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I have a survey data with Yes/No response variable and a categorical variable assigning survey takers to one of the 4 groups:

  • 16-24 years old
  • 25-34 years old
  • 35-54 years old
  • 55+ years old

I want to test the significance of my hypothesis:

People in the age group 55+ are more likely to use smartphones.

What test should I use to test this hypothesis.

If I had to change the response variable to multiple categories, how would my choice of the statistical test be affected?

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  • $\begingroup$ Hi Sha, what will your hypothesis be if you change your response to multiple categories ? Still the same question? $\endgroup$ Commented Jan 28, 2019 at 22:34
  • $\begingroup$ Hi V.Aslanyan, Thank you for your response. Yes it would be the same question. Thanks $\endgroup$
    – Sha
    Commented Jan 28, 2019 at 23:02

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To test your first hypothesis you want to transform your data from Yes/No to 1/0 and perform one way ANOVA as a first step. The hypothesis for one way ANOVA is that all means within the group are the same. If your p-value is less than your threshold, your hypothesis is not supported since the test found no statistically significant differences between your group means. If the one way ANOVA fails, you need to perform post-hoc tests. I would personally start with LSD (Least Square Difference) test. This test will be useful for the second part of your question too.

This is a decent guide to one way ANOVA. This has a good list of some popular post-hoc tests.

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  • $\begingroup$ Thank you! I was just wondering if the Binomial test would work for the first hypothesis? $\endgroup$
    – Sha
    Commented Jan 29, 2019 at 11:44
  • $\begingroup$ if you want to compare your 55+ year to every one else combined, then yes, it would work for the first hypothesis. I was under impression that you want to keep age groups separated based on your setup. $\endgroup$ Commented Jan 29, 2019 at 17:01

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