1. What is Critical Value?

The critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. It represents the threshold for statistical significance in hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( z \) — Critical value (z-score)
• \( \Phi^{-1} \) — Inverse standard normal cumulative distribution function
• \( CL \) — Confidence level (decimal form)

Explanation: The formula calculates the z-score that corresponds to the given confidence level for a two-tailed test.

3. Importance of Critical Value

Details: Critical values are essential in hypothesis testing as they define the rejection region for statistical tests. They help determine whether observed results are statistically significant or occurred by chance.

4. Using the Calculator

Tips: Enter confidence level as a decimal between 0 and 0.9999. For example, for 95% confidence level, enter 0.95.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between confidence level and critical value?
A: Higher confidence levels result in larger critical values, widening the confidence interval around the sample estimate.

Q2: How is critical value different from p-value?
A: Critical value is a predetermined threshold, while p-value is the probability of obtaining results as extreme as the observed results.

Q3: When should I use one-tailed vs two-tailed critical values?
A: Use one-tailed tests when the hypothesis is directional, and two-tailed tests when the hypothesis is non-directional.

Q4: What are common confidence levels used in research?
A: 90%, 95%, and 99% are the most commonly used confidence levels in statistical analysis.

Q5: Can critical values be negative?
A: Yes, critical values can be negative for left-tailed tests or when dealing with distributions that extend to negative values.