Understanding p-value & Effect Size

p-values and effect sizes answer different questions. p-value tells you if an effect exists. Effect size tells you how large or meaningful that effect is. Both are essential for complete statistical reporting.

p < 0.05
Statistical Significance Threshold
d = 0.5
Cohen's d (Medium Effect)
r = 0.3
Correlation Effect Size
Key Formulas at a Glance
p-value
Probability of observing data (or more extreme) if null hypothesis is true. Ranges 0-1.
Cohen's d
(Mean₁ - Mean₂) / Pooled SD. Standardised difference between two means.
η² (Eta Squared)
SS_effect / SS_total. Proportion of variance explained in ANOVA.

What Does p-value Really Mean?

Interpretation guidelines and common thresholds in academic research

p-value Interpretation Scale
p < 0.001
Very Strong Evidence
Highly statistically significant. Strong evidence against null hypothesis.
p < 0.01
Strong Evidence
Statistically significant at 1% level. Robust finding.
p < 0.05
Statistically Significant
Conventional threshold. Reject null hypothesis at 5% significance level.
p < 0.10
Marginal Significance
Trend toward significance. May warrant discussion in exploratory research.
p ≥ 0.10
Not Significant
Insufficient evidence to reject null hypothesis. May indicate small effect or low power.
Common Misconceptions

p = 0.03 means 3% probability that results occurred by chance.

p-value is probability of observing data IF null hypothesis is true, not probability null hypothesis is true.

p < 0.05 means the effect is practically important or large.

Significance does not equal importance. Effect size measures magnitude.

p > 0.05 proves the null hypothesis is true.

Failure to reject null does not confirm it. Could be small sample or low power.

Why Effect Size Matters Beyond Significance

Effect size quantifies the magnitude of an effect, independent of sample size

Statistical vs Practical Significance

A statistically significant result (p < 0.05) can still be trivial if the effect size is tiny. Conversely, a non-significant result may hide a meaningful effect if sample size is small. Always report and interpret effect sizes alongside p-values.

"p-values tell you if an effect exists. Effect sizes tell you if it matters."
Cohen's d - Effect Size Benchmarks
d = 0.2
Small Effect
Difference of ~0.2 standard deviations. Noticeable only with careful measurement.
d = 0.5
Medium Effect
Difference of ~0.5 standard deviations. Visually noticeable effect.
d = 0.8
Large Effect
Difference of ~0.8 standard deviations. Substantial, practically meaningful effect.
r = 0.1
Small Correlation
Explains 1% of variance. Weak relationship.
r = 0.3
Medium Correlation
Explains 9% of variance. Moderate relationship.
r = 0.5
Large Correlation
Explains 25% of variance. Strong relationship.

Reporting p-values & Effect Size in Your Thesis

APA 7th edition guidelines for reporting statistical results

01
Run Your Statistical Test

Perform appropriate test (t-test, ANOVA, correlation, regression) using software (SPSS, R, JASP).

First
02
Report Exact p-value

Write "p = .032" not "p < 0.05" (except for p < .001). Include test statistic and degrees of freedom.

Required
03
Calculate & Report Effect Size

Include Cohen's d, η², or r. Interpret magnitude using field-specific benchmarks.

Critical
04
Report Confidence Intervals

Include 95% CI for effect sizes (e.g., d [95% CI: 0.32, 0.68]).

Best Practice
APA Format Examples

t(58) = 2.34, p = .023, d = 0.61 [95% CI: 0.28, 0.94]

F(2, 87) = 4.56, p = .013, η² = 0.09

r(112) = .42, p < .001, 95% CI [.25, .56]

χ²(1, N = 150) = 6.83, p = .009, φ = 0.21