Critical Value for Right Tailed Test Calculator

Example Data Table

Formula Used

Z test: critical value = inverse normal probability at 1 − alpha.

T test: critical value = inverse t probability at 1 − alpha, using degrees of freedom.

Chi square test: critical value = inverse chi square probability at 1 − alpha.

F test: critical value = inverse F probability at 1 − alpha, using numerator and denominator degrees of freedom.

Decision rule: reject H0 when the observed statistic is greater than the critical value.

How to Use This Calculator

Select the distribution for your hypothesis test. Enter alpha as the right tail area. Use 0.05 for a common five percent test. Add degrees of freedom where needed. Enter your observed statistic. Press the calculate button. The result appears above the form. Then export the result as CSV or PDF.

Right Tailed Critical Value Guide

What This Calculator Does

A right tailed test checks whether a statistic is unusually large. This calculator finds the boundary that separates common results from rare right tail results. That boundary is called the critical value. When the observed statistic is greater than this value, the test result falls in the rejection region.

Why Alpha Matters

Alpha is the chosen probability of a Type I error. It also equals the area in the right tail. A smaller alpha gives a larger critical value. That makes rejection harder. A larger alpha lowers the critical value. That makes rejection easier, but it also increases false alarm risk.

Choosing the Distribution

Use the z option when the standard normal model is suitable. Use the t option when sample size is limited and the population standard deviation is unknown. Use chi square for variance related tests. Use F for variance ratio tests, ANOVA work, and model comparison settings.

Degrees of Freedom

Degrees of freedom describe how much independent information supports the statistic. A t test usually uses sample size minus one. A chi square variance test often uses sample size minus one. An F test needs two values. The first belongs to the numerator. The second belongs to the denominator.

Interpreting the Output

The calculator reports the selected family, alpha, confidence level, critical value, and decision. The decision compares your observed statistic with the critical value. For a right tailed test, only large positive evidence supports rejection. Negative or smaller values usually do not reject the null hypothesis.

Good Statistical Practice

Choose alpha before reviewing results. Match the distribution to the test design. Check sample assumptions. Confirm that the test is truly right tailed. Report the critical value with enough decimals for your class, lab, or audit standard. Save the CSV or PDF file for documentation.

FAQs

What is a right tailed critical value?

It is the cutoff on the right side of a distribution. Values above it fall in the rejection region for a right tailed test.

What alpha should I use?

Common choices are 0.10, 0.05, and 0.01. Use the value required by your study, class, or reporting standard.

When should I use the z option?

Use it when the standard normal distribution is appropriate. This often applies with known population standard deviation or large samples.

When should I use the t option?

Use it for many mean tests when the population standard deviation is unknown. Enter the correct degrees of freedom.

Why does the F test need two degrees of freedom?

The F distribution compares two variance based quantities. One degree value belongs to the numerator. The other belongs to the denominator.

What is the rejection rule?

For a right tailed test, reject the null hypothesis when the observed statistic is greater than the critical value.

Can I download the result?

Yes. Use the CSV button for spreadsheet work. Use the PDF button for a clean report copy.

Are results exact for every distribution?

The calculator uses strong numerical approximations. For regulated work, compare results with approved statistical software or official tables.