Quickly and accurately perform Z-Test calculations using your Z-Score and the direction of your hypothesis test (one-sided or two-sided). Ideal for researchers, students, and statisticians needing immediate insights into their data analysis.

Z-Test Calculator (Z-Score, Sides)

Z‑Test Calculator

Calculate the p‑value from a given z‑score.

* Enter the z‑score and select whether the test is one‑tailed or two‑tailed.

Step 1: Enter Z‑Score and Test Type

e.g., 1.96

Select one-tailed or two-tailed test.

For a two-tailed test: \( p = 2\bigl[1-\Phi(|z|)\bigr] \)
For a one-tailed test: \( p = \begin{cases}1-\Phi(z), & z\ge0,\\ \Phi(z), & z<0.\end{cases} \)
where \( \Phi(z)=0.5\Bigl[1+\operatorname{erf}\Bigl(\frac{z}{\sqrt{2}}\Bigr)\Bigr] \).

How to Use This Calculator:

  1. Enter your Z-Score: Input the calculated Z-Score from your data analysis.
  2. Select Test Side: Choose either:
    • One-sided Test (direction-specific)
    • Two-sided Test (direction-neutral)
  3. Click Calculate: Obtain instant results for statistical significance.

Example Calculation:

If your Z-Score is 1.96 and you select a two-sided test, the calculator will quickly provide the associated p-value, indicating significance at typical alpha levels (e.g., α = 0.05).

Frequently Asked Questions:

  • What is a Z-Test? A Z-Test checks for statistical significance between a sample mean and a known population mean, assuming the population variance is known.
  • When should I use a one-sided vs. two-sided test? Use a one-sided test for directional hypotheses (greater than or less than). Use a two-sided test when testing for any difference without direction.
  • Why is Z-Score important in a Z-Test? The Z-Score measures how many standard deviations the sample mean differs from the population mean, directly influencing significance.

Understanding Results:

  • P-value: Represents the probability of observing your result if the null hypothesis is true. A lower p-value (usually ≤ 0.05) indicates significant results.
  • Interpretation Guide: Clearly explains practical implications of significant or non-significant outcomes.

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