P-Value Calculator (from Z-Score)
P-Value Calculator (from Z-Score)
Enter a z-score and choose whether you're running a two-tailed test (checking for any difference) or a one-tailed test (checking for a difference in a specific direction). This converts the z-score into its corresponding p-value using the standard normal distribution.
A two-tailed test accounts for an extreme result in either direction (either notably higher or notably lower than expected), while a one-tailed test only counts an extreme result in one specific pre-chosen direction — which one is appropriate depends entirely on how the original research question was framed, and choosing after seeing the data is considered poor statistical practice. A z-score of 1.96 is a commonly cited reference point specifically because it corresponds almost exactly to a two-tailed p-value of 0.05, the traditional (if somewhat arbitrary) threshold for statistical significance in many fields.
- Two-tailed p-value: p = 2 × (1 − Φ(|z|)), accounting for extreme values in either direction.
- One-tailed p-value: p = 1 − Φ(z) (right-tailed) or p = Φ(z) (left-tailed), accounting for an extreme value in only one specific direction.
- Common reference points: z = 1.96 gives a two-tailed p-value of 0.05, and z = 2.576 gives a two-tailed p-value of 0.01 — the two most widely used significance thresholds.
What is a z-score, and where do I get one?
A z-score measures how many standard deviations a value is from the mean; it's typically the output of another statistical test (like a z-test) that you're now converting into an easier-to-interpret probability.
Why does the same z-score give a different p-value for one-tailed vs. two-tailed?
A two-tailed test splits your significance threshold across both extremes of the distribution, so it requires a more extreme z-score to reach the same p-value as a one-tailed test, which only looks at one side.
P-Value Calculator (from Z-Score)
Enter a z-score and choose whether you're running a two-tailed test (checking for any difference) or a one-tailed test (checking for a difference in a specific direction). This converts the z-score into its corresponding p-value using the standard normal distribution.
A two-tailed test accounts for an extreme result in either direction (either notably higher or notably lower than expected), while a one-tailed test only counts an extreme result in one specific pre-chosen direction — which one is appropriate depends entirely on how the original research question was framed, and choosing after seeing the data is considered poor statistical practice. A z-score of 1.96 is a commonly cited reference point specifically because it corresponds almost exactly to a two-tailed p-value of 0.05, the traditional (if somewhat arbitrary) threshold for statistical significance in many fields.
- Two-tailed p-value: p = 2 × (1 − Φ(|z|)), accounting for extreme values in either direction.
- One-tailed p-value: p = 1 − Φ(z) (right-tailed) or p = Φ(z) (left-tailed), accounting for an extreme value in only one specific direction.
- Common reference points: z = 1.96 gives a two-tailed p-value of 0.05, and z = 2.576 gives a two-tailed p-value of 0.01 — the two most widely used significance thresholds.
What is a z-score, and where do I get one?
A z-score measures how many standard deviations a value is from the mean; it's typically the output of another statistical test (like a z-test) that you're now converting into an easier-to-interpret probability.
Why does the same z-score give a different p-value for one-tailed vs. two-tailed?
A two-tailed test splits your significance threshold across both extremes of the distribution, so it requires a more extreme z-score to reach the same p-value as a one-tailed test, which only looks at one side.