Hi all, I am analysing body weights and feed intakes from a study involving chickens. I had 4 treatments in a randomised block design, 20 pens per treatment. I arranged the treatment groups into blocks of 4 so each treatment would appear once per block, to account for factors in the shed like proximity to the door, or to the heater. Now I'm analysing my data using one-way and two-way ANOVAs in Genstat and I'm including the blocks. However, I'm noticing my P values for the female chickens only are higher than I expected, but when I ignore the blocking, they are lower. For example for feed conversion ratio, with the blocks I get p = 0.043 and without, I get 0.008. Why is this? And is it ok to ignore the blocks and just analyse the data without taking them into account, if they are just complicating matters?
Thanks so much!
Lindsay
The two-way ANOVA uses one degree of freedom per block, so this reduced the residual degrees of freedom for the tests of the treatment effects. This may explain the higher p-value. I suggest using a mixed model with "block" as random factor. This uses only two d.f. so there is more power left to test treatment effects. If the experiment was designed in blocks, then you should report this and use this information in your statistical analysis. Ignoring this is not ok. And anyway, even the high p-value was still below 0.05, the usual "demarcation line" to consider the direction of the estimated effect as "conclusive". You don't win an extra price for having a smaller p-value. This would only be relevant (indirectly) if your aim is a precise as possible estimation of the treatment effect (so you don't care about the rough things like distinguishing a positive from a negative effect; you want to know if an effect of x or y is still compatible with your data).
If you do comparison among just treatments (pairs comparisons), you will get lower p-value than if you insert another factor which is "block" . This latter can increase p-value (which it may increase the probability of acceptance of the null hypothesis) and so on. Studying or inserting other factors to an experiment may increases p. For example, take an experiment with latin design, you will insert three factors: treatments, columns and rows, and hence you can expect obtaining high values for p, so on.
Safaa Kadhem Thanks for you input. So what I'm trying to work out is... would it be wrong to remove the blocking factor and pretend I didn't use blocks? Just look at the treatments alone? For some of my results, removing the blocks would mean that my results show a significant difference between groups, whereas if I include the blocks then it is not significant.
The two-way ANOVA uses one degree of freedom per block, so this reduced the residual degrees of freedom for the tests of the treatment effects. This may explain the higher p-value. I suggest using a mixed model with "block" as random factor. This uses only two d.f. so there is more power left to test treatment effects. If the experiment was designed in blocks, then you should report this and use this information in your statistical analysis. Ignoring this is not ok. And anyway, even the high p-value was still below 0.05, the usual "demarcation line" to consider the direction of the estimated effect as "conclusive". You don't win an extra price for having a smaller p-value. This would only be relevant (indirectly) if your aim is a precise as possible estimation of the treatment effect (so you don't care about the rough things like distinguishing a positive from a negative effect; you want to know if an effect of x or y is still compatible with your data).
It should be a matter of d.f.; anyway, if you designed an experiment with blocks to control “extra” variability, they should be included in the analysis,
Non-significant blocks could be excluded, although it does not necessarily mean that blocks were ineffective. Therefore, I suggest to keep them.
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