## Probability of survey item-responses when participants could choose multiple items

Hi there,

I am trying to reanalyze some data from published research.

My question is: how do you compare 2 proportions of responses, drawn from the same sample, when participants had the option of choosing "up to three" items on a 6-item scale?

The survey question was: Under which circumstances do you consider yourself at most risk for sexual assault? Participants then chose "up to three" risk factors (out of six), such as "when intoxicated," "walking alone," "after taking drugs," etc. I have copied and pasted the data below.

But, for example, “after drinking" was chosen by 72% of the sample, "walking alone at night" was chosen by 70% of the sample, and "after having a drink spiked" was ranked by 75% of the sample.

The researchers concluded that participants were "more likely" to rank "having a drink spiked" as a more significant risk factor than any of the other items. No statistical test was performed to determine this “likelihood.”

Given that participants had a choice to choose "up to three" responses, and that many of the items had very similar proportions, I feel that the conclusion of the study may be unsound.

Does anyone have advice about how to explore this question? I would like to know how to compare the probability of these responses, given the same sample of participants, and the option (but not the requirement) to choose 3 items.

I would very much appreciate any advice you may have!

Here is more information on the data, in case any part of my explanation is unclear:

1) After drinking: 144 (72%)
2) Walking alone at night 140 (70%)
3) After taking drugs 44 (22%)
4) Drink-spiking 150 (75%)
5) In your home 10 (5%)
6) Walking in high-crime-area 58 (29%)

144+ 140 + 44 + 150 + 10 + 58= 546 total responses.

The authors do not report how many participants chose 3 options, 2 options, or 1 option.

The authors do not do a great job of reporting sample size, but I am assuming it is 200. So, not everyone would have responded to the maximum of 3 items.

But each proportion must have been derived from the sample size of 200.