Question

Using R and R Commander, perform a Chi-squared test of independence with marstatus in the Columns and gender in the Rows. Click on Statistics tab and select the first three options under Hypothesis Tests. Copy the output and paste it below this question. Is the Chi-squared test significant at the 5% alpha level? Are the results reliable? Please see data below. Can you explain?

Frequency table:

        marstatus

gender   Divorced Married Single

Female        2       6      9

Male          1       0      6

        Pearson's Chi-squared test

data: .Table

X-squared = 3.3479, df = 2, p-value = 0.1875

Expected counts:

        marstatus

gender   Divorced Married Single

Female    2.125    4.25 10.625

Male      0.875    1.75 4.375

Chi-square components:

        marstatus

gender   Divorced Married Single

Female     0.01    0.72   0.25

Male       0.02    1.75   0.60

Answer 1

Chi-Square Test:

H0: Gender and Marital Status are independent.

H1: Gender and Marital Status are dependent.

df = (2-1)*(3-1)

= 2

p-value = 0.1875 > 0.05 i.e. we fail to reject H0 and gene we can't say that Gender and martial status are dependent on each other significantly.

One condition to conduct chi-square test is: Sample data displayed in a contingency table, the expected frequency count for each cell of the table should be at least 5.

Since this condition is not fulfilled, we can't claim this test to be totally reliable.

Please upvote if you have liked my answer, would be of great help. Thank you.