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I have data that shows intent to purchase a car dependent on country (measured on 7 point Likert scale). So for example, I have 50 participants that rated how likely they would be to purchase a car made in the US, Japan or Germany. I also measured their rating (again on a 7 point Likert scale) of various car criteria (visual appeal, performance, safety etc.) When I work out the means for each country for intent to purchase I can see a difference in the means and I can also see a consistent different in the means of the car criteria ratings by country. When I run an ANOVA test this comes out as not statistically significant. Am I running the wrong test for this?

Edit: My data has been weighted to make it more representative of the population.

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    $\begingroup$ If you only worry about which test you should have used after you failed to reject, you're significance hunting (if you rejected with the ANOVA would you have asked about using the wrong test?). It's important to plan your analysis properly, before you start looking at your data or your p-values don't mean much. Even ignoring that it's difficult to see what you mean when you assert that there are differences that the test failed to find; your question lacks important detail. Sample means will always vary, of course, but that may not point to anything but random variation due to sampling. $\endgroup$ – Glen_b -Reinstate Monica May 20 '18 at 1:33
  • $\begingroup$ Thank you for @Glen_b. When I ran the ANOVA test on the unweighted data, the results were very different and were statistically significant. As my sample was not huge a couple of the gender and age groups had very high weightings (one was over 16), which has meant that my values are much bigger than in the data that was collected. Do you think in this instance it would have been better to not weight the data? $\endgroup$ – DL1984 May 20 '18 at 4:05
  • $\begingroup$ I don't follow what your weights are or why you would weight/not weight -- again, there's a lack of information about what's going on here. [Only one of the two analyses is likely to make sense; but you should know which one that is before starting any analysis, and preferably before even collecting data.] $\endgroup$ – Glen_b -Reinstate Monica May 20 '18 at 8:01
  • $\begingroup$ ANOVA seems fine for comparison of (weighted) means, but we can't really judge accurately without exact information. You are basically only telling that the test is not significant but that has nothing to do with the test being wrong or right ( and as Glen_b rightfully mentions sounds much like p-hacking ). $\endgroup$ – Sextus Empiricus May 22 '18 at 18:53
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Obviously, the intent to purchase and ratings are not 100% linearly dependent. There are three categories of reasons people make a decision. First is the product, second is personal preference, third is external factors. External could be that society is car driven. Intent to purchase is a combined measure of all three. The ratings only measure the first category.

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