What is Chi-square?

History and Definition

A chi-square distribution is the distribution of the sum of squares of k independent standard normal random variables with k degree of freedom. A chi-square test is a statistical hypothesis test where the null hypothesis that the distribution of the test statistic is a chi-square distribution, is true.

While the chi-square distribution was first introduced by German statistician Friedrich Robert Helmert, the chi-square test was first used by Karl Pearson in 1900. The most popular chi-square test is Pearson's chi-squared test and is also called 'chi-squared' test and denoted by 'Χ²'. A classical example of chi-square test is the test for fairness of a die where we test the hypothesis that all six possible outcomes are equally likely.

Illustration

Say, you are a technology company selling different software solutions and you want to predict customer acceptance of your latest offering. You could conduct a pilot test among your prospects and collect the customer experience data. The normality of this data would then be checked and verified and chi-square analysis conducted. The analysis may reveal that additional features are required in the software to make it more useful and user-friendly. Hence, this would give you a better idea of your customer's probable acceptance of your new software solution.

Practical Applications and Benefits of Chi-square

A chi-square test is useful for testing the 'goodness of fit' of an observed distribution with a theoretical distribution; and in qualitative data to test the 'independence' of two criteria of classification. It is also used to estimate the confidence interval for a normally distributed population's standard deviation from the sample standard deviation; or for other tests like ANOVA and Friedman's Rank ANOVA.

The advantages of chi-square test are based in the fact that it is a non-parametric test. Firstly, it is extremely easy to calculate and interpret. Next, it can be used on nominal data.

Further, it can be applied in a wide area including surveys, business decision making, quality control, biological research, medical research, etc. Also, chi-square tests are commonly used in studies dealing with demographics, Likert scales, and other discrete data.

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