Chi Square Test Tutorial

Chi Square test tutorial, Welcome to the world of chi Square test in Data science. Now, we are going to cover the introduction of chi square test tutorial. Along with this, we will study various uses of it and formula to calculate with example.

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What is a Chi Square Test?

The data used in calculating a chi square test must be random, raw, mutually exclusive, drawn from independent variables, and drawn from a large enough sample. It is often in hypothesis testing.

Example: The results of tossing a coin 1000 times meet these criteria

Why we need a Chi Square Test?

There are two main types of chi-square tests:

The test of independence, that asks a question of relationship, like, “Is there a relationship between gender and SAT scores?”

The goodness-of-fit test, that asks something like “If a coin is tossed 1000 times, will it head 500 times and tails 500 times?”

For these kinds of tests, degrees of freedom are to identify if a specific null hypothesis can be rejected based on the total number of variables and samples taken in the experiment. For example, Consider, employees and their vehicle was chosen to travel home, a sample size of 30 or 40 employees is likely not large enough to create significant amount data. Getting the same or similar results from a study using a sample size of 400 or 500 employees is more valid.

Chi Square Test Formula

Chi Square Test Example

The people who responded were classified according to their gender and whether they were republican, democrat or independent.

Imagine a grid with the columns labeled republican, democrat, and independent, and two rows labeled as male and female. Assume the data from the 20,000 respondents is as follows:

Step 1) Find the expected frequencies.

These are calculated for each “cell” in the grid. As such there are two categories of gender and three categories of political view, there are total six expected frequencies. The formula for the expected frequency is:

Hence:

• E(1,1) = (9000*8000)/20000 =3600
• E(1,2) =(9000*8000)/20000 =3600
• E(1,3) =(2000*8000)/20000 =800
• E(2,1) =(9000*12000)/20000 =5400
• E(2,2) =(9000*12000)/20000 =5400
• E(2,3) =(2000*12000)/20000 =1200

Step 2) These values are the used to calculate the chi squared statistic using the following formula:

• O(1,1)=(4000-3600)²/3600 = 44.44
• O(1,2)=(3000-3600)²/3600 = 100
• O(1,3)=(1000-800)²/800 = 50
• O(2,1)=(5000-5400)²/5400 = 29.63
• O(2,2)=(6000-5400)²/5400 = 66.66
• O(2,3)=(1000-1200)²/1200 = 33.33

Chi-squared = 324.66

The chi squared statistic then equals to the sum of these value, or 324.66. We can then look at a chi squared statistic table to see, given the degrees of freedom in our set-up, whether the result is statistically significant or not.

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