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Chi Square: Definition & Analysis

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  • 0:04 What Is Chi Square?
  • 1:53 Using Chi Square to…
  • 3:42 Lesson Summary
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Lesson Transcript
Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

In this lesson, you will learn the definition of chi square and how it is used to determine whether a null hypothesis should be accepted or rejected. We will work through an example, then you can take a brief quiz to see what you learned.

What Is Chi Square?

Chi square is used in statistics, science and other professions where data is analyzed. Let's pretend that I want to compare the driving habits of males and females. I predict that consistent seatbelt use is not related to gender. This is my null hypothesis, or the hypothesis that the variables gender and seatbelt use are not related.

For the sake of simplicity, we're not going to go into chi square calculations for both genders and seatbelt use, but let's say that past studies have shown that 80% of males will use seatbelts consistently if seatbelt use doesn't depend on gender. Given that information, I survey 100 males and predict that, if gender and seatbelt use are not related, then 80 of them will use seatbelts consistently. I can use the data that I collect to accept or refute my hypothesis. The results are outlined in the 'Seatbelt survey results' image:

Seatbelt survey results.
chi1

So what can be concluded from the results? We can see that more of the survey participants use seatbelts consistently than expected. But I don't have enough information to confidently accept or refute my null hypothesis. For this, I need to do a chi square test.

Chi square is a calculation used to determine how closely the observed data fit the expected data. If the chi square value is small, we can accept our null hypothesis. If it is a large value, we can refute our null hypothesis and know that there is some factor, perhaps gender, which is affecting seatbelt use. In the Chi square calculation image on your screen, x represents chi, while o and e represent the observed and expected values, respectively.

Chi square calculation.
chi2

After completing the calculation, we get a chi square value of 3.06.

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