Appropriate statistical test binary variables

by Anita   Last Updated September 14, 2018 15:19 PM

Basic questions, I know.. any help is appreciated!

I conducted a survey on people with an impairment. This survey was either filled online, or by phone: the respondent could choose. I want to know if the people I reached by phone are significantly more likely to be severely impaired. Let's say my data looks like this:

------------------------------ Internet ----- Phone

Severe impairment ------- 52 ---------- 26

Not severe impairment -- 401 --------- 95

(Not my real figures, these are slightly different)

Should I conduct a z-test or a chi-square test? I would say chi-square, but I don't know how to interpret the result I get in R. chisq.test(table(impairment, phone)), where both phone and impairment are two binary variables, gives me: X-squared = 1.7012, df = 1, p-value = 0.1921 How to interpret these results? I don't even know how to phrase my null hypothesis in a "statistical" way (both groups are just as likely to be severely impaired - isn't there a better way to phrase this?)

Additionally, I want to know if the people I reached by phone are significantly more likely to be older.

------------------------------ Internet ----- Phone

Average age ---------------- 63 ---------- 68

Since I am comparing means, I am thinking that a t-test would be appropriate, with t.test(age ~ phone). My null hypothesis is that there is no difference in age among the two groups. My command in R gives me: t = 3.3718, df = 522, p-value = 0.0008022. Alternative hypothesis: true difference in mean is not equal to 0 . This means that I need to reject my null-hypothesis, right?

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