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P-value Calculator

Calculate p-values from Z-scores for statistical hypothesis testing.

How to Use This Calculator

  1. Select the test type (one-tailed or two-tailed)
  2. Enter your Z-score (number of standard deviations from the mean)
  3. Click "Calculate P-value" to see the results

The calculator will return the p-value and an interpretation of statistical significance. For example, a Z-score of 1.96 in a two-tailed test gives a p-value of 0.05, which is considered the traditional threshold for statistical significance.

Understanding P-values in Statistical Testing

A p-value is a statistical measure that helps researchers determine the significance of their results. It represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

What is a P-value?

The p-value helps us make decisions in hypothesis testing:

  • • P-value < 0.05: Generally considered statistically significant
  • • P-value < 0.01: Considered highly statistically significant
  • • P-value > 0.05: Results are not statistically significant

One-tailed vs Two-tailed Tests

There are two types of hypothesis tests:

  • One-tailed Test: Examines the possibility of a relationship in one direction. The p-value represents the probability in one tail of the distribution.
  • Two-tailed Test: Examines the possibility of a relationship in both directions. The p-value includes both tails of the distribution, making it twice the one-tailed value.

Using Z-scores

This calculator uses Z-scores to compute p-values. A Z-score tells you how many standard deviations away from the mean a data point is:

  • • Z = ±1.96 corresponds to p = 0.05 (two-tailed)
  • • Z = ±2.576 corresponds to p = 0.01 (two-tailed)
  • • Z = ±1.645 corresponds to p = 0.05 (one-tailed)
  • • Z = ±2.326 corresponds to p = 0.01 (one-tailed)

Common Misconceptions

  • • A p-value is NOT the probability that the null hypothesis is true
  • • A p-value is NOT the probability that the results occurred by chance
  • • A p-value does NOT measure the size or importance of an effect
  • • Statistical significance (p < 0.05) does NOT always imply practical significance

Example Calculation

Let's say we have a Z-score of 2.1 in a two-tailed test:

  • 1. The Z-score of 2.1 indicates our result is 2.1 standard deviations from the mean
  • 2. For a two-tailed test, we consider both positive and negative deviations
  • 3. The resulting p-value would be approximately 0.0357
  • 4. Since 0.0357 < 0.05, this result would be considered statistically significant

Enter the Z-score (standard deviations from mean)

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