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) and the degrees of freedom in the statistical test.

2. How Does the Calculator Work?

The calculator determines critical values from statistical tables based on:

Where:

• \( \alpha \) — Significance level (probability of Type I error)
• \( df \) — Degrees of freedom (depends on test and sample size)
• Distribution — The probability distribution being used (t, z, chi-square, F)

3. Importance of Critical Values

Details: Critical values are essential for hypothesis testing. They define the threshold for statistical significance and help determine whether to reject the null hypothesis.

4. Using the Calculator

Tips: Select the appropriate distribution type, significance level, degrees of freedom, and whether you're conducting a one-tailed or two-tailed test.

5. Frequently Asked Questions (FAQ)

Q1: When should I use t-distribution vs z-distribution?
A: Use t-distribution when population standard deviation is unknown (most common). Use z-distribution when population standard deviation is known or for large samples (n > 30).

Q2: How do I determine degrees of freedom?
A: For t-test: df = n-1 (sample size minus 1). For chi-square: (rows-1)*(columns-1). For ANOVA: more complex calculations.

Q3: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for an effect in one direction only. Two-tailed tests look for an effect in either direction (more conservative).

Q4: Why are critical values important in hypothesis testing?
A: They define the rejection region for your test statistic. If your test statistic exceeds the critical value, you reject the null hypothesis.

Q5: Can I use this calculator for any statistical test?
A: This provides critical values for common distributions (t, z, chi-square, F). For exact values, consult detailed statistical tables or software.