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Introduction to Statistics: Help and Review9 chapters | 137 lessons

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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.

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:

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.

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

To understand the meaning of the chi square value, we must use a chi square table. The values along the left side are the **degrees of freedom (DF)**. To find the degrees of freedom, we subtract one from the number of categories in our data. Our example has two categories: 'consistent seatbelt use' and 'inconsistent seatbelt use.' This gives us 1 for our degrees of freedom.

Along the top of the table are the p-values that correspond to degrees of freedom. The **p-value** is used to determine whether we should accept or reject the null hypothesis. It is common to accept the null hypothesis for a p-value of 0.05 or higher.

To find our p-value, we look for the number closest to our chi square value for a degree of freedom equal to 1. Our chi square value of 3.06 falls between 2.706 and 3.841, giving us a p-value between 0.05 and 0.10. We can accept our null hypothesis because it is greater than 0.05. According to this data, there is no relationship between seatbelt use and male gender. Any differences between our expected and observed data are simply due to chance.

What if we had a different value for chi square, such as 6.5? Using the chi square table for a degree of freedom of 1, 6.5 is closest to 6.635. This has a p-value of 0.01, which is less than 0.05, so we would have to reject our null hypothesis. Remember, unless you are told otherwise, the p-value must be 0.05 or higher to accept the null hypothesis.

**Chi square** is used to determine whether a **null hypothesis** should be rejected or accepted. By using a chi square table, we can identify the **p-value** for the data. Typically, if the p-value is 0.05 or higher, the null hypothesis is accepted.

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Introduction to Statistics: Help and Review9 chapters | 137 lessons

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- Defining the Difference between Parameters & Statistics 5:18
- Estimating a Parameter from Sample Data: Process & Examples 7:46
- What is Quantitative Data? - Definition & Examples 4:11
- What is Categorical Data? - Definition & Examples 5:25
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- Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples 8:29
- The Purpose of Statistical Models 10:20
- Experiments vs Observational Studies: Definition, Differences & Examples 6:21
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- How Randomized Experiments Are Designed 8:21
- Analyzing & Interpreting the Results of Randomized Experiments 4:46
- Confounding & Bias in Statistics: Definition & Examples 3:59
- Bias in Polls & Surveys: Definition, Common Sources & Examples 4:36
- Misleading Uses of Statistics 8:14
- Causation in Statistics: Definition & Examples 3:28
- Deductive Argument: Definition & Examples
- Dot Plot in Statistics: Definition, Method & Examples 3:57
- Observational Study in Statistics: Definition & Examples 5:55
- Skewness in Statistics: Definition, Formula & Example 6:49
- Uniform Distribution in Statistics: Definition & Examples 4:58
- Confidence Interval: Definition, Formula & Example 7:33
- Chi Square Distribution: Definition & Examples 4:55
- Chi Square Practice Problems 6:53
- Chi Square: Definition & Analysis 4:04
- Go to Overview of Statistics: Help and Review

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