P-value Calculator
Calculate p-values for Z-tests, T-tests, and Chi-square tests with statistical interpretation, visualization, and decision guidance.
P-value Calculator
P-value Results
P-value
0.012419
p < 0.05
Statistical Decision
Reject H₀
α = 0.05
Test Statistic
2.500
Z-score
The result is statistically significant
Since p-value (0.0124) < α (0.05), we reject the null hypothesis.
Test type: Standard Normal
Alternative hypothesis: μ ≠ μ₀
Critical value(s): 1.960, -1.960
What this means:
• The p-value (0.0124) is less than α (0.05)
• This provides strong evidence against the null hypothesis
• The difference observed is unlikely to be due to random chance
• We can conclude there is a statistically significant effect
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What is P-value Calculator?
A p-value is the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. It helps determine whether your results are statistically significant and provides evidence for or against your research hypothesis.
Understanding P-values
- P-value: Probability of observing your result (or more extreme) if H₀ is true
- Small p-value (< α): Strong evidence against null hypothesis
- Large p-value (≥ α): Insufficient evidence to reject null hypothesis
- Significance level (α): Threshold for decision making (commonly 0.05)
Types of Hypothesis Tests
- Z-test: Known population variance, normal distribution
- T-test: Unknown population variance, small samples
- Chi-square test: Categorical data, goodness of fit, independence
- One-tailed vs Two-tailed: Directional vs non-directional hypotheses
Interpreting P-values
- p < 0.001: Very strong evidence against H₀
- p < 0.01: Strong evidence against H₀
- p < 0.05: Moderate evidence against H₀ (commonly used threshold)
- p ≥ 0.05: Insufficient evidence to reject H₀
Common Applications
- Medical Research: Drug efficacy, treatment comparisons
- A/B Testing: Website design, marketing campaigns
- Quality Control: Process monitoring, defect rates
- Psychology: Behavioral studies, cognitive assessments
- Economics: Policy evaluation, market analysis
Important Considerations
- P-values don't measure the size of an effect, only its statistical significance
- Statistical significance doesn't always mean practical significance
- Multiple testing requires p-value adjustments (Bonferroni, etc.)
- Consider effect size and confidence intervals alongside p-values
- P-hacking (data dredging) can lead to false discoveries
FAQ - P-value Calculator
A p-value of 0.03 means there's a 3% chance of observing your results (or more extreme) if the null hypothesis were true. Since 0.03 < 0.05, this provides moderate evidence against the null hypothesis.