Goodness Of Fit Test

Question 1

What is the chi-square goodness of fit test used for?

Answer 1

It is used when there is one categorical variable to compare the squared difference between observed and expected frequencies.

Question 2

What is the expected frequency distribution based on?

Answer 2

Theoretically equal frequencies in each category.

Question 3

If there are 36 participants in a study with 3 categories, what is the expected frequency in each category?

Answer 3

12 (36/3 = 12).

Question 4

What does the null hypothesis (H0) state in a goodness of fit test?

Answer 4

All proportions are equal.

Question 5

What does the alternative hypothesis (Ha) state in a goodness of fit test?

Answer 5

All proportions are not equal.

Question 6

How is the degrees of freedom (df) calculated for a goodness of fit test?

Answer 6

df = k - 1, where k = number of categories.

Question 7

How is the expected frequency (E) calculated?

Answer 7

E = n / k, where n is the sample size and k is the number of categories.

Question 8

For a sample size of 300 and 3 categories, what is the expected frequency for each category?

Answer 8

100 (E = 300 / 3 = 100).

Question 9

What conclusion can be drawn if the calculated x2 is greater than the critical value?

Answer 9

Reject the null hypothesis.

Question 10

What is the APA format for reporting chi-square results?

Answer 10

x2 (df, N) = Calculated x2, p < 0.05 or p > 0.05.

Question 11

What does it mean if there is not enough evidence to suggest that the observed proportions are not equal?

Answer 11

There is not a statistically significant difference in the proportions.