# hypothesis testing dependent proportions /repeated mesurements proportions

#### nivons

##### New Member
Dear community,

I have two groups, e.g. young (N=57) and old adults (N=61), and 4 sights in a city. The task for all participants was to visit either one, two, three or all four sights in the city.
The result is a frequency table of how many participants visited the four sites.
Sight 1 Sight 2 Sight 3 Sight 4
Old 80% 45% 33% 45%
Young 78% 60% 30% 42%

I would like to test 1) sights were visited in similar proportions across the participant groups and 2) whether the proportion of participants visiting each sight was higher/lower in old people.

Looking at the table, I would expect that the sights visited are equally distributed across the groups meaning that Sight 1 has been visited by both groups more than Sights 2-4. Also I would expect that the proportion of young people that visted sight 2 is higher compared to old people. How would I test this?

I thought about a chi-square test but the as the participants can visit one or more sights the sample is not independent, this test seems not appropriate. Also, I would like to avoid the multiple testing problem as much as possible.

Thanks

#### Karabiner

##### TS Contributor
I would like to test 1) sights were visited in similar proportions across the participant groups
Cochran's Q test.

whether the proportion of participants visiting each sight was higher/lower in old people.
4 Chi² tests.

You could additionally perform a Mann-Whitney U-test with age as grouping variable and
number of sights as dependent variable.

Are old and young clearly separated (i.e. there is a "medium age" group which was left out)?
If not, a dichotmiziation such as old/young seems not very useful or even misleading, and you
should rather use age in years, if available.

With kind regards

Karabiner

#### nivons

##### New Member
Dear Karabiner, thanks for your response.

After a bit of research the Cochran's Q test is not valid on aggregates (here the percentage). As far as I understand it can only be used on
n*k matrices with 1 or 0 (n = subjects, k = condition).

Do you have any other idea how to compare if the distribution of proportions is the same in both groups?

#### Karabiner

##### TS Contributor
After a bit of research the Cochran's Q test is not valid on aggregates (here the percentage). As far as I understand it can only be used on
n*k matrices with 1 or 0 (n = subjects, k = condition).
So you mean you want to compare the two groups, not the 4 sites?

1) sights were visited in similar proportions across the participant groups and 2) whether the proportion of participants visiting each sight was higher/lower in old people.
What is the difference between these 2 questions?

With kind regards

Karabiner