car colors - let\'s say a model comes in Black, White, Silver, and Champagne Gol

Question

car colors - let's say a model comes in Black, White, Silver, and Champagne Gold. This independent variable would be measured on a nominal scale, as we can only assign each car to a unique color group and there is no order of magnitude associated with car color. With these factors in mind: As the researcher, what statistical analysis technique would you apply to detect a statistically significant difference between the 4 means? What are the underlying assumptions of using your selected technique? If a statistically significant difference was detected between the means, what other testing would you perform to isolate specific differences between pairs of the means? Now, think about your team project - Would there be an application for these techniques to conduct your hypothesis testing?

Explanation / Answer

Sol)

here we need to test the homogenity of 4 samples, we use Anova one way

Procedure for ANOVA one way

Given that you are comparing kk independent groups, the null and alternative hypotheses are:

H0:1=2==kH0:1=2==k

:Ha: Not all are equal

Decision Rule

The decision will be to reject the null hypothesis if the test statistic from the table is greater than the F critical value with k-1 numerator and N-k denominator degrees of freedom.

If the decision is to reject the null, then at least one of the means is different. However, the ANOVA does not tell you where the difference lies. For this, you need another test, either the Scheffe' or Tukey test

SS df MS F Between SS(B) k-1 SS(B)
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k-1 MS(B)
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MS(W) Within SS(W) N-k SS(W)
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N-k . Total SS(W) + SS(B) N-1

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