How are the expected values calculated for the contingency table of a test if independence and...

How are the expected values calculated for the contingency table of a test if independence and what is the reason that this formula works?

Solutions

Expert Solution

The Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables. The frequency of each category for one nominal variable is compared across the categories of the second nominal variable. The data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable.

To find the expected frequency of cell do the following:

(Row total of cell * Column total of cell) / Grand total

Example:

This formula works because the expected value we got is the representative of observed value and is also close to observed value so that we can apply chi square test to find the independence.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

When performing a χ2 test for independence in a contingency table with r rows and c...

When performing a χ2 test for independence in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances. a. α=0.05, r=6, c=5 d. α=0.01, r=5, c=6 b. α=0.01, r=3, c=4 e. α=0.01, r=4, c=5 c. α=0.01, r=3, c=6 a. The critical value is ____. (Round to three decimal places as needed.) b. The critical value is _____. (Round to three decimal places as needed.) c. The...

Given the following contingency table, conduct a test for independence at the 1% significance level. (You...

Given the following contingency table, conduct a test for independence at the 1% significance level. (You may find it useful to reference the appropriate table: chi-square table or F table) Variable A Variable B 1 2 1 28 38 2 30 66 a. Choose the null and alternative hypotheses. H0: The two variables are independent.; HA: The two variables are dependent. H0: The two variables are dependent.; HA: The two variables are independent. b. Calculate the value of the test...

1. Given the following contingency table, conduct a test for independence at the 1% significance level....

1. Given the following contingency table, conduct a test for independence at the 1% significance level. (You may find it useful to reference the appropriate table: chi-square table or F table) Variable A Variable B 1 2 1 31 32 2 34 58 Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) 2. A market researcher for an automobile company suspects differences in preferred color between...

Use the provided contingency table and expected frequencies. At alpha equals 0.01, test the hypothesis that...

Use the provided contingency table and expected frequencies. At alpha equals 0.01, test the hypothesis that the variables are independent. What is the test statistic? Result stretched not stretched injury 16(20.979) 24(19.021) No injury 209(204.021) 180(184.979)

3. How many qualitative variables is the chi-square test of a contingency table a test of...

3. How many qualitative variables is the chi-square test of a contingency table a test of independence for? 11.3 Chi-Square Test for Independence 4. How many expected cell frequencies satisfy subsequent assumptions, so that the chi-square test of a contingency table is valid? 11.3 Chi-Square Test for Independence Page 368 Test Review Questions Chapter 12 1. What is the name of the variable that's used to predict another variable? 12.1 The Simple Linear Regression Model 2. What is the “standard...

When testing for independence in a contingency table with 2 rows and 2 columns at 5%...

When testing for independence in a contingency table with 2 rows and 2 columns at 5% level of significance, the critical value of the test statistic is____

What is Cramer's V for each of the following values for the chi-square test for independence?...

What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.) (a) X2 = 7.95, n = 130, df smaller = 2 V = (b) X2 = 4.14, n = 60, df smaller = 1 V = (c) X2 = 12.66, n = 190, df smaller = 3 V =

What is Cramer's V for each of the following values for the chi-square test for independence?...

What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.) (a) X2 = 3.95, n = 50, dfsmaller = 1 V = (b) X2 = 8.81, n = 110, dfsmaller = 2 V = (c) X2 = 11.62, n = 180, dfsmaller = 3 V =

Use a x2 test to test the claim that in the given contingency table, the row variable and the column variable are independent.

Use a x2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. 1) Use the sample data below to test whether car color affects the likelihood of being in an 1) accident. Use a significance level of 0.01

When we run a chi-square test of independence on a 2x2 table, the resulting Chi-square test...

When we run a chi-square test of independence on a 2x2 table, the resulting Chi-square test statistic would be equal to the square of the Z-test statistic from the Z-test of two independent proportions. True or false

Subjects