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Calculate the p-value from a z-score for one-sample z-tests. Supports two-tailed, left-tailed, and right-tailed tests.
P-Value from Z-Score:
Z = (x - mu) / (sigma / sqrt(n))
Two-tailed: p = 2 * min(P(Z<z), P(Z>z))
Left-tailed: p = P(Z < z)
Right-tailed: p = P(Z > z)
p < 0.05 is typically considered statistically significant
The p-value is the probability of observing results as extreme as (or more extreme than) the actual results, assuming the null hypothesis is true. A small p-value suggests the null hypothesis may be false.
The significance level (alpha) is the threshold for rejecting the null hypothesis. The most common threshold is 0.05 (5%). If p < alpha, you reject the null hypothesis and call the result statistically significant.
A two-tailed test checks whether the parameter is different in either direction (greater or less than). Use this when you have no prior hypothesis about which direction an effect will go.
Use a one-tailed test when you have a specific directional hypothesis — for example, that a treatment will increase scores, not just change them. One-tailed tests are more powerful but require justification.
No. Statistical significance (p < 0.05) means the observed result would be unlikely under the null hypothesis, not that your hypothesis is proven. Significance depends on sample size, and practical significance (effect size) matters separately.