# Test for significance binary data

A test was conducted on the staff at my workplace to identify each persons lung capacity. The data we got from the tester was whether or not each person "passed" or "failed". Lets say 50 people were tested and 30 passed.

I now want to split the workers into two groups "factory workers" and "Office workers" and see if there is a difference between their results. Would my null hypothesis be that factory workers and office workers have the same lung capability?.

What test for significance should I use? Would my population mean be 60% (30/50)?

• Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. – gung - Reinstate Monica Apr 12 '16 at 23:12
• No it's a real question from my workplace – Dominic Smith Apr 13 '16 at 23:25

The proper hypothesis and test depends on what data you have. In your question you say that all you have is "passed" and "failed". In that case, you cannot test lung capacity but only whether the same proportion passed. You could do this with a t-test of proportions.

If you can get data on their actual lung capacity (in mm or however you measure this) then you could do something else but what you should do would depend on the nature of the data. A comparison of means or medians would be likely candidates.

But if you have more information (e.g. age, sex, etc.) on the people, then you could include that and do a regression with "type of worker" as one independent variable.

First, Do you want to compare your factory worker and office worker on their result on the test or with the binary variable passed and failed?

Because there a chi-square, a t-test or an anova, you would need to check those an see there assumptions

• This is really something that could be a comment...its not an answer. – user75138 Apr 13 '16 at 1:43
• I want to do a test that tells me whether or not the difference in lung function between office workers and factory workers can be considered statistically significant. So lets say 80% of the people who failed were factory workers and the other 20% of those who failed were factory workers. How do I test for significance – Dominic Smith Apr 13 '16 at 23:29
• If you have the mean score or exact score for everybody go read about t-test or anova on the web, if you just want to use the categorie pass and failed go read about chi-square if you are using spss or excell – lili Apr 14 '16 at 1:31