t statistic: what it means and how to read it
In the report: t — A difference measured in standard errors; its sign is the sign of the difference. Its p comes from the t distribution with the degrees of freedom next to it.
How to read it
How many standard errors the difference is away from zero. Beyond about ±2 a difference usually becomes significant.
In a report t goes with its degrees of freedom: t(48) = 2.35, p = .023.
In plain words
A coach saw a gap of 5 points between two teams, but the scores inside each team jumped around a lot, so she could not tell whether 5 was big. She counted t and it came out 2.35. Now she can say the gap is more than twice the size of the usual wobble in such gaps, which here is about 2 points. A gap more than about twice its usual wobble is usually hard to put down to chance alone. A gap of only 1 point would have been small next to that wobble and could easily be luck. A minus sign would only say that the second team was higher.
Example
The cell with t is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_LINEAR(Data!A1:T51, "y", "x1,x2", 0) - —
=STATS_SPEARMAN(Data!A1:T51, "x,y",0.95,"two-sided") - —
=STATS_PAIRED(Data!A1:T51, "before,after",0.95,"two-sided")
Where you see it
STATS_LINEAR— Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.STATS_PEARSON— Pearson correlation (r).STATS_SPEARMAN— Spearman rank correlation (rho): the correlation for rating scales, ranks and skewed data — does one go up as the other goes up?STATS_PAIRED— Paired-samples t-test for two related measurements (e.g., pre vs post).STATS_INDEPENDENT— Independent-samples t-test for two groups: the two selected columns are the groups.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
- Likelihood-ratio chi-square — How much −2 Log Likelihood dropped compared with the model with the intercept only.
- Wald statistic — The Wald statistic of the coefficient: (B / StdError)². Empty when lambda is above 0.
- F change — The F test of R Square Change: whether the predictors added at this step explain more than chance. At the first step it equals the F of the model. Empty when the step entered no predictor (df1 = 0).
- z statistic — The test statistic on the normal scale.
- 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.
Get it in your sheet
One formula in a cell gives the whole report, t statistic included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)