If I have to evaluate the effect on a dependent variable across three treatment conditions (Control , Mild , Severe) and along three time points (0 hour, 24 hours , 48 hours) in four different genotypes what kind of ANOVA should i choose ( Three way ANOVA or Three way Mixed ANOVA ) and Why?
I have three factors (1) Treatment (2) Time points (3) Genotype.
For each condition I had three biological replicates.
The sample collected in my case is plant leaf sample and the dependent variable is gene expression fold change. The sample collected for different time point for each treatment condition are from different biological replicates.
Sufficient biological replicates were kept for sampling to avoid sample collection from same plant and ensure that the changes in gene expression due to mechanical damage(detaching a leaf ) is not carried forward in the next time point.
Thanks Ette Etuk for replying to my question. Few people suggested me to do 3 way repeated measures ANOVA?
Will it be applicable in my experimental design?
Can you please let me know which 3 way ANOVA will be applicable in my case?
(1) Three-Factors Repeated Measures ANOVA (2)Three-factor mixed ANOVA (3) Three- way factorial ANOVA or any other 3 way ANOVA applicable.
I don't have much idea regarding the different form of ANOVA stated above and often get confused . Can you please clarify which ANOVA would be applicable for my experiment design and dataset.
When I analyze only one genotype I can consider the treatments as between subject variable (Control, Mild , Severe) and time points(0 , 24, 48 hrs) as within subject variable. In this case there is not much problem. It ll be a 3X3 two way ANOVA.
However when I want to analyze all the four genotypes together then it becomes 3X3X4 three way ANOVA. In this situation what kind of variable will be the genotypes (4 no.s)?? Within subject or between subject? Can you please give your suggestion??
I repeat that this is a 3x3x4 TreatmentXTimeXGenotype fixed effects factorial model. The three levels of the treatment factor: control, mild and severe, are fixed in the sense of being specifically rather than randomly chosen. The same argument is applicable to the three levels of time (0 hour, 24 hours, 48 hours) and the four levels of genotype. The design is not mixed effects because no factor is random effects. This is a 3-way fixed effects factorial design.
Ette Etuk, If this were analyzed with a mixed model, the random effect would be plot, which acts as the subject of the experiment. This is often done with repeated measures designs to account for the non-independece of observations.
Dear sir (Salvatore S. Mangiafico),
My experiments was carried out with two year old seedling in pots and for all the conditions and time points for each genotype i had enough biological replicates as destructive sampling was carried out and none of the plants used for sampling at each stage was used further. For each sampling stage i had collected samples from three biological replicate and therefore i have three values for each stage. Other than this i dont have any other experimental replication. From this the genotype and treatment conditions appears to be fixed factors. Now my concern is the time point sample colllection. I have seen in many papers that time point sample collection is considered as repeatable measure . Again this may may noted that the data collection in time points are carried out in the same samples in many papers and so it was taken as repeatable measure. However in my case the data or sample collection have been made on different biological replicates of the same genotype or clone as destructive sampling was carried out. So, In my case does time point as repeatable measure applicable or not? Can you please share your views on applicability of mixed model and time series as repeatable measure in the conditions mentioned above in my experiment. Regarding the plots as repeatable measure i dont think the condition arises as the experiment was carried out in pots. Please correct me if i am wrong anywhere as i dont have much knowlegde in statistics .
Correction :
The plants were raised from vegetative cuttings (clones )and not seedlings.
If it is reasonable to think of some experimental unit as a subject, then you can consider your experiment repeated measures and use a repeated measures analysis or mixed model. This would be for example if you have the three plants used across time in the same pot. Or if each plant is in its own pot but the ones used across time were all clustered together.
If the plants used across time cannot be though of as a subject like this, you can just treat the experiment as a completely random factorial design.
I suspect in your case, because you are using uniform plant material and the whole experiment is over in a couple of days, that there won't much effect due to different plants or location in the greenhouse. That is, that analyzing the experiment as either regular factorial or as repeated measures won't matter much.
Dear sir (Salvatore S. Mangiafico),
In my case the plants were almost kept in the same location. So , there won't be much effect of location overall. Although biological replicate were used for sample collection for each time point they were from the same planting material (vegetative clones) for each genotype so there won't be much of difference in terms of planting material and no biological replicate was used again once it underwent destructive sampling. Regarding time, the treatment lasted for around 3 months and thereafter the sample collection was over within 48 hours consisting of all the time points.
In this scenario would you suggest me to go on with 3-way fixed effects factorial design analysis with Treatment, Time, Genotype as fixed effects or factors ( 3x3x4 Treatment X Time X Genotype) as suggested by Ette Etuk sir.
Hello,
I think there is no "best model" here.
I agree with the previous suggestion that treatment can be a fixed effect. Time can be used as the repeated measurement and in this case the format of the data will change.
As I am a fish breeder and working in quantitative genetics (Animal Breeding and Genetics), we normally see genotype as random or fixed effects. First of all, I highly recommend to define what is the definition of the genotype (come form a random sample of infinite number of genotypes VS all the genotypes were used here)? because that will help to determine why genotype should be either random or fixed effect and that will lead to the conclusion of " mixed model or not" Second, if the repeatability is of interest you may fit the model for this effect. This depends mainly on your research question. Of course, it may be interesting to understand the repeatability of your measurement at different time points.
So there is no one model for all. You may start explore things first.
Perhaps, start with assumption testing would be the best, i.e. residual analysis.
Best Wishes, Panya
I think my advice is that, if there is a sensible way to consider the plants used over time as a subject ---- for example if the three plants were all kept together while they were growing for three months and then one was used at 0, one 24, and one at 48 hrs.---- then it makes sense to use a repeated measures or mixed model accounting for the repeated measures.
If you can't sensibly define a subject like this, then there is no subject which is subjected to repeated measures, and the observations are independent even though they occur over time.
I think based on your description that you can make the argument to use a fixed-effects anova.
Panya Sae-Lim makes a good point about genotype, too, that you might consider.
Three way repeated measure ANOVA is sufficient for your expt.
@Kurian Mathew Abraham
Sir,
If I consider using three way repeated measure ANOVA then can you please tell me what will be my within subjects factors and between subject factors (Treatment, Time points, Genotype). I am a bit confused with this.
Or else Should I take Treatment, Time points, Genotype as Fixed factors?
Thanks in advance.....
i agree with
Afruza Zaman
My experiments was carried out with two year old seedling in pots and for all the conditions and time points for each genotype i had enough biological replicates as destructive sampling was carried out and none of the plants used for sampling at each stage was used further. For each sampling stage i had collected samples from three biological replicate and therefore i have three values for each stage. Other than this i dont have any other experimental replication. From this the genotype and treatment conditions appears to be fixed factors. Now my concern is the time point sample colllection. I have seen in many papers that time point sample collection is considered as repeatable measure . Again this may may noted that the data collection in time points are carried out in the same samples in many papers and so it was taken as repeatable measure. However in my case the data or sample collection have been made on different biological replicates of the same genotype or clone as destructive sampling was carried out. So, In my case does time point as repeatable measure applicable or not? Can you please share your views on applicability of mixed model and time series as repeatable measure in the conditions mentioned above in my experiment. Regarding the plots as repeatable measure i dont think the condition arises as the experiment was carried out in pots. Please correct me if i am wrong anywhere as i dont have much knowlegde in statistics .
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