Sum of ranks: what it means and how to read it

How to read it

An intermediate number: the test statistic is computed from it.

In plain words

A teacher lined up 20 students from the lowest score to the highest and gave each one a place number, 1 for the lowest. She wanted one number for each group of 10 students that shows where the group stood in the line. She asked for the sum of ranks, which puts the place numbers of each group together. Group A came out 130 and group B 80. Now she knows that group A stood higher in the line. The test then starts from these two numbers to judge whether such a gap is hard to put down to chance alone.

Example

The cell with Sum of Ranks is selected in each report; point at a label to see its note.

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.

Related values

• 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.
• Variance ratio — The largest group variance divided by the smallest. 1 — the variances are equal.

Get it in your sheet

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

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