You can compare observed data to expected data with the chi-square test to measure the probability of being expected to chance. Also, you can use it to find out if two populations are statistically different from each other and often used in survey research, market research, and other types of studies. 

Make sure to see other related calculators, such as Negative Binomial Distribution, and Class Width Calculator.

What is the chi-square test?

The chi-square test is a statistical test used to assess the degree to which observed data matches the predictions of a theoretical model. You can also use the chi-square to test the goodness of fit of the data to a particular distribution and analyze qualitative data. 

How to calculate chi-square?

If you are in a statistics class and struggling to understand how to calculate chi-square, our calculator will help you. The chi-square calculator is a device that helps calculate the chi-square statistic for testing the goodness of fit of data to a distribution. 

Many scientists have difficulty understanding chi-square, a statistical measure of how much variation there is in a data set. 

This article will explore chi-square by comparing the statistical measure to the golf analogy. Chi-square is a statistical measure of how much variation is in a data set. You can use it to test the difference between two categorical variables. Ten would be a perfect score in golf, while a four would be a bad score. If you are a golf enthusiast, you might want to know how often you get a score of 10 versus a score of 4. The more you play, the more you might be able to answer this question. You could then compare your results to others in your group to see if your score is better or worse than the average.

You can also compare your score to an average for your group using our Average calculator. It is like calculating chi-square to see if there is a significant difference between your group’s scores and the average for your group. 

 Chi-square formula

The chi-square formula is a statistical technique that you can use to compare a categorical variable’s observed and expected values. You can compare two or more variables. You can use it to test the probability that the observed distribution of a categorical variable is a chance occurrence. You can use the chi-square formula to find a difference in two or more groups’ mean, variance, or shape.

x^{2} = \sum_{}^{}\frac{\left ( O_{i} - E_{i} \right )^{2}}{E_{i}}


x2 – Chi-square
Oi – Observed value
Ei – Expected value

The chi-square formula calculates the difference between the observed and expected values. 

After that, the difference is squared and divided by the expected values. 

Finally, you need to multiply the answer by the total number of expected values.

Chi-square critical value

A chi-square critical value is a statistical measure that helps researchers evaluate whether or not the results of an experiment are statistically significant. You can use it to determine if a difference between two populations is due to chance or the result of a considerable difference between the two populations. Chi-square critical values are based on degrees of freedom, the number of different values in the two populations being compared.

For example, if one population has five values and the other has ten, the degrees of freedom would be 15. A chi-square critical value helps researchers determine if the difference between two populations is statistically significant. You can do it by comparing the results of an experiment to the chi-square critical value. If the experiment results are more effective than the chi-square critical value, you can consider it statistically significant.

Using chi-square calculator: an example

You can use the chi-square calculator in statistics and math to reach:

  • Assurance interval estimation for an inhabitant’s standard deviation of a normal distribution from a representative standard deviation,
  • Independence of two measures of a variety of qualitative variables,
  • Connections between definite variables,
  • Sample variance analysis when the underlying distribution is normal,
  • Deviation tests of discrepancies between expected and observed frequencies,
  • A goodness of fit test.

You can use the test to answer questions:

  • Do people who drink more alcohol also drink more soda?
  • Do people who drink more alcohol also drink more coffee?
  • Do people who drink more alcohol also eat more pizza?
  • Do people who drink more alcohol also have a higher BMI? 

The chi-square test is performed by identifying two categorical variables and then identifying how many people have a specific value on each variable. The results are then input into a chi-square formula, which will tell you about a relationship between the two variables.

This calculator is a helpful tool for math, statistics, and engineering students. The calculator is useful for testing hypotheses, calculating odds ratios, and more. It will allow you to efficiently compute chi-square statistics and determine whether a categorical distribution fits a specified absolute distribution.

Using the Chi-Square Calculator, you can input data from a categorical distribution, select a hypothesized distribution, and compute the chi-square statistic.