1. What is Z Critical Value?

The Z critical value is the number of standard deviations from the mean required to achieve a certain confidence level in a normal distribution. For α = 0.005 (two-tailed), it's approximately 2.807.

2. How Does the Calculator Work?

The calculator uses the inverse standard normal distribution function:

Where:

• \( \Phi^{-1} \) — Inverse standard normal CDF
• \( \alpha \) — Significance level (0.005 for 99.5% confidence)

Explanation: The function finds the Z-score where the cumulative probability equals 1 - α/2.

3. Importance of Z Critical Value

Details: Critical Z values are essential for hypothesis testing, confidence intervals, and determining statistical significance in normally distributed data.

4. Using the Calculator

Tips: Enter the desired significance level (α) between 0 and 1. For 0.005 significance (99.5% confidence), the default value is pre-filled.

5. Frequently Asked Questions (FAQ)

Q1: Why use α = 0.005?
A: This corresponds to 99.5% confidence level, providing very stringent criteria for statistical significance.

Q2: How is this different from common Z values?
A: Common values are 1.96 (α=0.05) and 2.576 (α=0.01). The 2.807 value is for more extreme significance testing.

Q3: When would I need this critical value?
A: In high-stakes research where very small p-values are required, or when multiple testing corrections are applied.

Q4: Is this one-tailed or two-tailed?
A: The calculator provides two-tailed values. For one-tailed, use α instead of α/2.

Q5: What's the relationship between Z and p-value?
A: Z-scores can be converted to p-values and vice versa using the standard normal distribution.