Critical Value Calculator for Z, T, F, Chi-Square & Correlation Tests

In hypothesis testing, a critical value is a threshold or cutoff point that defines the boundary of the rejection region for a statistical test. It is determined based on the chosen significance level (alpha) and the type of test (one-tailed or two-tailed). If the test statistic falls beyond the critical value, the null hypothesis is rejected. Critical values are essential in tests such as the Z-test, T-test, F-test, Chi-square test, and correlation test. Each test has its own distribution and parameters. Understanding how to find and use critical values ensures valid conclusions in statistical analysis. This critical value calculator simplifies the process by instantly computing accurate critical values without referring to statistical tables.

Try Our Critical Value Calculator Now

Use the calculator below to find critical values quickly and accurately. It’s free, fast, and supports both one-tailed and two-tailed tests.

Just follow three simple steps:

1. 1. Select your distribution (Z, T, F, Chi-square, or correlation)
2. 2. Enter the required parameters (like significance level and degrees of freedom)
3. 3. Click calculate to get your critical value instantly.

What is a Critical Value?

A critical value is a number used in hypothesis testing to help you decide whether to reject the null hypothesis. It marks the point where the results of your test become statistically significant. You compare your test statistic to the critical value to make this decision. If the test statistic goes beyond the critical value, you reject the null hypothesis. The critical value depends on the alpha level (like 0.05) and whether the test is one-tailed or two-tailed. Each type of test—Z, T, F, Chi-square, or correlation—has its own way of calculating it.

Distributions Supported by Our Critical Value Calculator

Not sure which distribution to choose? Our Critical Value Calculator makes it easy for you by supporting the most commonly used distributions in hypothesis testing. Each distribution plays a unique role in statistical analysis, and this tool adjusts the input fields automatically based on your selection—so you only see what you need.

Here’s a quick overview of each supported distribution and the parameters required:

• Z Distribution – Best for large samples with a known population standard deviation. To compute the critical value, simply enter the alpha level and select whether the test is one-tailed or two-tailed.
• T Distribution – Ideal for small samples or when the population standard deviation is unknown. You’ll need the degrees of freedom (n – 1) and the alpha level.
• F Distribution – Used to compare two variances, such as in ANOVA tests. Input the numerator and denominator degrees of freedom, along with the alpha level.
• Chi-Square Distribution – Common in tests of independence and goodness-of-fit. The calculator requires the degrees of freedom and alpha level.
• Correlation (r) – For testing the significance of Pearson correlation coefficients. Enter the degrees of freedom (n – 2), the alpha level, and whether the test is one-tailed or two-tailed.

One-Tailed vs Two-Tailed Tests: What’s the Difference?

In hypothesis testing, choosing between a one-tailed and a two-tailed test depends on your research question. A one-tailed test checks for an effect in only one direction (either greater than or less than a certain value). It’s commonly used when you have a specific prediction about the outcome. In contrast, a two-tailed test checks for an effect in both directions (either significantly higher or lower than expected). This is the standard choice when you’re simply testing for a difference, without specifying the direction.

Our Critical Value Calculator is designed to handle both types of tests effortlessly. Once you select your desired distribution, you can easily choose between a one-tailed or two-tailed test. The calculator automatically adjusts the computation and provides the correct critical value based on your choice. This makes it simple to perform accurate statistical tests, even if you’re not a stats expert.

Frequently Asked Questions