I would like to compare 20 years data and three treatments (single factor). I don't have replicates for each treatment, and therefore I am unable to perform ANOVA. What test could I use instead of analysis of variance? My data are quantitative ones and normally distributed.
So you measure these treatments through time and you measure them 20 times, isn't so??
If so, you can perform a repeated measure analysis. It's like paired t-test but here you have three treatments instead of two.
As far as I get it you have a repeated measurement over time. I would suggest to build a simple linear mixed-effect model with the year added as a random effect. You find examples for that in the net, just google "mixed effect repeated measures". What do you mean by "my data are quatitative ones"? Good luck!
If you have 20 years and three treatments in each year (without replication, so each treatment appears only once each year and all years have the three treatments) you can analyze it with a linear model, but with some restrictions:
1) you have to assume no year by treatment interaction
2) you have to check the assumption of independence between years or better, include a correlation structure over years.
A good starting point is a very simple model for a block design with year as block (random) and treatment as a fix effect. Then do a residual analysis to see if you see correlation year to year within each treatment and also check heteroskedasticity year to year. If you see reasonably uncorrelated residuals and homoskedasticity, just go with that. If you see correlation or very unequal variances, try to model it (good luck, it may be difficult with a few data points). You can do the initial analysis with lmer or proc mixed
Dear Juan and Christian, I agree with your suggestions. My repeated mesures (20 years) should be considered random variable, since treatments are the fixed effect I want to compare. Since Juan mentioned linear model, I suppose 1-way-aov could then be used (I am interested to find differences between the treatments), coudln't it?
ThAnk you for all suggestions!
Francesco:
1 way AOV us definitely not appropriate. a 2 way anova without interaction might be appropriate. In fact if your data is completely balanced, then treated year as random or fixed will not make any difference. But if your data is unbalanced, it is better to treat year as random.
Behind this reasoning is the assumption that years are independent (not correlated) and homoskedastic. If that is not the case, then you need a true linear mixed model with random year effect and a correlation structure.
But as I said before: you can start with a fixed effects model to at least check the assumptions by doing residual analyses.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA