Descriptive Statistics

Analyze → Descriptive Statistics. These six procedures summarise a dataset before you model it: how each variable is distributed, how categorical variables relate, and where the holes in it are. They are the right first stop for any new dataset.

Frequencies

When to use it. To see how often each value of a categorical (or coarse-numeric) variable occurs.

Dialog. Move one or more variables into Variables. Optional statistics (mean, median, quartiles) and a bar/pie chart can be requested.

Output. One frequency table per variable: each value, its count, percent, valid percent (excluding missing) and cumulative percent.

Example. StudyZone and SmokingStatus from the sample data each yield a table of category counts — e.g. how many participants are from each region, and the split of Never/Former/Current smokers.

Descriptives

When to use it. To get the standard summary statistics for scale variables side by side.

Dialog. Move scale variables into Variables. The Options section lets you choose which statistics appear (mean, SD, variance, range, min, max, S.E., skewness, kurtosis) and whether to save standardised (z) scores as new variables.

Output. A single Descriptive Statistics table: one row per variable with N, minimum, maximum, mean and standard deviation (plus any extras you enabled).

Example. Age, BMI, SystolicBP, FastingGlucose_mmolL → a compact table of their valid N, range, mean and SD.

Explore

When to use it. For a deeper look at a scale variable's distribution, on its own or split by a factor — including normality and outliers.

Dialog. Put the scale variable(s) in Dependent List and an optional grouping variable in Factor List.

Output.

• Descriptives with a confidence interval for the mean, trimmed mean, median, variance, skewness and kurtosis.
• Tests of Normality — Shapiro-Wilk and Kolmogorov-Smirnov (with Lilliefors significance), and a Decision column that rejects normality at your chosen α.
• Percentiles.

Example. BMI by Sex shows each group's distribution and whether each is plausibly normal — useful before choosing a t-test vs a nonparametric test.

Crosstabs

When to use it. To cross two categorical variables and test whether they are associated.

Dialog. Choose a Row and a Column variable; optionally a Layer variable for a stratified (three-way) table. Tick the tests and measures you want.

Output.

• The contingency table of counts (with optional row/column/total percents).
• Chi-square tests — Pearson, likelihood-ratio, Fisher's exact and (for 2×2) McNemar.
• Association measures — phi and Cramér's V, Goodman & Kruskal's gamma and lambda (with its significance), and Cohen's kappa for a matched table.
• With a layer: the Cochran/Mantel-Haenszel statistics — conditional-independence test, the common odds ratio, and the Breslow-Day test of homogeneity.

Example. SmokingStatus × Hypertensive tests whether smoking and hypertension are associated; adding Sex as a layer asks whether that association holds within each sex.

Missing Value Analysis

When to use it. Before you model anything on a dataset with gaps — to find out how much is missing, where, and whether the pattern looks random.

Dialog. Move at least two numeric variables into Variables. Save EM imputed values optionally writes single-imputed columns back as <variable>_imp.

Output.

• A per-variable summary — valid N, missing count and missing percent.
• The distinct missingness patterns across the chosen variables, with how many cases follow each.
• Little's MCAR test — a single test of whether the missingness is unrelated to the data (Missing Completely At Random). A non-significant result is the reassuring one.

Example. FastingGlucose_mmolL, TotalCholesterol_mmolL and PhysicalActivity_minWk from the sample data: the summary counts each gap, the patterns show whether the same participants are missing all three, and Little's test asks whether the gaps carry information.

A note on single imputation. The saved EM values fill each hole with one number, which understates uncertainty — every later standard error is computed as if those values had been measured. Use them for exploration; use Multiple Imputation below for anything you will report.

Multiple Imputation

When to use it. When you need estimates and standard errors that account honestly for what is missing, rather than dropping incomplete cases or filling them with one guess.

Dialog.

• Variables — the analysis variables to pool. For a linear regression, the outcome first, then the predictors; for a mean, a single variable.
• Analysis — what is run on each completed dataset and then pooled (linear regression by default, or a mean).
• Auxiliary variables — extra numeric variables used only to help impute. They improve the imputations without joining the pooled analysis.
• Imputations (m, default 5), iterations per imputation (default 10), confidence level and seed — the seed makes the whole thing reproducible, which matters because imputation is a random procedure.

Output. The pooled estimates — coefficient, standard error, confidence interval and p — combined across the m completed datasets by Rubin's rules, together with the fraction of missing information (FMI) per term: how much of what you would like to know was supplied by imputation rather than by data.

Example. Regress SystolicBP on Age and BMI with TotalCholesterol_mmolL as an auxiliary: each of the m datasets is completed by chained equations, the regression is run on each, and the results are pooled into one table with an FMI column saying how much the gaps cost you.

How this is computed

This section names which method each procedure prints — the estimator, the statistic, its degrees of freedom, and the tie, missing-value and weight rules — and links the recorded convention that explains the choice. The full index is the convention inventory; every number here is validated against independent packages per the validation suite.

• Frequencies / Descriptives / Explore — mean, SD and variance with divisor n − 1, SE = s/√n; skewness and kurtosis are the bias-adjusted G₁ / G₂ (SPSS, SAS, R type 2) (moments); percentiles, the median and the quartiles are Hazen's (k − ½)/n, weighted on cumulative weight (quantiles · tolerances). A frequency weight counts a case that many times (case weighting). Explore's box plot uses Tukey's 1.5 × IQR fences (charts); its normality table is Shapiro–Wilk (Royston) and Kolmogorov–Smirnov with Lilliefors significance (normality tests).
• Crosstabs — Pearson χ² without a continuity correction on every table, the likelihood-ratio χ², Fisher's exact test by the sum-of-less-likely-tables rule, McNemar exact for b + c ≤ 25 and continuity-corrected above, φ and Cramér's V uncorrected, Mantel–Haenszel with and Cochran's without the correction (tables). Gamma, τ-b/τ-c, Somers' d, λ and κ are the standard forms.
• Missing Value Analysis / Multiple Imputation — chained equations with 10 cycles, Rubin's rules with the Barnard–Rubin df, a seeded reproducible PRNG (validation). Every procedure is listwise on its own variables (missing-data policy).

See also

• Compare Means — when one variable is a scale outcome.
• Graphs — histograms and boxplots for these distributions.
• Module 9 of the tutorial — the same two procedures taught step by step on the sample data.