P-value to Z-score Calculator
Use this P to Z calculator to easily convert P-values to Z-scores (standard scores) and see if a result is statistically significant. Supports one-tailed and two-tailed p-values. Detailed information about what a Z-score is.
Using the p-value to z-score calculator
If you have a p-value statistic for a given set of data and want to convert it to its corresponding Z score this P to Z calculator will help you accomplish that. Simply enter the P-value and choose whether it was computed for a one-tailed or two-tailed significance test to calculate the corresponding Z score using the inverse normal cumulative PDF (probability density function of the normal distribution). If you have made a directional inference, saying something about the sign or direction of the effect, then your p-value should have been calculated as one-tailed, corresponding to a one-sided composite null hypothesis. If the direction of the effect did not matter in the initial p-value calculation, select two-tailed, which corresponds to a point null hypothesis.
Since the normal distribution is symmetrical, it does not matter if you are computing a left-tailed or right-tailed p-value: just select one-tailed and you will get the correct result for the direction in which the observed effect is. If you want the Z score for the other tail of the distribution, just reverse its sign, e.g. 1.7 becomes -1.7.
What is a "Z score"
The Z-score is a statistic showing how many standard deviations away from the normal, usually the mean, a given observation is. It is often called just a standard score, z-value, normal score, and standardized variable.
The standard score is calculated by estimating the variance and standard deviation, then deriving the standard error of the mean, after which a standard score is calculated using the formula [1]:
X (read "X bar") is the arithmetic mean of the population baseline or the control, μ0 is the observed mean / treatment group mean, while σx is the standard error of the mean (SEM, or standard deviation of the error of the mean).
The interpretation of a Z-score has problems similar to that of p-values and confidence intervals, on which you can read more in our respective pages.
One of the applications of standard scores is in constructing prediction intervals. A prediction interval [L,U] is an interval such that a future observation X will lie in the interval with a given probability, i.e. 90%.
P value to Z-score conversion table
Below are some commonly encountered p-values and their corresponding standard scores, assuming a one-tailed hypothesis.
| Percentile | P-value | Standard score (Z) |
|---|---|---|
| 80% | 0.2000 | 0.8416 |
| 90% | 0.1000 | 1.2816 |
| 95% | 0.0500 | 1.6449 |
| 97.5% | 0.0250 | 1.9600 |
| 98% | 0.0200 | 2.0537 |
| 99% | 0.0100 | 2.3263 |
| 99.9% | 0.0010 | 3.0902 |
| 99.95% | 0.0005 | 3.2905 |
References
[1] Mayo D.G., Spanos A. (2010) – "Error Statistics", in P. S. Bandyopadhyay & M. R. Forster (Eds.), Philosophy of Statistics, (7, 152–198). Handbook of the Philosophy of Science. The Netherlands: Elsevier.
Cite this calculator & page
If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "P-value to Z-score Calculator", [online] Available at: https://www.gigacalculator.com/calculators/p-value-to-z-score-calculator.php URL [Accessed Date: 01 Apr, 2023].
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