Chi-Square Test: Basics

One of the advanced statistical tools used as a hypothesis test, a Chi-square test is also known as Pearson’s Chi-squared test. There are two types of chi-squared tests: one determines a goodness of fit test and the other is a test for independence. A mention of any of these two terms can determine the usage of Chi-Square test. For an in depth explanation you can check out our chi-square assignment help and chi-square homework help.

Chi-Square Test: Explanation by an example

In simple examples, we can understand the chi-square test with the instance of a coin toss. In the scenario of a coin toss, there is a fifty-fifty chance of the outcome being heads or tails. We can say that if the coin is flipped 100 times, 50 times the result would be heads and the other 50 times it would be tails. But the actual results may be different from the expected. In reality, the coin may land 40 times as heads and the remaining 60 times, the outcome was tails. This discrepancy is measured by the Chi-square test.

What is Chi-Square goodness of fit test?

This test is used to determine that one single sample is a representative of the population. The goodness of fit test is used to verify if the sample data is consistent with a hypothesised distribution of the population. There some conditions which have to be fulfilled for the goodness of fit test

A Simple random sampling method is used
The variable has to be categorically defined
The number of sample observations is equal to or greater than 5

What is the Chi-Square test for independence?

This is the second form of Chi-squared test. In this test, there are two variables and the independence between these two terms are verified. It can also be explained in another way. If there are two variables, Chi-square test for independence is used to determine of these two the distribution of these two variables are independent of each other.

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It is also important to emphasise that

If a chi-square test statistic is very small, there is a relationship between the two variables
If a chi-square test statistic is very large, then the variables are not interrelated

What is the Chi-Square Test Statistic?

There are two terms involved in the computation of the Chi-Square test statistic. The observed value and the expected value. The expected value can be considered as the mean. The difference between these two terms is squared and totalled up. The resultant value is then divided by the expected value to arrive at the Chi-Square test statistic. Mathematically, the formula for the test statistic is

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A reference to Chi-Square Table

The Chi-square test statistic is compared with a table of values to make a statistical inference. This table is called as the chi-square table. It represents different values based two parameters: degrees of freedom and the confidence levels. The value as per the table represents the area under the chi-square distribution. Based on this value, the hypothesis under question may be accepted or rejected.

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