A researcher completes a chi-square test for independence and obtains \chi^2=6.2 for a sample

Naeem Stanton

Naeem Stanton

Answered question

2022-03-01

A researcher completes a chi-square test for independence and obtains χ2=6.2 for a sample of n=40 participants.
a. If the frequency data formed a 2×2 matrix, what is the phi-coefficient for the test?
b. If the frequency data formed a 3×3 matrix, what is the Cramer’s phi-coefficient for the test?
c. Explain why a very small value for an expected frequency can distort the results of chi-square test.

Answer & Explanation

homofilirix

homofilirix

Beginner2022-03-02Added 8 answers

Provided that : χ2=6.2
Total number of participants = N = 40
a. If the frequency data formed a 2×2 matrix, what is the phi-coefficient for the test?
phi-coefficient(2×2)=χ2N=6.240=0.394
b. If the frequency data formed a 3 X 3 matrix, what is the Cramer’s phi-coefficient for the test?
Now the matrix is bigger than 2×2, it is now 3×3 matrix
Hence the formula for Cramer’s phi-coefficient would be :
phi-coefficient=χ2N(k1), where K = the smaller of the number of rows or columns
phi-coefficient=χ2N(k1)=6.240(31)=0.278
c. Explain why a very small value for an expected frequency can distort the results of chi-square test.
The formula for chi-square statistic is:
χ2=(OiEi)2Ei
Oi: Observed value
REi: Expected Value
For a very small value for an expected frequency , a small difference between the Observed value and Expected Value can result in a very large number as we are squaring the difference and dividing it by the expected value. This can change the value of chi-square statistic and can distort the results of chi-square test.

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