Well what I understand is you did some research / experiment to observe (GPD, VFA, NH4, N, PH)
There are 3 types of treatment A, b, C
And 3 to 4 observation for each trial were recorded
Trials were done in 2 groups
1. 8 hours after treatment
2. 24 hours after treatment
The process of observation was divided into 2 part
1. to observe GPD, NH4, N, PH
2. to observe VF4
the result that you want to see is which treatment gave best results
You want to see the effect of treatment
(a) Within-Subjects Main Effect – Does the output changes within the subject with change in treatment. Here we will check are the means of four repalicate are significantly different for each treatment (ABC) for one measure (say) GPD and so on
(b) Between-Subjects Main Effects- Does Measures(GPD, NH4, N, PH) influence the output of treatment (ABC). Here we se the influence of interaction of measures and treatment.
(c) Between-Subjects Interaction Effect- Here we see the influence of trials( 8 hourss , 24hours ) and Measures(GPD, NH4, N, PH) over treatments9ABC) output
Now we will set the hypothesis
Remember you have taken samples to understand about population there fore you are not giving inference about sample BUT you are giving inference about population. So you test the null hypothesis of no differences between population means.
Therefore you state the hypothesis saying
(a) there is no difference between the population means within the subjects main effect i.e.
H0= treatment A = treatment B = treatment C
(b) there is no difference between the measures and treatment interaction population mean
© there is no difference between trials interaction with measures interaction with treatment.
Set the significant level or accuracy level . I here take an example of 95% accuracy. Therefore I say that type I error or alfa should be 0.05 thus I will check for P values = <> 0.05
In the test results if the P value is less than 0.05 then I reject the null hypothesis i.e. I say that there are less than 5% chances that there exist no difference between the outputs of the treatments.
I have created a fictitious data for understanding purposes
Please see the attachment
In the example I have created the data running command “=RAND () “ in excel there fore it may not be in exact line with the actual observed data
This computer generated data gives an output in MINITAB where P values are all >0.05 that means there is no difference in means of the observation samples BUT in real time days in many cases you may get P<0.05 and that will mean that there is significant difference in observation outputs.
Thus once you recognize that there is significant difference in the means you will want to know which one is the best
F Statistics will give the variance between the means
So you can observe the F and P column in the notepad attached
