cramér’s V, Cohen’s d, Cohen’s h, eta-squared, or a correlation. Those magnitudes are also banded as weak, moderate, or strong so a long list of tests can be ranked and colored.
Every table and chart
Tables report bases, unweighted and weighted counts, percentages, and an index versus the total. Numeric columns report means and standard deviations, plus medians, quantiles, and box plots where the chart calls for a distribution.
4 methods
Pick one column and every other question is ordered by how strongly it differs across that column. In the table, cell shading uses one of two significance tests, or compares every segment with a column you choose.
Ranked subgroup differences →| When | AddMaple uses |
|---|---|
| Order the questions | The test follows the two column types, as in related columns |
| Significant highs/lows | Each segment versus everyone else, two-proportion z-test |
| Expected vs actual | Standardized residual from the chi-square of independence |
| Compare to column | Each other segment versus a baseline you pick |
One column against the rest of the project
The column you choose is the banner: Ranked differences by that column, as charts or as a table, sorted by significance or left in data order. Each other question is tested with the method for those two column types and ordered by effect size. A coded open-end theme is a categorical column and is ranked with the rest.
A segment versus everyone else
For each answer, a two-proportion z-test compares that segment’s share with the share among everyone else. Holm adjustment is within that answer, across the segments. A shaded cell is higher or lower than the rest of the sample. Cohen’s h is the effect size.
A cell versus independence
The count expected if the banner and the question were independent, from the chi-square on that table. The standardized residual, with a Holm-adjusted p-value within each answer, shows whether that segment’s answer is higher or lower than expected.
Every other segment versus one baseline
Pick the baseline in the control, or click a column header. Total can be that baseline. Each other segment is compared with it on each answer, using a two-proportion z-test. Holm adjustment is within that answer and that baseline. Cohen’s h is the effect size.
3 methods
Pick one column and AddMaple tests it against the other columns in the project, then ranks the pairs by statistical strength. The test follows the two column types. A coded open-end theme is a categorical column and enters the same scan.
How related columns work →| When | AddMaple uses |
|---|---|
| Categorical × categorical | Chi-square, Cramér’s V |
| Numeric outcome, two groups | Welch t-test, Cohen’s d |
| Numeric outcome, three or more groups | One-way ANOVA, eta-squared |
| Unweighted, and two or more groups have fewer than four observations | Kruskal–Wallis |
| Numeric × numeric, both axes within the skew and kurtosis check | Pearson correlation |
| Numeric × numeric, otherwise | Spearman correlation |
One column against the project
Each pair is tested with the method in the table above and ranked by effect size and significance. The list is a shortlist of associations for a later driver model or a focused table.
Linear association
Used when both numeric axes pass a normality heuristic: absolute skew under 1 and absolute excess kurtosis under 2. Weighted Pearson correlations are approximate.
Rank association
Rank correlation for numeric pairs that fail the skew and kurtosis check, including skewed scores and ranks.
6 methods
Key drivers rank many factors against one outcome. Regression estimates a focused relationship between a named predictor and an outcome. Automatic driver selection follows the outcome type, in the order below. These models describe association in the observed data. A causal claim still depends on the study design.
Key driver analysis →| When | AddMaple uses |
|---|---|
| Two-class outcome | Logistic regression |
| Predictive-importance run on a categorical or ordinal outcome | Random Forest |
| Numeric outcome | Elastic Net |
| Ordered outcome with three or more categories | Ordinal Elastic Net |
| Unordered categorical outcome with three or more categories | Multinomial Elastic Net |
Numeric outcome, many predictors
A linear model with both L1 and L2 penalties, so many mixed-type predictors can be ranked without keeping every one. Coefficients keep a sign and a magnitude. The penalty is chosen along a lambda path.
Ordered scales
The same regularized family for an ordered outcome such as an agreement scale or NPS, where the category order matters. It needs at least three ordered categories.
Unordered categories
A regularized model for an unordered outcome with at least three categories. Coefficients are class-specific, so a Likert or multiclass target can show a different driver pattern for each class.
Binary outcome
Fitted by iteratively reweighted least squares. Coefficients are signed log-odds, with an odds-ratio reading and a pseudo-R². Key drivers use it for a two-class outcome. The regression tool uses it for a numeric predictor and a binary outcome, with a fitted curve.
Predictive importance
A classification forest of CART trees split on Gini impurity. Importance is the mean decrease in Gini across splits, and fit is reported with out-of-bag accuracy. Split importance rises for predictors with many distinct values. Direction comes from the coefficient models.
Numeric predictor and outcome
Ordinary least squares in the regression tool. The result shows the fitted line, R², the coefficient, and a confidence interval.
9 methods
Respondents are grouped from the columns you choose. The algorithm follows the variable types and whether you want a fixed number of groups. Quality measures describe the fitted solution. They are computed on the features that built the groups.
Segmentation in the product →Shown as Auto Clustering
Density-based clustering for mixed or categorical data. The number of groups comes from the data. Rows outside a dense region are labelled noise.
