Reconcile ANOVA & correlation results

[ColinD]

Hi there, my first post here.

I have 6 sets of annual data of the number of flowers on individual plants sampled from a population. N = 39,54,73,72,66,57. The varying N are because the same individuals were sampled and some were not present in some years.

Using Minitab 16, 1-way ANOVA results are F(5,355)=2.21, p=0.063 with 95%CI's all overlapping. However a simple calculation of Pearson's r of mean flowers against year gives r=0.974 p=0.001. The mean increases from 7.6 - 15.7 over the 6 years.

How to reconcile no significant difference between the means from the ANOVA and a significant increase over the years as shown by the r value?

Many thanks

Colin

[ichbin]

You are seeing the classic disadvantage of (mis-)using an ANOVA when your independent variable is ordinal. ANOVA is meant for situations when the independent variable is categorical (e.g. political party or fifth grade teacher). It has no notion that there is an ordering between years and thus can only detect the case when one year shows a significant deviation from others, not the case when there is a gradual trend over the years. If such a trend is clear when looking at the years in order, but not when looking at any two given years, the ANOVA is likely to miss it.

[ColinD]

Many thanks ichbin & HNY all around!

I'd appreciate some follow-up advice now that I've been and done some reading. I'm still left with not knowing how to best explore and present this type of data. I trawled a lot of papers that described 'between years' effects and a few used ANOVA the way I had (not implying that is justified). So back to reconciling a time series plot of means that shows the 95% CI all substantially overlapping (indicating that the variance is too great to reject the null hypothesis that the means are not different?) and the significant Pearson's r from means v years.

What would be the recommended way to determine the level/significance of between years effect? I find some that have categorised this data format as repeated measures (measuring the same thing on same subjects several times) and used 1-way ANOVA to determine between years effects (followed up with Tukey or Bonferri where there was a significant difference). Other tests that have been applied over two time periods have been Kruskal-Wallis, Mann-Whitney U or Kolmogorov-Smirnoff for example.

[bugman]

This a very intersesting paper on this subject.