p-value: what it means and how to read it

How to read it

p answers one question: if in reality there were no difference (or no link), how often would chance alone give a result this strong? A small p means: rarely, so the result is hard to explain by chance.

The usual line is 0.05: below it the result is called statistically significant.

p does not say how big or how important the effect is — effect sizes (η², r, Cohen's d) do.

Below 0.05 is usually called significant. A p of 0.05 or above means the difference was not shown in your data — it does not prove that there is none.

In the text round p to two or three decimals (0.02947 → p = .029); if the cell shows 0, a number like 7e-8 or anything below 0.001, write p < .001.

In a paper: "the difference is statistically significant, p = .012" or "no significant difference was found, p = .33".

In plain words

A coach tried a new warm-up with one team, and that team ran half a second faster than another team. She could not tell whether that gap meant something or was just luck. She counted p and it came out 0.012. Now she can say: if the two teams were really the same, a gap this big would show up only about once in 80 tries, so it is hard to put down to chance alone. If chance alone gave such a gap 33 times in 100, she would say the gap could easily be luck. But p does not tell how big or how important the gap is.

Example

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

Where you see it

• STATS_LINEAR — Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.
• STATS_LOGISTIC — Binary logistic regression with optional ridge regularization (lambda >= 0).
• 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_KENDALL — Kendall rank correlation (tau-b): the correlation of the order of two columns — for small samples and scales with many tied answers.
• STATS_PARTIAL — Partial correlation: the Pearson correlation of two variables with the controls held constant (SPSS PARTIAL CORR). Two variables give one correlation, three or more a matrix, as STATS_PEARSON.
• STATS_CHI2 — Pearson chi-square test for association between two categorical columns.
• STATS_CRAMER — Cramer's V effect size for association between two categorical columns.
• STATS_NORMALITY — Shapiro–Wilk test of normality for every selected column — the Shapiro–Wilk part of the SPSS EXAMINE table "Tests of Normality" (without its Kolmogorov–Smirnov test).
• STATS_PAIRED — Paired-samples t-test for two related measurements (e.g., pre vs post).
• 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_INDEPENDENT — Independent-samples t-test for two groups: the two selected columns are the groups.
• 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_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_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.
• STATS_ONE_SAMPLE — One-sample t-test against mu0.
• STATS_ANALYZE — Runs several analyses on one range and returns one report.

Related values

• Adjusted p of the pair — The p of the pair corrected for the number of comparisons by the posthoc method.
• Lower bound of the interval — The lower bound of the confidence interval, at the level in the label.
• Upper bound of the interval — The upper bound of the confidence interval, at the level in the label.
• p of the F change — The p of F Change: P(F(df1, df2) > F Change). Empty when F Change is.
• Confidence interval — The confidence interval of the estimate: its level and its two bounds.

Get it in your sheet

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

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