1. What is Critical Value?

The critical value is a point on the scale of the test statistic beyond which we reject the null hypothesis. It's determined by the significance level (α) and the degrees of freedom in the statistical test.

2. How Does the Calculator Work?

The calculator uses the inverse distribution function:

Where:

• \( \alpha \) — Significance level (typically 0.05 or 0.01)
• \( df \) — Degrees of freedom
• \( \text{inv\_dist} \) — Inverse distribution function (t, z, or chi-square depending on context)

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

3. Importance of Critical Value

Details: Critical values are essential in hypothesis testing to determine statistical significance. They help establish confidence intervals and make decisions about rejecting null hypotheses.

4. Using the Calculator

Tips: Enter the significance level (α) between 0 and 1, and degrees of freedom (positive integer). The calculator will compute the two-tailed critical value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed critical values?
A: One-tailed tests use α while two-tailed tests use α/2 in the calculation.

Q2: How do degrees of freedom affect the critical value?
A: As df increases, the t-distribution approaches the normal distribution, and critical values decrease.

Q3: When should I use t-distribution vs normal distribution?
A: Use t-distribution when population standard deviation is unknown and sample size is small (<30).

Q4: What if my test statistic exceeds the critical value?
A: You would reject the null hypothesis at your chosen significance level.

Q5: Are critical values the same for all statistical tests?
A: No, they vary based on the distribution (t, z, F, chi-square) and the specific test being performed.