Categorical and multi-select indicators
A finite mixture fit by expectation-maximization. Items can be categorical, ordinal treated as categorical, boolean, or multi-select indicators, under a local-independence assumption. Class counts are compared with AIC, BIC, and entropy. Weighted BIC uses Kish effective sample size.
A chosen number of groups
HDBSCAN finds dense regions, then k-medoids fits the number of groups you set. The density labels affect the starting centers. Group sizes are not forced to be equal.
Numeric and opinion scales
Euclidean clustering with a chosen number of groups. Numeric columns can stay raw, be row-centered, or be ipsatized: row-centered and divided by the row standard deviation.
Mixed data, fixed number of groups
A chosen number of groups on mixed survey variables. Centers are real respondents, and the distance is Gower.
Mixed-type clustering
The distance behind k-medoids and the density methods. Numeric and ordinal columns are range-scaled, categorical columns contribute a match or a mismatch, and multi-select columns use Jaccard overlap.
Separation of the fitted groups
Measures how well each respondent sits inside its group versus the neighboring group, on the distance the algorithm used. Compare scores inside one distance family: Euclidean for k-means, Gower for the others.
In-sample check of a partition
A permutation test of whether the fitted groups differ on the distance matrix that produced them. It uses the same features as the clustering, so it describes that fitted partition.
Stability across refits
Agreement between a partition and refits on resamples, adjusted for chance. Reported for k-means, k-medoids, HDBSCAN, and HDBSCAN-seeded k-medoids. Latent class runs are compared with AIC, BIC, and entropy.
3 methods
MaxDiff, TURF, and conjoint run on the live project. MaxDiff and conjoint are aggregate counting models: they pool best, worst, and win counts across respondents, shrink those rates with a Beta prior, and estimate one utility per item or level.
MaxDiff, TURF, and conjoint →Best–worst tasks
Each item gets a best rate and a worst rate, shrunk with a Beta prior. Utility is the difference of the two logit probabilities, centered across items. Preference share is a softmax of those utilities. Share intervals come from a Monte Carlo sample of that uncertainty. Rank by utility, or by best minus worst.
Choice tasks and attribute levels
Each level records wins and exposure across the concepts where it appeared. A Beta prior shrinks the win rate. Part-worths are those logits, centered within the attribute. Importance is the range of part-worths, also shown as a share of the total range. Scenario shares are a softmax of summed part-worths, with Monte Carlo intervals.
Unduplicated reach
Searches item combinations from a multi-select or a set of binary reach columns. A respondent counts toward a combination when they selected at least one of its items. Weights apply to that reach. You choose the combination sizes; the search stops at an evaluation cap.
1 method
A correlated battery of ratings or opinion scales can be summarized as a smaller set of components. The components describe co-movement. They are not a causal model of the outcome.
PCA in the product →Numeric and scale batteries
Correlation PCA. Columns are standardized, the correlation matrix is decomposed, and components are kept with their loadings and the variance they explain. Optional Varimax rotation keeps the components orthogonal and simplifies which questions load where.
5 methods
Standard measures are calculated columns on the project, so the same definition flows into tables, tests, drivers, and segments.
Scores and scales →A 0–10 recommend scale
0–6 are detractors, 7–8 are passives, and 9–10 are promoters. NPS is the percent promoters minus the percent detractors.
Standard experience scores
Calculated columns for CSAT on a 5- or 7-point scale, CES on a 5- or 7-point scale, UMUX-Lite from two items, and UMUX from four items.
Likert and just-about-right scales
Scale polarity produces top-box, bottom-box, and net scores, including top-2 and bottom-2 boxes. A 0–10 scale is recognized as NPS. Just-about-right batteries can be charted as JAR scales.
Multi-item reliability
Coefficient alpha for the items in a scale, with a reliability band, before that score is used as a driver, a segment input, or a headline metric.
A measure you define
Numeric calculated columns for indices and other composites. The formula stays on the project with the columns it reads.
2 methods
A weight can be imported or raked inside the project. Tables, charts, tests, and exports then share that population definition.
Weighted analysis →Raking to target margins
Iterative proportional fitting adjusts respondent weights toward demographic target proportions. The result reports iterations, remaining margin error, the weight range, Kish effective sample size, and weighting efficiency.
Any weighted result
Effective n is the square of the sum of weights, divided by the sum of squared weights. Weighted chi-square uses weighted cell totals and is approximate. Weighted ANOVA uses this effective n for variance and degrees of freedom and is approximate.
1 method
When multiselect brand questions are grouped as a category-entry-point family, AddMaple computes the brand-association measures below. They describe memory structure in the category. They are a different family from a crosstab of the same columns.
Mental availability →Brand × buying situation
Mental penetration is the share of respondents who associate a brand with at least one category entry point. Mental market share, network size, mental advantage, and share of mind summarize how broad and how strong those associations are. The CEP-by-brand matrix compares brands across entry points.