P-value Calculator

How it works

Calculate P-values from Z-scores (Normal Distribution).

Calculate probability values from Z-scores

Description

The P-Value Calculator is a critical tool for hypothesis testing in statistics. It converts a Z-score (which tells you how many standard deviations a value is from the mean) into a P-value (the probability of observing a result as extreme as yours, assuming the “null hypothesis” is true). This tool helps researchers determine the “statistical significance” of their findings.

Inputs

• Z-score: The standard score calculated from your data set.

Outputs

• Two-tailed P-value: Used when you are testing for a difference in either direction (most common).
• Left-tailed P(Z < z): The probability of obtaining a value less than the Z-score.
• Right-tailed P(Z > z): The probability of obtaining a value greater than the Z-score.

Chart

• N/A: This tool provides precise probability levels for normal distributions.

“Good to Know”

• Significance Level ($\alpha$): In most scientific fields, a P-value lower than 0.05 (5%) is considered “statistically significant,” meaning the result is unlikely to have happened by chance.
• One-tailed vs. Two-tailed: Use a two-tailed test if you want to know if a value is “different” (higher OR lower). Use a one-tailed test if you only care if a value is “higher” (right-tailed) or “lower” (left-tailed) than the mean.
• Standard Normal Distribution: This calculator assumes a distribution with a mean of 0 and a standard deviation of 1.

Examples

Example 1: Iconic Significance (1.96)

• Input: Z-score: 1.96
• Output:
  • Two-tailed: 0.05000
  • Interpretation: This is the classic 5% significance threshold.

Example 2: Highly Significant Result

• Input: Z-score: 3.0
• Output:
  • Two-tailed: 0.00270
  • Interpretation: Extremely likely that this is NOT a random chance.

Example 3: Below the Mean

• Input: Z-score: -1.5
• Output:
  • Left-tailed: 0.06681
  • Right-tailed: 0.93319