z statistic: what it means and how to read it
In the report: z — The test statistic on the normal scale.
How to read it
A step on the way to p: beyond about ±1.96 a two-sided test is significant at 0.05.
In plain words
A teacher compared the marks of two classes and could not tell whether the gap was just luck. The test turned the gap into z, and it came out 2.3. A z beyond about 1.96, above or below zero, means the gap is hard to put down to chance alone. Last year the same comparison gave 1.2, and that one could easily be chance. Now she knows that this year the gap between the classes deserves a closer look. In some tests the add-on, like SPSS, shows z only below zero, so she looks at the groups themselves to see which one is higher.
Example
The cell with z is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two-sided
=STATS_WILCOXON(Data!A1:T51, "before,after") - — two-sided
=STATS_MANN_WHITNEY(Data!A1:T51, "before,after")
Where you see it
STATS_KENDALL— Kendall rank correlation (tau-b): the correlation of the order of two columns — for small samples and scales with many tied answers.STATS_WILCOXON— Wilcoxon signed-rank test for two related measurements of the same rows (before / after) — the rank replacement for STATS_PAIRED when the differences are not normal.STATS_MANN_WHITNEY— Mann–Whitney U test for two independent samples — the rank replacement for STATS_INDEPENDENT when the data are not normal (see STATS_NORMALITY), are ranks or rating scales (1–5), or have outliers.
Related values
- Mann–Whitney U — How often a value of one group comes before a value of the other when all values are sorted (ties count half) — the smaller of the two counts, as SPSS.
- Wilcoxon W — The rank sum of the group whose U is the smaller one — Wilcoxon's rank-sum form of the same test, as SPSS.
- Kruskal–Wallis H — How far the mean ranks of the groups are apart, with the tie correction.
- Statistic — The test statistic.
- Pearson chi-square — Pearson's chi-square: how far the observed counts are from those expected if the two variables were unrelated. No continuity correction.
Get it in your sheet
One formula in a cell gives the whole report, z statistic included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)