1. What is the Critical Value from Z?

The critical value from Z represents the threshold value in a standard normal distribution that corresponds to a given significance level (α). It is used in hypothesis testing to determine the rejection region for a statistical test.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution formula:

Where:

• \( Z_c \) — Critical Z value
• \( \Phi^{-1} \) — Inverse standard normal cumulative distribution function
• \( \alpha \) — Significance level (0.0001 to 0.5)

Explanation: The formula calculates the Z-score that corresponds to the (1-α) percentile of the standard normal distribution.

3. Importance of Critical Value Calculation

Details: Critical values are essential for hypothesis testing as they define the boundary between rejecting and failing to reject the null hypothesis. They help determine statistical significance in various tests.

4. Using the Calculator

Tips: Enter the significance level (α) between 0.0001 and 0.5. The calculator will return the corresponding critical Z value for a one-tailed test.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use α directly, while two-tailed tests use α/2 for each tail. This calculator provides values for one-tailed tests.

Q2: How do I interpret the critical value?
A: If your test statistic exceeds the critical value (in absolute terms), you reject the null hypothesis at the given significance level.

Q3: What are common significance levels used in research?
A: Common α values are 0.05, 0.01, and 0.001, corresponding to 95%, 99%, and 99.9% confidence levels respectively.

Q4: Can this calculator be used for two-tailed tests?
A: For two-tailed tests, use α/2 as input to get the critical value for each tail.

Q5: What if I need critical values for other distributions?
A: Different distributions (t, F, chi-square) require different critical value calculators specific to those distributions.