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HomeStatisticsHypothesis Tester

Example: Hypothesis Tester

A worked example, rendered from real sample data. Sign in to run the tool on your own input.

Input
24 25 26 23 27 25 24 26 25 23
25
0.05
Output
═══ Verdict ═══
✗ Fail to reject H₀: p = 0.642415 ≥ α = 0.05
ℹ H₀: μ = 25.0000    H₁: μ ≠ 25.0000 (two-tailed)
ℹ One-sample t-test, df 9: statistic -0.4804, critical ±2.2622
ℹ Effect size: Cohen's d = -0.152 (negligible)
⚠ Normality: not testable with n = 10; judge from the histogram and be cautious

═══ Hypotheses and Decision Rule ═══
Null hypothesis (H₀): μ = 25.0000
Alternative (H₁): μ ≠ 25.0000
Significance level (α): 0.05
Tail: two-tailed
Test statistic: t = (x̄ − μ₀) / (s/√n)
Critical value: 2.2622
Rejection region: t ≤ -2.2622 or t ≥ 2.2622
Observed statistic: -0.4804 → outside the rejection region
Fix α and the direction before seeing the data; changing either afterwards is not a valid test.

═══ Sample ═══
n: 10
Sample mean: 24.8000
Sample std dev (n-1): 1.3166
Standard error: 0.4163
Degrees of freedom: 9
p-value: 0.642415
95% CI for μ: 23.8582 to 25.7418
The CI contains μ₀ = 25.0000, which matches the decision above.

═══ Effect Size and Power ═══
Difference from μ₀: -0.2000
Cohen's d: -0.1519 (negligible)
Approximate power at the observed effect: 3.7%
n needed for 80% power at this effect: 342
⚠ Post-hoc power computed from the observed effect is a known trap: it is just a restatement of the p-value. Use it to plan the next study, not to judge this one.

═══ Assumptions ═══
Skewness (G1): 0.0876
Excess kurtosis (G2): -0.7513
D'Agostino-Pearson K²: needs n ≥ 20 (n = 10)
Jarque-Bera: 0.4015 (p 0.818125)
✓ No outliers beyond the 1.5×IQR fences
⚠ n = 10: the t-test needs roughly normal data at this size
Observations must be independent and drawn from one population.
…

About Hypothesis Tester

Hypothesis Tester preview - Statistics tool

Test statistical hypotheses with detailed results. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.

Use Cases

  • Test whether a measured difference between two groups is statistically significant using a t-test.
  • Perform a chi-squared test to evaluate independence between categorical variables.
  • Calculate the required sample size for a study to achieve specified power and significance level.
  • Run an ANOVA to compare means across three or more groups.

Tips

  • State the null hypothesis precisely before collecting data — vague hypotheses produce vague conclusions and lead to cherry-picking.
  • Check statistical power before interpreting a non-significant result — a p > 0.05 result from an underpowered study doesn't mean the effect doesn't exist.
  • Report effect sizes (Cohen's d, eta-squared) alongside p-values — statistical significance doesn't indicate practical significance, especially in large samples.

Fun Facts

  • The p-value threshold of 0.05 was proposed by Ronald Fisher in 1925 in 'Statistical Methods for Research Workers' as a 'convenient' cutoff, not a mathematically-derived boundary. Fisher himself later argued against treating it as a universal rule.
  • A 2016 Nature survey of 1,576 scientists found that 52% agreed that science was facing a 'reproducibility crisis', with p-hacking (testing multiple hypotheses until one passes p < 0.05) identified as a primary cause.
  • The American Statistical Association (ASA) issued a statement in 2019 recommending that statistical significance and p-values not be used to make binary pass/fail decisions — a significant shift from decades of scientific practice.

FAQ

Which tests does it support?
One-sample and two-sample t-tests, paired t-test, chi-squared test of independence, ANOVA (one-way and two-way), Mann-Whitney U test, and Wilcoxon signed-rank test.
How do I interpret a p-value?
P-value is the probability of observing results at least as extreme as yours, assuming the null hypothesis is true. A p-value of 0.03 means there's a 3% chance of this result if H0 is true — not a 97% chance H1 is true.
What's statistical power?
Power is the probability of correctly rejecting a false null hypothesis. Power = 1 - β (Type II error rate). Target 80% power minimum (β = 0.20). Low-power studies produce false negatives.

Related Statistics Tools

A/B Test CalculatorStatistical Significance TesterConfidence Interval CalculatorSample Size CalculatorChi-Square TesterT-Test CalculatorCorrelation AnalyzerRegression Analyzer
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