In my experiment, I have four groups namely A, B, and C. I have made the observations in all three groups in 4 different days namely 7th , 14th, 21st and 28th day. Now, I want to perform a statistical analysis that can answer me following questions:
1. Which groups are significantly different ( p value
Possibly most simple is the following solution:
- Create a vector (factor) combining day and group, let's call this DayGrp.
- fit a linear model, like model
You try to analyse through ANOVA the interaction between the groups and the day of sampling. If you have a significant difference, you apply the Tukey HSD post-hoc test.
see the code added
data were put in the "long format" (see data.txt) - the column dayNum numeric translation for "day" was added just in case but not used here.
if you find the code not explicit enough just let me know.
the Anova part is rather simple, the insight part more ... evolved.
On the whole my opinion is there are significant differences everywhere but between B anC at time day7.
Don't bother with multiplicity of tests, the p-values are so low you don't need any correction
best.
I think you can also approach repeated measures ANOVA to analyze your data.
https://stats.idre.ucla.edu/wp-content/uploads/2016/02/mixedglm.pdf
@Bui Xuan Hung, there is no indication that the observations are made on the same subject at different times, hence mixed models are hard to justify unless Shantanu Tamuly give us the infomration.
@Jean Maccario: I agreed. I assumed that the observations were recorded on the same subject/group.
@Jean Maccario
The readings were taken on same group. That is the readings were taken on same groups in different days.
@Shantanu I would like to be more precise,
in your table data.xlsx, the first row for treatment A is
day 7 : 3,1381359, day 14 : 5,292443885, day 21 : 5,438267108 and day 28 : 7,715641623
are these results observed for the same individual (or group)
and for the second row, are the results :
3,04149554; 5,4053029; 6,117426922; 5,599389366
observed/obtained for ANOTHER individual (or group)
and so on for each row in the table.
Then mixed models should or might be used - disregard my first proposal which is too simple now. you might follow Bui Xuan Hung advice.
I will give another look at your data in a few days.
Regards.
As you were asking for some hints on the code (your point 5) attached some R code 1) with the aov() function - which you may use because of the perfect balance of your data - 2) with the lmer() function of the package lme4.
The data have been modified to display the subject indicators.
If you have questions feel free to ask.
Regards.
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