I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is it wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)

2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is it wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)

2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?

I read in several books as well as in different posts (e.g. here) that independency is required for two-proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is it wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)
2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is it wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)

2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?

I read in several books as well as in different posts (e.g. here) that independency is required for two-proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)
2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?

I read in several books as well as in different posts (e.g. here) that independency is required for two-proportions z tests. But so far I could not find an explanation why this is the case and what would happen if such a test were used for comparing proportions in non-independent data.

As an example: All participants answered two questions. One question was answered correctly by 85% and the other question was answered correctly by 65%. I am interested in whether the proportion of correct answers is significantly larger for the first than the second question.

Therefore, I would like to understand:

1. Why is it wrong to use a two-proportions z test in this case? (Does it also depend on the question one would like to answer with the statistical test?)
2. What are the consequences of using the procedure nonetheless (e.g. will the significance values be systematically too high or low)?