Mean difference: what it means and how to read it
In the report: Mean difference — The mean of the first group minus the mean of the second.
Also shown as: meanDelta
How to read it
The mean of the first group minus the mean of the second.
How far apart the two groups are, in the units of your data: 0.54 means the first group scored 0.54 points higher on average; a negative value — the second group of the pair is higher.
This is the number readers understand best: name the groups in the report — "Third-year students scored 2.18 points higher than first-year students (Tukey, p < .001)."
The difference that is tested.
How big the difference is, in the units of the data — the number readers understand best.
In plain words
The mean of the first group minus the mean of the second.
A teacher wanted to say in plain points how far apart two years of students were. First-year students averaged 62 points and third-year students averaged 64.18. She looked at the mean difference, with the third year first in the pair, and it came out 2.18. Now she can write that third-year students scored 2.18 points higher than first-year students, on average. A minus sign would have meant the second group of the pair scored higher. Readers understand this number best of all, since it is in the same points as the test itself, so she names both groups when she writes it.
The difference that is tested.
A teacher wanted to know how far her class is from the school target of 70 points. The class average was 73. She asked for meanDelta and got 3, which means the class is three points above the target. If the answer had been minus 3, the class would be below it. When she compares two columns, like marks before and after a course, it works the same way: how much the first column is above the second, on average. A positive number means the first one is higher, so the sign follows the order of the columns.
How it is computed
x̄₁ − x̄₂Example
The cell with Mean difference is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_PAIRED(Data!A1:T51, "before,after",0.95,"two-sided") - — regex selector: every column whose name starts with x
=STATS_ANOVA(Data!A1:T51, "/^x/") - —
=STATS_ONE_SAMPLE(Data!A1:T51, "score", 5, 0.95,"two-sided")
Where you see it
STATS_PAIRED— Paired-samples t-test for two related measurements (e.g., pre vs post).STATS_ANOVA— One-way ANOVA: each selected column is a group. Classic (Student) or Welch ANOVA, chosen by welch (auto by default), with homogeneity of variances and post-hoc comparisons.STATS_ONE_SAMPLE— One-sample t-test against mu0.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Standard error of the difference — How much the mean difference would vary from sample to sample.
- Standard deviation of the differences — The sample standard deviation of the row-by-row differences (n − 1).
- Mean of the group — The mean of the values of the group.
- Standard deviation of the group — The sample standard deviation of the group (n − 1).
- N — The number of valid values in the group of the row.
Get it in your sheet
One formula in a cell gives the whole report, Mean difference included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)