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Statistical Significance Calculator

📅Last updated: October 3, 2025
✓Reviewed by: LumoCalculator Team

Calculate statistical significance for your research and business decisions. Determine p-values, effect sizes, and statistical power with our comprehensive calculator designed for researchers, analysts, and data scientists.

Statistical Significance Calculator

Sample Size (n)
Effect Size (Cohen's d)

Small: 0.2, Medium: 0.5, Large: 0.8

Significance Level (α)
Test Type

Statistical Results

p = 0.6111
Not Significant

Detailed Analysis

P-value
Probability of Type I error
0.6111
Effect Size
Cohen's d
0.5
Statistical Power
Probability of detecting effect
50.2%
Confidence Level
1 - α
95%

Interpretation

The result is not statistically significant (p = 0.6111 ≥ α = 0.05). The effect size is large. The statistical power is moderate.

Statistical Significance Levels

α = 0.0595% confidence

Standard significance level (95% confidence)

  • • p < 0.05
  • • Most common
α = 0.0199% confidence

High significance level (99% confidence)

  • • p < 0.01
  • • High confidence
α = 0.00199.9% confidence

Very high significance level (99.9% confidence)

  • • p < 0.001
  • • Very high confidence

How to Calculate Statistical Significance

Statistical Test Formula

t-statistic: t = d × √n
p-value: P(T ≥ |t|) where T ~ t(n-1)
Effect size: Cohen's d = (μ₁ - μ₂) / σ

Calculation Steps:

  1. 1
    Define your hypothesis
    Set null hypothesis (H₀) and alternative hypothesis (H₁)
  2. 2
    Choose significance level
    Typically α = 0.05 (5% chance of Type I error)
  3. 3
    Calculate test statistic
    Compute t-statistic based on effect size and sample size
  4. 4
    Determine p-value
    Find probability of observing this result under H₀

References

  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Routledge. DOI
  • Student (1908). The probable error of a mean. Biometrika, 6(1). Standard reference for the t-distribution. JSTOR
  • Fisher, R. A. (1925). Statistical Methods for Research Workers. Clarendon Press. Foundational treatment of p-values and significance testing.

Important Considerations

⚠️ Statistical Limitations

This calculator provides estimates. Consider effect size, power, and practical significance alongside statistical significance.

📊 Sample Size Impact

Larger samples increase power but may detect trivial effects

  • • Power increases with sample size
  • • Very large samples can find tiny effects
  • • Consider practical significance
🎯 Effect Size Matters

Statistical significance ≠ practical importance

  • • Small effects may be significant
  • • Large effects may not be significant
  • • Consider Cohen's d interpretation
⚖️ Type I vs Type II Errors

Balance false positives and false negatives

  • • α controls Type I error rate
  • • Power = 1 - β (Type II error)
  • • Consider consequences of each error
🔬 Multiple Comparisons

Multiple tests increase false positive risk

  • • Bonferroni correction
  • • False Discovery Rate (FDR)
  • • Pre-specify hypotheses

Example Cases

Case 1: Marketing Campaign A/B Test

Input Parameters: n = 1000, d = 0.3
Test: Two-tailed, α = 0.05
Hypothesis: New design vs control
Result: p = 0.023, Significant
Power: 85.2%
Effect Size: Medium (0.3)

Use Case: Marketing team can confidently implement the new design with 95% confidence that it performs better than the control.

Case 2: Medical Treatment Study

Input Parameters: n = 50, d = 0.8
Test: One-tailed, α = 0.01
Hypothesis: Treatment > Placebo
Result: p = 0.008, Significant
Power: 92.1%
Effect Size: Large (0.8)

Use Case: Clinical researchers can conclude with 99% confidence that the treatment has a large, clinically meaningful effect.

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