Exam 15: Chi-Square

You want to do a chi-square test but one of the cells in the crosstab has an expected frequency of 0.5. What should you do?

A cell in a crosstab table has an observed count of 15. The row has a total of 30 cases. The column has a total of 20 cases. The table has a total of 100 cases. What is the expected frequency for the cell?

Chi-square indicates

Answer the questions that follow this SPSS output: PELNTEN ' SEX Crosstabulation 0 male 1 female total RELINTEN 0 no religon Count 41 25 66 Residual 8.6 -8.6 1 not very strong Count 61 58 119 Residual 2.5 -2.5 2 somewhat strong Count 16 18 34 Residuat -7 7 3 strong Count 50 73 123 Residuai -10.4 10.4 Total Count 168 174 342 Chi-Square Tests Value dr Asymp. Sig. (2-sided) Pearson Chr-8quare 8.27 3 041 Likelihood Ratio 8.332 3 040 Linear-by-Linear 7.902 1 005 Association NofValid Cases 342 a. 0 cells $(0 \%)$ have expected count less than 5 . The minimum expected count is 16.70 Your research hypothesis is "In the population, SEX and strength of religious affiliation (RELINTEN) are related." A) What is your null hypothesis? B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research) C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".) D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?) E) Are your results statistically significant? (yes / no)

The text talks about the expected count in a cell of a crosstab. This is the expected count if

Which one of the following messages from SPSS indicates it is OK to use chi-square?

You want to know if there is a significant difference in the average incomes of persons living in New York, Los Angeles, and Honolulu. Which would be an appropriate procedure to use?

For each of the following, calculate the cell residual: observed count expected count residual a. 50 75 b. 20 20 c. 90 30

Which religious group is most over-represented in the South? RELIGION * REGION Crosstabulation Residual RELIGION 1 Northeast 2 Midwest 3 South 4 West RELIGION 1 Protestant -45.4 -4.3 84.9 -35.2 2 Catholic 44.9 1.3 -42.9 -3.3 3 Jewish 5.1 .4 -4.7 -.8 4 other -.2 -3.5 -4.3 8.0 5 none -4.4 6.1 -32.9 31.3

Variables included in a chi-square hypothesis test can have which levels of measurement?

Your research hypothesis is "In the population, the effect of type of vehicle being driven on average speed differs by driver's sex." What type of hypothesis test should be used?

What can you do if the expected cell frequencies are too small for a chi-square hypothesis test?

Your crosstab has 4 rows and 4 columns. Chi-square has how many degrees of freedom?

What should you do next if chi-square is significant?

What expected counts would indicate that the value of chi-square may be unstable because the cases are too thinly spread across the crosstab?

Answer the question that follows this SPSS output: SATJOB * SEX Crosstabulation sex 0 male 1 female total SATJOB 1 very dissatisfed Count 2 4 6 Expected Count 2.8 3.2 6.0 2 a limite dissatisfied Count 15 14 29 Expected Count 13.7 15.3 29.0 3 moderately satisfled Count 62 57 119 Expected Count 56.4 62.6 119.0 4 very satisfied Count 66 86 152 Expected Count 72.0 80.0 152.0 Total Count 145 161 306 Expected Count 145.0 161.0 306.0 Chi-Square Tests Value df Asymp. Sig. (2- sided) Pearson Chi-Square 2.71 3 438 Likelihood Ratio 2.726 3 436 Linear-by-Linear 761 1 383 Association Nor oalid Cases 306 a. 2 cells $(25.0 \%)$ have expected count less than 5 . The minimum expected count is 2.84 You want to do a chi-square test but the crosstab has an expected count problem. How could you transform one or both of the variables to remedy the problem?

Answer the questions that follow this SPSS output: RELINTEN ' COL.ATH Crosstabulation RELINTEN 0 no religon Count 5 41 46 Residual -3.8 3.8 1 not very strong Count 19 72 91 Residual 1.6 -1.6 2 somewhat strong Count 5 18 24 Residual 1.4 -1.4 3 strong Count 19 76 95 Residual .8 -8 Total Count 49 207 256 Chi-Square Tests Value df Asymp. Sig (2-sided) Pearson Chi-Square 2.78 3 425 Likelihood Raso 3.043 3 385 Linear-by-Linear 887 1 346 Association N of Valid Cases 256 a. 1 cells (12.5\%) have expected count less than 5 . The minimum expected count is $4.59$ . Your research hypothesis is "In the population, whether or not a person would allow an atheist to teach college (COLATH) and strength of religious affiliation (RELINTEN) are related." A) What is your null hypothesis? B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research) C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".) D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?) E) Are your results statistically significant? (yes / no)

Your research hypothesis is "In the population, there is a difference in the average speed of persons driving sports cars, minivans, motorcycles, and sedans." What type of hypothesis test should be used?

Your research hypothesis is "In the population, persons drive at an average speed that is greater than 70 mph." What type of hypothesis test should be used?