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Chapter 9

Chapter 9. Chi-square tests of Association. Examples. Suppose you wish to find out whether Gender (Nominal variable) is related to Learning Style (Individual or Group – Nominal variable) For nominal with nominal data, we use the Chi-square analisis

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Chapter 9

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  1. Chapter 9 Chi-square tests of Association

  2. Examples • Suppose you wish to find out whether Gender (Nominal variable) is related to Learning Style (Individual or Group – Nominal variable) • For nominal with nominal data, we use the Chi-square analisis • Chi-square analisis ( ) is carried out if you wish to test the association between two nominal variables.

  3. Example To find whether there is a significant (p < .05) association between Gender and Learning Style. Table below shows the number of students using the two learning style based on gender Cell 1,2 Row Total 50 50 45 Column Total 55 100 Cell 1,1 Sample size Cell numbers (row, column) The numbers in the box are observed values or students in the various cells. We need to calculate the expected number of students in the various cells if There is no association between Gender and Learning Style (Null Hypothesis)

  4. Step 1: State the null and alternative hypothesis Ho: There is no association between Gender and Learning Style (or Gender and Learning Style are independent) H1: There is an association between Gender and Learning Style (or Gender and Learning Style are dependent) Step 2: Select the distribution to use. We use the distribution to test the independence or association.

  5. Step 3: Determine the rejection and nonrejection regions The significance level is .05 or 5%. Because the test of independence is always right-tailed for the distribution. Area in the right tail = α = .05 The degree of freedom, df = (No of rows – 1)(No of columns – 1) = (2 – 1)( 2 – 1) = 1 From the table, for df = 1, α = .05, = 3.841 α = .05 3.841 Critical Value Do not reject Ho Reject Ho

  6. To calculate the expected number of students in the various cells if there is no Relationship between Gender and Learning Style: STEP 4: Calculate the expected number or frequency for each cell Use this formula for each cell: For cell 1,1: For cell 1,2: For cell 2,1: For cell 2,2:

  7. Step 5: Calculate using this formula O = Observed values E = Expected values O = 29 O = 21 E = 22.5 E = 27.5 O = 16 O = 34 E = 22.5 E = 27.5

  8. Step 6: Make a decision: 6.84 obtained is greater than the critical value (3.841) and it falls in the rejection zone. Therefore we reject Ho and retain the H1 that is, there is significant (p < .05) association between Gender and Learning Style ( = 6.84, p < .05). The observed numbers indicate that male students tend to use individual learning styles while the female students tend to use group learning styles. 6.84 is in the rejection zone α = .05 3.841 Critical Value Do not reject Ho Reject Ho

  9. Exercise 1 State whether the obtained are significant at the respective degree of freedom and levels of significance.

  10. Exercise 1 (WITH ANSWERS) State whether the obtained are significant at the respective degree of freedom and levels of significance.

  11. Exercise 2: Suppose in your research you wanted to find out whether there is an association between gender and stream. Table below shows the number of male and female students and the stream they chose. State the null hypothesis and your decision based on your analysis. Set the level of significance for your study at α = .05. Write a report based on the results obtained.

  12. Question 3: You want to find out if there are significant differences between male and female teachers’ views on whether students should be allowed to bring hand-phones to the classroom. Table below shows classification of responses. Develop a suitable Ho and test it at (α = .01). Interpret your results and write a report on your findings.

  13. Exercise 4: A random sample of 300 parents were selected and were asked if they favor giving more freedom to school teachers to punish students for violence and lack of discipline. The aim was to find out if fathers significantly (α = .05) differ from mothers in their view on punishment. The table below shows the classification of the results. • State Ho and H1. • State your finding. • Write your report based on your interpretation of the finding

  14. Exercise 5: You want to find out if English proficiency is dependent on the level of the socioeconomic status of the students. The table below shows the classification. a) Write the null and alternative hypothesis. b) Calculate the expected frequencies for all cells assuming the null hypothesis is true. c) For α = .025, find the critical value of . Show the rejection and non-rejection regions on the chi-square distribution curve. d) Find the value of the test statistic . e) Using α = .025, would you reject the null hypothesis? f) Would your result change if you set α = .05?

  15. Exercise 6: The following is the SPSS output to test the significance of the association between SX (sex) and RA (race). Count = Observed frequency of subjects Expected Count = Expected frequency of the subjects The Chi-square test results show that the chi-square value calculated is 3.33 and the corresponding p value is .189. Question: State your Ho. What is your decision? Would you reject Ho at α = .05? Is there a significant association between SX and RA at α = .05?

  16. Exercise 7 (NEW) According to the TNS Online Kids Report based on a survey conducted in April 2004 of 660 children 6 – to 14 – years old, children were asked whether they worried about having enough money. Assuming that the sample consisted 325 boys and 335 girls, the percentages given in the newspaper would yield the Numbers shown in the following table. ------------------------------------------------------------------------------ Boys Girls ------------------------------------------------------------------------------ Worried About Yes 198 181 Money? No 127 154 ------------------------------------------------------------------------------- At the 5% significance level, can you conclude that worries about money and gender are related?

  17. Exercise 8 The following table gives the distributions of grades for three professors for a a few randomly selected classes that each of them taught during the past 2 years. --------------------------------------------------------------------------------------------------------- Professor ---------------------------------------------------------------------------------------------------------- Mona Sim Mala --------------------------------------------------------------------------------------------------------- A 18 36 20 B 25 44 15 Grade C 85 73 82 D & F 17 12 8 _______________________________________________________________ Using the 2.5% significance level, test the null hypothesis that the grade distributions are homogeneous for these three professors.

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