Mean rank: what it means and how to read it

In the report: Mean Rank — The average rank of the values of the group; rank 1 is the smallest value of all groups together.

How to read it

The rank-test counterpart of the mean: the group with the higher mean rank tends to have the higher values. Report it next to the test, or the medians of the groups.

In plain words

A teacher gave a hard puzzle to two groups of 10 students and wanted to know which group did better. The scores were ratings, so averages did not feel right. She lined up all 20 students from the lowest score to the highest and gave each a place number, 1 for the lowest. Then she asked for the mean rank of each group. Group A came out 13 and group B 8. Now she can answer: students of group A mostly stood nearer the top of the line, students of group B nearer the bottom. She writes it next to the test result.

Example

The cell with Mean Rank 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")
— three groups =STATS_KRUSKAL(Data!A1:T51, "x,x1,x2")

Where you see it

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.
STATS_KRUSKAL — Kruskal–Wallis test for two or more independent groups (usually three or more; for two it agrees with STATS_MANN_WHITNEY) — the rank replacement for STATS_ANOVA when the data are not normal, or are ranks or rating scales. Each selected column is a group, as in STATS_ANOVA; no column is dropped.

Sum of ranks — The sum of the ranks of the values of the group.
Negative ranks — Pairs where the second column is smaller than the first (the difference second − first is negative), as SPSS.
Positive ranks — Pairs where the second column is larger than the first (the difference second − first is positive).
Ties — Pairs where the two values are equal; they are left out of the test.
Test variant — student — the classic test, which assumes equal variances in the groups; welch — Welch's test, which does not.

Get it in your sheet

One formula in a cell gives the whole report, Mean rank included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)