# comparison of proportions in one sample

#### vals

##### New Member
Hello,
i'm new in the community. I tried to solve my problem checking several websites. However, I have still doubts.

In a master project we are collecting indicators to track the progress towards sustainability. We have built 4 categories to which each indicator can be linked (the categories are mutually exclusive). The categories reflect the typology of action that the indicator is tracking. Anyways. We have analyzed 270 indicators and linked them to the 4 categories.
We have then that 10% is under the category A, 80% under the category B, 5% in category C, 5% in category D.

Now, we could just present the results with a pie chart and saying that the majority goes into category B. But can we do something more professional (and statistically correct).
Our idea was to first do a chi square test to check the significance of the difference with an hypothesized 25% 25% 25% 25%. does this make sense? We do it, and we see that the percentages deviate significantly from this pattern.

second, we would like to test if that 10% is significantly higher than 5% (so that category A is significantly more populated than category C).
we could also do it with all the pairs of categories, even though, for our case, the difference between 80% and 10% is pretty clear. However, we would like to do it methodically.

I checked online and come across 2 website that suggest how to do it.
https://measuringu.com/preference-data/ this suggests to use the analysis of the confidence interval. Does it make sense?

https://www.statpac.com/statistics-calculator/percents.htm suggests to use one sample t-test. However, it is a calculator and I cannot really see how the calculation is made.
If for example I want to test if 10% is higher than 5% for my sample, these 2 methods give different results.

Any help?
Thanks so much!

#### obh

##### Active Member
Our idea was to first do a chi square test to check the significance of the difference with an hypothesized 25% 25% 25% 25%. does this make sense? We do it, and we see that the percentages deviate significantly from this pattern.
Yes (if meet the assumptions: independense, expected value>5)

second, we would like to test if that 10% is significantly higher than 5% (so that category A is significantly more populated than category C).
we could also do it with all the pairs of categories, even though, for our case, the difference between 80% and 10% is pretty clear. However, we would like to do it methodically.
I assume you can use chi test as well (assumptions), is it a specific combination? do you check all the combinations? or the minimum proportion to maximum proportion (if you compares the minimum to the maximum or all the combinations you need to take a smaller p-value )