Critical Value Calculator Giveen C and N

This critical value calculator helps you determine the critical value for statistical tests when you know the confidence level (C) and sample size (N). Critical values are essential for hypothesis testing in statistics, helping you decide whether to reject or fail to reject the null hypothesis.

What is a Critical Value?

A critical value is a threshold value from a statistical distribution that is used to determine whether results are statistically significant. In hypothesis testing, you compare your test statistic to the critical value to decide whether to reject the null hypothesis.

Critical values depend on:

The type of test (z-test, t-test, chi-square, etc.)
The confidence level (C)
The sample size (N)
The degrees of freedom (often N-1 for t-tests)

This calculator focuses on the most common scenario where you have a confidence level and sample size, and you want to find the corresponding critical value for a t-test.

How to Use This Calculator

Enter your confidence level (C) as a decimal between 0 and 1 (e.g., 0.95 for 95% confidence)
Enter your sample size (N)
Select the type of test (t-test is most common)
Click "Calculate" to get the critical value
Review the result and interpretation

Note: This calculator assumes a two-tailed test. For one-tailed tests, you would use a different critical value.

Formula

The critical value for a t-test is calculated using the inverse of the cumulative distribution function (CDF) of the t-distribution. The formula is:

t_critical = t.ppf(1 - α/2, df) where: α = 1 - C (significance level) df = N - 1 (degrees of freedom)

For example, with C = 0.95 and N = 30:

α = 1 - 0.95 = 0.05 df = 30 - 1 = 29 t_critical = t.ppf(1 - 0.05/2, 29) = t.ppf(0.975, 29)

Worked Example

Let's calculate the critical value for a t-test with 95% confidence (C = 0.95) and a sample size of 30 (N = 30).

Calculate the significance level: α = 1 - 0.95 = 0.05
Calculate degrees of freedom: df = 30 - 1 = 29
Find the critical value: t_critical = t.ppf(0.975, 29)
Using statistical tables or software, we find t_critical ≈ 2.045

This means that for a 95% confidence level with 30 samples, the critical value is approximately 2.045. If your calculated t-statistic is greater than 2.045 or less than -2.045, you would reject the null hypothesis.

Interpreting Results

The critical value tells you:

How extreme your test statistic needs to be to be statistically significant
Whether to reject or fail to reject the null hypothesis
That there's a 5% chance (for C=0.95) of rejecting the null hypothesis when it's actually true

Common critical values for different confidence levels and sample sizes:

Confidence Level (C)	Sample Size (N)	Critical Value (t)
90%	20	1.725
95%	20	2.086
99%	20	2.845
95%	30	2.045
95%	100	1.984

FAQ

What's the difference between a critical value and a p-value?

A critical value is a fixed threshold from a distribution table, while a p-value is calculated from your sample data. Both help determine statistical significance, but they're used differently in hypothesis testing.

Can I use this calculator for z-tests?

This calculator is designed for t-tests. For z-tests, you would use the standard normal distribution instead of the t-distribution.

What if my sample size is very large?

For large sample sizes, the t-distribution approaches the normal distribution, and the critical values become similar to those from the standard normal distribution.