THE EXPERIMENT AS RANDOM FACTOR: OUTPUT with SPSS

Let’s go with the analysis, by using the variable “experiment” as random factor.

 

Note that, as for a classical two-way ANOVA, we will have the significant effects of group alone,

experiment alone and the INTERACTION between factors. Interaction means that it evaluates if the trend among experiments is parallel or not. I will show you the meaning with a graph.

Let’s go to the output, looking at the most important tables. The reader may repeat the analysis with normalized data.

 

It is interesting to note that: (1) the significance of the factor group is confirmed (p<0.001); (2) the factor experiment is significant (p=0.002). It means that experiments are not properly homogeneous looking at crude values; (3) interaction is not significant (p=0.185). It means that the trend in the three experiments is substantially parallel; (4) the use of the random factor influences the results of Dunnett’s test, slightly increasing the significance of the difference (as evident in the 1 vs 0 group comparison). Graphically, the trend is the following:

 

It is quite evident that experiment 3 is always the highest, and that experiment 1 is that with major deviations from parallelism, although not significant (e.g. a highest relative effect, to be tested with variable norm1).

CONCLUSION: All the concentrations of the toxicants are significantly effective as compared to controls with p<0.001, but experiments are not perfectly homogeneous (experiment 3 has always higher values as compared to the others), although the trend is overall parallel.

This analysis takes into account both the number of experiment and replicates, and it is particularly efficient with a low number of experiments (3-5). With a higher number of experiments, we may consider other possibilities, as the random factor has too many experiments and therefore a great influence on the statistical analysis, with the risk to create artifacts. I will show you other methods in the next posts.

Note: there is not a best “gold standard” number of experiments to make this approach efficient. It is only my opinion. The conclusions may vary depending on the number of replicates and exposure conditions.