Critical Values Calculator with N

Critical values are essential in statistical hypothesis testing. They help determine whether your sample results are statistically significant. This calculator helps you find critical values for various statistical tests based on your sample size (n).

What are Critical Values?

Critical values are specific points on a distribution curve that help determine whether your sample results are statistically significant. They are used in hypothesis testing to compare your test statistic to a standard distribution (like the t-distribution or normal distribution).

Critical values are often called "critical t-values" or "critical z-scores" depending on the test type. They are used to establish the rejection region for null hypotheses.

Why Critical Values Matter

Critical values help you decide whether to reject or fail to reject the null hypothesis. If your test statistic falls in the rejection region (beyond the critical value), you reject the null hypothesis. Otherwise, you fail to reject it.

Types of Critical Values

t-critical values - Used for t-tests (Student's t-distribution)
z-critical values - Used for z-tests (standard normal distribution)
chi-square critical values - Used for chi-square tests
F-critical values - Used for ANOVA tests

How to Use This Calculator

Select the test type (t-test, z-test, chi-square, etc.)
Enter your sample size (n)
Select the significance level (common values are 0.05 or 0.01)
Click "Calculate" to get the critical value
Interpret the result based on your test statistic

Remember that critical values are different for one-tailed and two-tailed tests. This calculator provides two-tailed critical values by default.

Critical Values Formula

The exact formula for critical values depends on the test type, but generally:

For t-tests: t_critical = t_{α/2, df} where: α = significance level df = degrees of freedom = n - 1

For z-tests: z_critical = ±z_{α/2} where: α = significance level

For chi-square tests, the formula is more complex and involves the chi-square distribution table.

Example Calculation

Let's find the critical t-value for a two-tailed t-test with n=20 and α=0.05.

Degrees of freedom = n - 1 = 19
Look up t_{0.025, 19} in the t-distribution table
The critical t-value is approximately 2.093

This means if your calculated t-statistic is greater than 2.093 or less than -2.093, you would reject the null hypothesis at the 0.05 significance level.

Common Test Types

Here are some common statistical tests and their corresponding critical values:

Test Type	Critical Value Name	Distribution
One-sample t-test	t-critical	t-distribution
Two-sample t-test	t-critical	t-distribution
One-sample z-test	z-critical	Normal distribution
Chi-square goodness-of-fit	chi-square critical	Chi-square distribution
ANOVA	F-critical	F-distribution

FAQ

What is the difference between critical values and p-values?: Critical values are fixed points on a distribution curve that define the rejection region. P-values are probabilities that indicate how likely your results would be if the null hypothesis were true.
How do I choose between one-tailed and two-tailed tests?: Use a one-tailed test when your research hypothesis specifies a direction (greater than or less than). Use a two-tailed test when you're testing for any difference without specifying direction.
What happens if my sample size is very large?: For large sample sizes, the t-distribution approaches the normal distribution, and critical t-values approach critical z-values.
Can I use critical values for non-parametric tests?: Critical values are primarily used for parametric tests. Non-parametric tests typically use different methods like ranks or counts.
How do I interpret negative critical values?: Negative critical values simply indicate the lower tail of the distribution. For two-tailed tests, you'll have both positive and negative critical values.