1. What is the Z Value from Alpha?

The Z value corresponding to a given alpha level is the critical value from the standard normal distribution that marks the boundary for statistical significance. It represents how many standard deviations away from the mean a value must be to reach a certain significance level.

2. How Does the Calculator Work?

The calculator uses the inverse normal distribution function:

Where:

• \( Z \) — Standard normal deviate (Z-score)
• \( \Phi^{-1} \) — Inverse standard normal cumulative distribution function
• \( \alpha \) — Significance level (0 to 1)

Explanation: The function finds the Z value where the cumulative probability is (1 - α) in a standard normal distribution.

3. Importance of Z Value Calculation

Details: Z values are crucial for hypothesis testing, confidence interval construction, and determining critical values in statistical analysis.

4. Using the Calculator

Tips: Enter the alpha value (significance level) between 0 and 1. Common values are 0.05, 0.01, or 0.001.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed Z values?
A: One-tailed uses the full alpha in one direction, while two-tailed splits alpha between both tails.

Q2: What are common Z values for standard alpha levels?
A: For α=0.05 (one-tailed), Z≈1.645; for α=0.01, Z≈2.326; for α=0.001, Z≈3.090.

Q3: How is this related to p-values?
A: The calculation is inverse - p-value converts Z to probability, while this converts probability (alpha) to Z.

Q4: Can I use this for non-normal distributions?
A: Only for standard normal distributions. Other distributions require different calculations.

Q5: Why use 1 - alpha in the formula?
A: Because we want the value where the cumulative probability is (1 - α), representing the cutoff point.