Mod 10

Question 1

When do you use chi-square goodness of fit test?

Answer 1

SINGLE categorical variable
- test if category proportions claimed in Ho are a good fit for the observed data

p1 = p1o (expected proportion), p2 = p2o (expected proportion), p3 = p3o (expected proportion)

Question 2

What are the conditions of the chi-square goodness of fit test?

Answer 2

• observed cell counts are based on a random sample or representative sample
• all expected cell counts ≥ 5

Question 3

What are the interpretations of the chi square (x^2) for goodness of fit test?

Answer 3

large x^2 = RTN

small x^2 = FTRN

Question 4

Compute the expected count for a cell in a chi square goodness of fit test

Answer 4

n (overall sample size) x expected proportion for that cell

EX: n = 178, expected proportion = 0.451

expected count, assuming that Ho is true, = (178)(0.451)

Question 5

Compute the test statistic for chi square goodness of fit test

What distribution does x^2 have when the null is true?

Answer 5

x^2 = (observed - expected count)^2/expected count + …..

df = (k-1)

When Ho is true, x^2 has chi-square distribution with df (k-1)
- right tail area of x^2 test statistic

Question 6

What are the steps to conducting hypothesis test for chi-square (goodness of fit test)?

Answer 6

1) Hypothesis
H0: p1 = p1o…
Ha: not all equalities in Ho are true

2) Conditions
- observed cell counts are based on random sample or representative sample
- all expected cell counts ≥ 5

3) Test statistic

4) P-value
- chi-square are right-skewed distribution characterized by df (k-1)
- find right tailed areas to get p-value

5) Conclusion

Question 7

When do you use chi-square test of independence/homogeneity?

Answer 7

TWO categorical variables
- whether the 2 categorical variables are associated or independent

H0: variables 1 and 2 are independent
Ha: variables 1 and 2 are associated

Question 8

What are the conditions of the chi-square goodness of fit test?

Answer 8

• observed cell counts are based on a random sample or representative sample
• all expected cell counts ≥ 5

Question 9

Compute expected cell counts of the table for chi-square test of independence

Answer 9

expected = row total * column total/overall total

Question 10

Compute the chi-square (x^2) for chi-square test of independence

What is the degrees of freedom for chi-square independence?

Answer 10

X^2 = (observed - expected)^2/expected count + …..

df = (r-1)(c-1)

Question 11

Compute p-value for chi-square test of independence

Answer 11

chi-square distribution with df (r-1)(c-1)

• get the right-tailed area of the test statistic (x^2)

Question 12

What are the steps to conducting hypothesis testing for chi-square test of independence

Answer 12

1) Hypothesis
H0: variables 1 and 2 are independent
Ha: variables 1 and 2 are associated

2) Conditions
- observed cell counts are based on a random sample or representative sample
- all expected cell counts ≥ 5

3) Test statistic
X^2 = (observed - expected)^2/expected count + …..
df = (r-1)(c-1)

4) P-value
chi-square distribution with df (r-1)(c-1)
- always get the right-tailed area of the test statistic (x^2)

5) Conclusion
- p-value ≤ alpha = RTN, enough evidence to conclude association
- p-value ≥ alpha = FTRN, not enough evidence to conclude association