1. What is a Critical Value?

A critical value is a point on the scale of a test statistic beyond which we reject the null hypothesis. It's determined by the significance level (α) of the test and the probability distribution of the test statistic.

2. How Does the Calculator Work?

The calculator uses the inverse distribution function:

Where:

• \( crit \) — Critical value (dimensionless)
• \( \alpha \) — Significance level (dimensionless)
• \( inv\_dist \) — Inverse distribution function

Explanation: The critical value separates the region where the null hypothesis is rejected from where it isn't rejected.

3. Importance of Critical Values

Details: Critical values are essential in hypothesis testing to determine statistical significance and make decisions about rejecting or failing to reject null hypotheses.

4. Using the Calculator

Tips: Enter the significance level (α) between 0 and 1. Common values are 0.01, 0.05, or 0.10.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between α and the critical value?
A: As α decreases, the critical value increases (for most distributions), making it harder to reject the null hypothesis.

Q2: How does the distribution affect the critical value?
A: Different distributions (normal, t, F, chi-square) have different critical values for the same α level.

Q3: What's a one-tailed vs two-tailed critical value?
A: One-tailed tests use α directly, while two-tailed tests typically use α/2 for each tail.

Q4: Can I use this for any statistical test?
A: The specific distribution must be known. This calculator provides a general concept - specialized versions exist for different tests.

Q5: How precise are critical value calculations?
A: Very precise, as they're based on exact mathematical distributions, though real-world applications may require adjustments.