“Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and...

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“Chi-Square Statistics” By Namrata Khemka
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Transcript of “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and...

Page 1: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

“Chi-Square Statistics”

By

Namrata Khemka

Page 2: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Table of Contents

1. What is Chi-Square?

2. When and why is Chi-Square used?

3. Limitations/Restrictions of Chi-Square

4. Examples

5. References

Page 3: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

What is “Chi Square”

• Invented by Pearson • Test for “Goodness of fit”• Tests for independence of variables• Non parametric test

Page 4: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Parametric vs. Non Parametric Data

Parametric data1. Numerical scores

2. Manipulate the scores

3. Example

• Average height of people in 10 cities

Non Parametric data1. Nominal data

2. Scores not manipulated

3. Example

• How many people are over 6ft and how many are below in 2 cities

Page 5: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

What is “Chi Square”

• Invented by Pearson • Test for “Goodness of fit”• Tests for independence of variables• Non parametric test• Analyze categorical or

measurement data• SPSS or Excel

Page 6: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Goodness of the Fit

1. Null Hypothesis

2. Observed frequency

3. Expected frequencies

4. Good Fit

5. Poor Fit

6. Sum of observed frequencies = sum of expected frequencies.

Page 7: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Computational Steps

• Scenario

Page 8: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Scenario:

• A movie theater owner would like to know the factors involved in movie selection by people.

• A sample of 50 people were asked, which of the following were important to them.

• They may choose one of the following:

1.Actors2.Directors3.Time the movies is playing4.Genre

Page 9: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Question

• Do any of these factors play a greater role than the others?

Page 10: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Computational Steps

• Scenario

• Threshold Value = 0.05

• Null Hypothesis

Page 11: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Null Hypothesis

• There is no difference in the importance of these 4 factors in determining which movie is selected

Page 12: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Computational Steps

• Scenario

• Threshold Value = 0.05

• Null Hypothesis

• Observed Frequencies

• Expected Frequencies

• p-value

Page 13: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Interpret the Results

• Since p is < 0.05, we reject the null hypothesis.

• There fore, some of the factors are mentioned more than others in response to movie selection

Page 14: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Test of Independence

• Examines the extent to which two variables are related

• Example

Page 15: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Scenario:

• University of Calgary is interested in determining whether or not there is a relationship between educational level and the number of flights taken each year.

• 150 travelers in the airport were interviewed and the results are:

Page 16: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Scenario - Continued

2 or less flights a year

More than 2 flights a year

University Student 

53  22 

High School Student

37  38 

Page 17: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Computational Steps

• Scenario

• Threshold Value = 0.05

• Null Hypothesis

Page 18: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Null Hypothesis

• The educational level of the travelers and the number of flights are independent of one another.

Page 19: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Computational Steps

• Scenario

• Threshold Value = 0.05

• Null Hypothesis

• Observed Frequencies

• Expected Frequencies

• p-value

Page 20: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Interpret the Results

• Since p is < 0.05, we reject the null hypothesis.

• These 2 variables are not independent of one another.

• Thus, the educational level of travelers and the number of flights they take are related

Page 21: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Requirements and Limitations

• Random sampling

• Data must be in raw frequencies

• Independence of observations

• Size of the expected frequencies

• Collapsing values

Page 22: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Collasping Values

Leather

Shoes

Sandals Boots Runners

Man 18 5 12 16

Women 20 19 6 10

Page 23: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Calculation - Details

• Fo – fe

• (Fo – fe)2

• ((Fo – fe)2)/fe

• Chi-square = SUM((Fo – fe)2)/fe

• Calculate the degrees of freedom = (R-1) (C-1)

Page 24: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Calculation - Fo – Fe

2 or less flights a year

More than 2 flights a year

University Student 

8 -8

High School Student

-8 8

Page 25: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Calculation – (Fo – Fe)2

2 or less flights a year

More than 2 flights a year

University Student 

64 64

High School Student

64 64

Page 26: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Calculation – ((Fo – fe)2)/fe

2 or less flights a year

More than 2 flights a year

University Student 

1.42 2.13

High School Student

1.42 2.13

Page 27: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Calculation – Continued

• Chi-square = SUM((Fo

– fe)2)/fe

• 7.1111

• Calculate the degrees of freedom = (R-1) (C-1)

• (2-1)(2-1) = 1

Page 28: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Distribution Tabledf 0.9 0.1 0.05 0.025 0.01

1 0.016 2.706 3.841 5.024 6.635

2 0.211 4.605 5.991 7.378 9.21

3 0.584 6.251 7.815 9.348 11.345

4 1.064 7.779 9.488 11.143 13.277

Page 29: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Interpretation

Page 30: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Chi-Square

Page 31: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Conclusion

• What is chi-square

• When should chi-square be used

• Limitations of Chi-square

• Examples

• Resources

Page 32: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

References

• www.ling.upenn.edu/courses/Summer_2002/ling102/chisq.html

• Statistical techniques in business and economics by Lind, Marchal and Mason

• Statistics for the behavioral sciences by Federick J. Gravetter and Larry B. Wallnau

Page 33: “Chi-Square Statistics” By Namrata Khemka. Table of Contents 1.What is Chi-Square? 2.When and why is Chi-Square used? 3.Limitations/Restrictions of Chi-Square.

Questions???