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Problem table:

https://i.stack.imgur.com/3MmFX.jpg

From that I am asked to:


1b. Create a correctly percentaged table.

Am stuck on how to do this part.


2b. Test the idea that attitudes about discrimination are independent of race. List the five hypothesis testing steps for this problem (α=0.05). Be certain to provide a substantive interpretation of the results. Calculate chi-square using the 2X2 method.

I think I have this but not sure if the solutions are right:

Ho: The variables attitudes about discrimination and respondents race are independent of each other.

Ha: The variables attitudes about discrimination and respondents race are NOT independent of each other.

a = 0.05

df = 1

X^2_critical = 3.841

X^2_achieved = (1133(301*96-100*636)^2) / ( (301+636)(100+96)(301+100)(636+100) ) = 25.175...

Now I could say since achieved is greater than critical, we can reject the null hypothesis.


3b. Calculate and interpret Yule’s Q and the strength of the relationship.

Not sure if this is correct:

YULE'S Q = (100*636 - 301*96) / (100*636 + 301*96) = 0.99...

By Yule's Q there is a very strong relationship.


4b. Calculate and interpret the: 1) odds of black respondents believing that discrimination is the cause of inequality

301 to 636

2) odds of white respondents believing that discrimination is the cause of inequality

100 to 96

3) the odds ratio of black to white.

196 to 937


Are these correct?

Please help

Thank you

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  • $\begingroup$ The data table is simple. You should type it into your Question, rather than showing a link. $\endgroup$
    – BruceET
    Apr 14, 2018 at 7:18

1 Answer 1

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The table of counts is:

        W    B   Total
----------------------
Y     301  100   401 
N     636   36   672
----------------------
Total 937  136  1073

Several kinds of 'percentage' tables are in use. Perhaps the simpler and most general would be obtained by dividing all counts and totals by 1073 and to get proportions of the whose and the multiplying by 100 to get percentages of the whole. For example, the percentage in cell YW would be $100(301/1073)\% = 28.05\%.$

Other possible styles would be to give column percentages, where that cell would be $100(301/937)\%$. Yet another would be to give row percentages. You will have to look at your text or notes to work out which of the three possibilties is intended.


Your null and alternative hypotheses seem appropriate. Also, you have 1 degree of freedom and the critical value for a test at the 5% level is correct. You are right that there is a strong pattern of association with a much higher proportion of B than of W reporting discrimination. (A table using column percents would express that directly.)

I will leave it to you to check the formulas and arithmetic. (I will have to say I can't see how you got 1133.)

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