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I performed a cluster analysis and now want to consider if the variable “I have a smartphone” (yes/no) significantly differs between the cluster solutions by using the chi-square test. The p-value was greater than 0.05, so I have to accept the null hypothesis (there is no significant difference between the clusters and having a smartphone). Within all cluster solutions, the majority of people have a smartphone. Can I, therefore, assume that all interviewees, no matter to what cluster they are assigned, use smartphones in their lives? Does this make sense?

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  • $\begingroup$ The majority of people nowadays use smart-phones in their lives. It looks like it does make sense to them. $\endgroup$
    – ttnphns
    Nov 12, 2013 at 13:47
  • $\begingroup$ No, you can't assume that all interviewees, no matter the cluster, use smartphones. Just ignore @ttnphns' answer ;-) $\endgroup$
    – Michael M
    Nov 12, 2013 at 14:28
  • $\begingroup$ But the majority (not all interviewees) in my data use smart phones, regardless of their cluster affiliation. I am confused now :-) $\endgroup$
    – cathy
    Nov 12, 2013 at 15:41
  • $\begingroup$ This last comment is correct. It has no relation to the chisquared test though. $\endgroup$
    – Michael M
    Nov 12, 2013 at 16:46
  • $\begingroup$ @cathy you might have noticed that my comment was a joke capitalizing on play of words in your qiestion $\endgroup$
    – ttnphns
    Nov 12, 2013 at 17:31

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Was the variable "having a smartphone" used in the cluster analysis? If so, that would invalidate the chi-square test.

Otherwise, it should be OK ... but as for your conclusion

Can I therefore assume that all interviewees, no matter to what cluster they are assigned, use smart phones in their lives? Does this makes sense?

you are jumping from "having a smart phone" to "use smart phones in their lives" which does not seem to be the same ...

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