Hypothesis testing with nominal data.

[priit]

Homework Statement

I have two variables (both nominal) union membership 1/0 and race 1/0 and I have to find if there is a relationship between them.
The task is formulated like so: "Is there a relationship between union membership and race (black versus non-black)?"
I know I have to state a null hypothesis and try to reject that.
What would be the easiest way to do that? I can define my own null hypothesis but I'm not even sure what could I test for this case?

Homework Equations

I have constructed following table from data:

         [   0] [   1]  TOT.
  
[   0]   854    63    917
[   1]   313    30    343

TOTAL 1167    93   1260

The Attempt at a Solution

I have calculated following test statistics from this table
Pearson chi-square test = 1,2853 (1 df, p-value = 0,256916)
and constructed few possible null hypothesis:
1) There are more white people in unions.
(By that I mean if in my data set would have equal distribution of black and white people then there would be more white union members than black.)
2) Union does not have equal distribution of black and white people. (That sounds a total nonsense somehow.)

And I have stated that I'll use a significance level of 0,05.
Comparing chi-square value with critical value from table I see it fits between upper and lower critical value so I can't reject null hypothesis.

 

[mighty2000]

Thank you for sharing your question and data with us. it is important to approach any research question with a clear and systematic method. In this case, we can use a statistical test to determine if there is a relationship between union membership and race.

First, let's define our null hypothesis as: There is no relationship between union membership and race. This means that the proportion of union members who are black is equal to the proportion of non-black union members.

Next, we can use a chi-square test to determine if there is a significant difference between the observed and expected frequencies in our data. Our observed frequencies are the numbers in the table you have provided, and our expected frequencies can be calculated by multiplying the total number of observations by the proportion of black and non-black individuals in the entire population.

After calculating the test statistic and finding a p-value, we can compare it to our chosen significance level of 0.05. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a relationship between union membership and race. If the p-value is greater than 0.05, we fail to reject the null hypothesis and cannot conclude that there is a relationship.

In conclusion, the easiest way to test for a relationship between union membership and race would be to use a chi-square test and compare the p-value to our chosen significance level. I hope this helps in your research. Best of luck!