Critical values calculator :
Welcome to our critical value calculator. This tool is used to find the left, right and two-tailed critical value for z, t-student, chi-square, r and F-distribution. Whether you're a student, researcher, or professional, this tool is designed to meet your statistical needs.
The critical value is the most important component in hypothesis testing as well as in the confidence interval. If the hypothesis test is one-tailed then it gives one critical value and if the hypothesis test is two-tailed then it gives two critical values i.e. one is positive and the other is negative.
Table of Contents
How to Use the Critical Values Calculator
The critical value calculator is an easy-to-use tool for determining critical value whether it is a one-tailed test or two-tailed test.
- Test type : in this fields enter the type of test from z-score, t-score, chi-square \( \chi^2 \), F-score or correlation coefficient r.
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Tail type : In this fields enter the type of test like one tailed ( left tailed or right tailed ) or
two tailed according to hypothesis testing.
- For T Critical Value: Enter the degrees of freedom and the significance level \(\alpha\).
- For Z Critical Value: Enter the significance level \(\alpha\).
- For Chi-Square Critical Value: Enter the degrees of freedom and the significance level \(\alpha\).
- For F Critical Value: Enter the degrees of freedom for both the numerator and the denominator, and the significance level \(\alpha\).
- For r Critical Value: Enter sample size, and the significance level \(\alpha\).
- Calculate : Click on calculate button to get the desired critical value.
What are Critical Values?
The critical value also known as critical point is used to decide whether to reject or fail to reject the null hypothesis while hypothesis testing. It is also used to find the lower and upper limits of the confidence interval. The critical value has left-tailed, right-tailed, and two-tailed critical values.
- Left-Tailed Test : As this is a left-tailed test, if the test statistic falls to the left of the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
- Right-Tailed Test : As this is a right-tailed test, if the test statistic falls to the right of the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
- Two-Tailed Test : As this is a two-tailed test, if the test statistic falls in the left or right tail beyond the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
The above figure shows left, right and two tailed critical value along with there rejection region for z distribution.
Different types of critical values
The different types of critical values are explained below.
t critical value :
In t distribution, the significance level \( ( \alpha ) \) and degrees of freedom are required to find the critical values. This distribution is used when the population standard deviation is unknown.
Z Critical Value :
In z distribution, the only significance level is required to find the critical values. This distribution is used when the population standard deviation is known.
Chi-Square Critical Value :
In Chi-Square tests, the degrees of freedom and the significance level \(\alpha \) are used to find the critical values
F Critical Value :
In f test the significance level \( ( \alpha ) \) and the degrees of freedom for the denominator and numerator are used to find the critical value. Note in the f test there are two degrees of freedom i.e \( df_1 \) and \( df_2 \)
Correlation Coefficient (r) critical Value
The sample size and significance level \( \alpha \) are used to find the critical value. The critical values for the correlation coefficient are used to determine the significance of the correlation between two variables.
How to find value from table ?
There are numbers in critical value tables, but the procedure is the same to find the critical value. Let's take one example of how to find the critical value on the z table.
Step 1 : Determine the Significance Level \( (\alpha) \)
- If the hypothesis test is a two tailed test, divide \( \alpha \) by 2.
- If the hypothesis test is a one tailed test, use \( \alpha \) directly.
Step 2 : Calculate the Critical Probability:
- For a left-tail test: Use the significance level.
- For a right-tail test: Subtract the significance level from 1.
- For two-tailed tests: Use both the above probabilities.
Step 3 : Locate the Critical Value:
- Use a Z table to find the Z-score corresponding to the calculated probability.
- The Z table provides the area to the left of a Z-score in a standard normal distribution.
Critical value table :
Left tailed critical value table for z test
Right tailed critical value table for z test
Two tailed critical value table for z test
Where does Critical Values Are Used ?
The critical values are used in various fields like statistical hypothesis testing and research. Here’s a summary of where they are applied:
Decision Making:
Based on the calculated test statistic ( T, Z, r, Chi-Square), critical values determine whether to reject or fail to reject the null hypothesis.
Significance Levels :
Critical values, which are usually set at \(0.05\) or \(0.01\), aid in assessing the degree of confidence in the statistical findings.
Two-Tailed vs. One-Tailed Tests:
Depending on whether the test is two-tailed (non-directional hypothesis) or one-tailed (directional hypothesis), different critical values apply.
Practical Examples:
The critical values are used in medical research for testing the effectiveness of a new drug compared to a placebo.
It can be used in market research for analyzing survey data to determine if there is a preference between two products.
It can also be used in quality control to assess if a manufacturing process meets specified standards.
Why Use Our Critical Values Calculator ?
- Accuracy: Our calculator provides precise critical values for your statistical tests.
- User-Friendly: The interface is intuitive, making it easy to input data and obtain results quickly.
- Versatile : Calculate T, Z, Chi-Square,r, and F critical values in one place.
- Free and Accessible: No cost and accessible online anytime, anywhere.