Chi-Square

What is the ‘problem of multiple comparisons’ in statistics?

• a)how to sort out the general meaning of a set of comparisons
• b)how to do many comparisons with an overall measure of confidence
• c)how to decide which of a large set of comparisons to do
• d)how to compute a large number of comparisons efficiently

What is the usual solution to  ‘problem of multiple comparisons’?

• a)ignore the problem
• b)carry out all comparisons but pay attention only to the one with the largest difference
• c)carry out all comparisons but pay attention only to the one with the smallest difference
• d)carry out a single overall test followed by a detailed follow-up analysis

: The chi-square statistic is similar to all other test statistics we have discussed  in that it compares observed values to values that would be expected if H0 were true. 

• True
• False

Which statement is NOT correct about the c2 test statistic?

• a)A value close to 0 would indicate expected counts are much different from observed counts.
• b)A large value of the test statistic would be in support of the alternative hypothesis.
• c)A small value of the test statistic would indicate evidence supporting the null hypothesis.
• d)The test statistic is the sum of positive numbers and therefore must be positive.

Here is a two-way table of counts. The expected counts are in red. The data are based on an SRS with two categorical variables.  Is it safe to use the chi-square test with critical values from the chi-square distribution?

50 51.35 36 31.65 12 14.99
16 18.34 13 11.31   6 5.36
 54 50.30 25 31.01 17 14.69

• Yes because all of the observed counts are 5 or greater
• b)Yes because all of the expected counts are 5 or greater.
• c)No because the expected counts are not whole numbers.
• d)Yes because the sum of observed counts = sum of  expected.

Using a computer program, the chi-square test statistic for the commuter data is c2 = 5.37 with P-value < 0.01.  If we use a = 0.05, what conclusion is appropriate?

• a)Don’t reject H₀; the results are significant.
• b)Don’t reject H₀; the results are not significant.
• c)Reject H_0; the results are significant.
• d)Reject H₀; the results are not significant.

Tags

CCSS.HSS.ID.B.5

CCSS.HSS.IC.B.5

If the chi-square test is significant, what should we do as a follow-up? 

• a)compare expected counts to observed counts in each cell
• b)examine the components of the chi-square test for each cell
• c)informally compare the conditional distributions
• d) all of the above

What are the hypotheses for the chi-square test for 2-way tables of   counts? 

• a)H0:  no relationship, Ha:  relationship
• a)H0:  relationship, Ha:  no relationship
• a)H0:  strong relationship, Ha:  weak relationship

Tags

CCSS.HSS.ID.B.5

CCSS.HSS.CP.A.4