# What can I conclude from the following one way ANOVA result?

I used a one-way ANOVA to test if importance levels of attributes have changed over the years (Data comes from a survey of consumers) with the following results (Mean ratings):

+-----+---------+
| Year|Attribute|
+-----+---------+
| 2000|     4.39|
+-----+---------+
| 2010|     4.30|
+-----+---------+
| 2011|     4.38|
+-----+---------+
| 2012|     4.43|
+-----+---------+


The overall ANOVA is significant and the Tukey post-hoc test of pairwise comparisons indicates that the mean rating for the year 2012 is greater than the mean rating for the year 2010 at $\alpha=0.05$ (i.e., $4.43 > 4.30$). None of the other comparison pairs are significant.

How can I translate the ANOVA results into plain English?

It seems an odd result. Importance levels seem stable for the years 2009, 2010 and 2011. But, the importance level for the year is greater for the year 2012 than the importance level for the year 2010 but not for the year 2009 and 2011. I understand the statistics as to why this can happen but am confused with how to translate the above into plain English.

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## 1 Answer

I think I know how to explain the 'paradox' in plain English.

The survey's sample size is not sufficiently high to detect differences that likely exists between the mean importance ratings for the year 2012 relative to the importance ratings for the years 2009 and 2011. In summary, the study's sample size is not sufficiently high.

PS: One should also point out that while the difference in importance ratings between the years 2012 and 2010 is statistically significant it is probably not practically significant (i.e., the increase in not of any practical importance).

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