Seminar 4.2 assignments
Statistical concepts to be discussed: All relevant statistical concepts have been discussed
earlier, but repeating the discussion of several concepts is always good. In this seminar
cross table analysis is combined with statistical testing.
Don’t forget watching the videos!
1. Problem
Given. A p-value as obtained in the chi-square test for a contingency table.
Question. What does the p-value express?
(a) How likely it is to obtain the observed chi-square value or an even larger value
if there is a relation between the row and column variable
(b) How likely it is to obtain the observed chi-square value or an even larger value
if there is no relation between the row and column variable
The p-value shows the probability of obtaining a chi-square as large or larger
than that we have observed and the chi-square is a test based on the fact that
there is no relation between the two categorical variables.
(c) How likely it is to obtain the observed chi-square value or an even smaller value
if there is no relation between the row and column variable
(d) How likely it is to obtain the observed chi-square value or an even smaller value
if there is a relation between the row and column variable
2. Problem
Given. A p-value of the chi-square test for a contingency table is above the significance
level α .
Question. What is our conclusion?
(a) There is a positive relation between the row and column variable
(b) There is a negative relation between the row and column variable
(c) There is no relation between the row and column variable
Null is that there is no relationship between the two categorical variables, while
the alternative states that there is a relationship. If p>alpha, we fail to reject the
null.
(d) There is a relation between the row and column variable
Version 2021/2022 1
, 3. Problem
Given. The p-value of a chi-square test for a 2x2 contingency table is below the
significance level α =0.10.
Question. What is your conclusion?
(a) There is enough counterevidence against the alternative hypothesis, so we
reject it
(b) There is enough counterevidence against the null hypothesis, so we reject it
P<alpha, so null will be rejected (which is enough counterevidence).
(c) The probability of the alternative hypothesis being true is below 10%, so we
reject it
(d) The probability of the null hypothesis being true is below 10%, so we reject it
THE P-VALUE IS NOT THE PROBABILITY THAT NULL IS TRUE!
4. Problem
Given. Suppose we perform an experiment into the effect of biofeedback (Yes or No)
on a person’s blood pressure (too high or not). Suppose the p-value of the chi-square
test for the resulting 2x2 contingency table is above the significance level alpha.
Question. What is your conclusion?
(a) In the population the relative risk for having a too high blood pressure is
smaller than 1
(b) In the population the relative risk for having a too high blood pressure is equal
to 1
P>alpha, so we fail to reject null, meaning there is no relation with the
biofeedback. So, the risk of getting high blood pressure is equal to not having a
high BP.
(c) In the population the relative risk for having a too high blood pressure is larger
than 2
(d) In the population the relative risk for having a too high blood pressure is equal
to 0
5. Problem
Given. Suppose we perform an experiment into the effect of biofeedback (Yes or No)
on a person’s blood pressure (too high or not).
Question. What assumption is made in case the data of the resulting contingency table
are analyzed by a chi-square test?
Version 2021/2022 2
Statistical concepts to be discussed: All relevant statistical concepts have been discussed
earlier, but repeating the discussion of several concepts is always good. In this seminar
cross table analysis is combined with statistical testing.
Don’t forget watching the videos!
1. Problem
Given. A p-value as obtained in the chi-square test for a contingency table.
Question. What does the p-value express?
(a) How likely it is to obtain the observed chi-square value or an even larger value
if there is a relation between the row and column variable
(b) How likely it is to obtain the observed chi-square value or an even larger value
if there is no relation between the row and column variable
The p-value shows the probability of obtaining a chi-square as large or larger
than that we have observed and the chi-square is a test based on the fact that
there is no relation between the two categorical variables.
(c) How likely it is to obtain the observed chi-square value or an even smaller value
if there is no relation between the row and column variable
(d) How likely it is to obtain the observed chi-square value or an even smaller value
if there is a relation between the row and column variable
2. Problem
Given. A p-value of the chi-square test for a contingency table is above the significance
level α .
Question. What is our conclusion?
(a) There is a positive relation between the row and column variable
(b) There is a negative relation between the row and column variable
(c) There is no relation between the row and column variable
Null is that there is no relationship between the two categorical variables, while
the alternative states that there is a relationship. If p>alpha, we fail to reject the
null.
(d) There is a relation between the row and column variable
Version 2021/2022 1
, 3. Problem
Given. The p-value of a chi-square test for a 2x2 contingency table is below the
significance level α =0.10.
Question. What is your conclusion?
(a) There is enough counterevidence against the alternative hypothesis, so we
reject it
(b) There is enough counterevidence against the null hypothesis, so we reject it
P<alpha, so null will be rejected (which is enough counterevidence).
(c) The probability of the alternative hypothesis being true is below 10%, so we
reject it
(d) The probability of the null hypothesis being true is below 10%, so we reject it
THE P-VALUE IS NOT THE PROBABILITY THAT NULL IS TRUE!
4. Problem
Given. Suppose we perform an experiment into the effect of biofeedback (Yes or No)
on a person’s blood pressure (too high or not). Suppose the p-value of the chi-square
test for the resulting 2x2 contingency table is above the significance level alpha.
Question. What is your conclusion?
(a) In the population the relative risk for having a too high blood pressure is
smaller than 1
(b) In the population the relative risk for having a too high blood pressure is equal
to 1
P>alpha, so we fail to reject null, meaning there is no relation with the
biofeedback. So, the risk of getting high blood pressure is equal to not having a
high BP.
(c) In the population the relative risk for having a too high blood pressure is larger
than 2
(d) In the population the relative risk for having a too high blood pressure is equal
to 0
5. Problem
Given. Suppose we perform an experiment into the effect of biofeedback (Yes or No)
on a person’s blood pressure (too high or not).
Question. What assumption is made in case the data of the resulting contingency table
are analyzed by a chi-square test?
Version 2021/2022 2
