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I am currently conducting a short research paper for my university course and am struggling to determine which statistical analysis would be appropriate for the data I have collected.

I surveyed two groups of 50 people:

50 x people aged 40 and over 50 x people aged under 40

My hypothesis is that there is a significant difference between the opinions of people aged 40 and over and that of people aged under 40 as to whether they would consider allowing a robot perform a filling on their teeth instead.

Tables of results are below:

40 and over

Yes: 9

No: 41

Under 40

Yes: 35

No: 15

I have looked into how to compare two groups but cannot seem to find one to best suit my data to be able to analyse and interpret results.

I was wondering if someone could point me in the right direction please?

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  • $\begingroup$ How large is the population you are studying and how did you draw your sample? What type of special survey design, if any did you employ? To analyze most survey data correctly you can't just use the formulas you find in most elementary statistical textbooks. You usually have to take into account things like a finite population correction, the design of your study, and know how many people are in the population you are trying to make inferences about. But since this is for an introductory university course, they may allow less rigorous analysis for pedagogical reasons. $\endgroup$ – StatsStudent Jan 20 at 21:26
  • $\begingroup$ You should try to better define your hypothesis and population too. I suspect some indigenous tribes who have had no contact with outside-tribe people may be more reluctant to have robots performing fillings on them than people who live in Boston. $\endgroup$ – StatsStudent Jan 20 at 21:32
  • $\begingroup$ Hi, many thanks for the replies. I stood in a busy market town on a Saturday afternoon and asked random people to fill out the questionnaire. It was very few questions, 1: are are 40 or over or under 40, and would you consider a robot performing the procedure. $\endgroup$ – robin rolfe Jan 20 at 21:50
  • $\begingroup$ OK. So do you think your survey is representative of "people" in general or of some other, more finely defined population? If so, you should think through what the implications are of sampling only at that place and at that time. Generally speaking it sounds like you've gone about the assignment backward - you thought about your population after having collected data. So, now you are stuck trying to determine who your data will generalize to. $\endgroup$ – StatsStudent Jan 20 at 22:01
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You want to check if the two samples come from populations with the same proportion of yes/no. That's a proportion test of two populations with independent samples. Googling for that you will be able to find a lot of sources about how to perform such test with any statistical tool (or even with just a pencil, a paper and a hand calculator).

Usually proportion tests have low power and therefore need large samples to detect difference in proportions between two populations. However, the difference between your samples is so large that it's likely to be significant even with such small samples.

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