which statistic parametric test should I use?

jgag

New Member
#1
I have doubts on a similar topic: in a laboratory experiment, specimens with 2 different compositions were subjected to a demineralization process and, later, to 5 different treatments for remineralization (n=8).
a) assuming a normal distribution of the data, since the same specimen was subjected to the 2 processes (demineralization and remineralization), is it mandatory to use a 2-way repeated measure ANOVA or is there any exception condition?
b) assuming a non-normal distribution of the data, which test should be conducted (equivalent to the 2-way repeated measure ANOVA)?
 

Karabiner

TS Contributor
#2
Well, normal distribution of "data" (sample data) is irrelevant. The model assumes normal distribution
in the populations from which the sample data are drawn. Or, more simply, the prediction errors from
the model should be normally distributed. Since your sample size is very small, violation of this
assumption could be problematic (AFAIK). At the same time, one cannot demonstrate with sufficient
evidence that indeed the error distribution in the population is normal. Maybe there is some
reference which demonstrates that ANOVA is robust against non-normality even in small samples.
is it mandatory to use a 2-way repeated measure ANOVA or is there any exception condition?
You did not state a clear research question, therefore it is difficult to comment on which approach
could be useful here.

With kind regards

Karabiner
 

jgag

New Member
#3
First of all, thank you for your reply.
In the first part, I understood that, in addition to normal distribution, homoscedasticity of the variances must also be checked.
About the research:
2 materials of different composition will be subjected to a substance that will cause demineralization of their structure. Then, they will be submitted to 5 different substances to verify if one of them is capable of promoting remineralization (n=8 for each experimental condition).
Each specimen will have its mechanical strength measured at 3 times: 1) before undergoing demineralization (initial measure); 2) after demineralization; 3) after remineralization treatment with each substance tested.
I understand that if measurements are performed on the same specimen, it would be recommended to conduct a 2-way repeated measurements ANOVA. Am I right? Are there any exceptions in a similar experiment? A simple 2-way ANOVA could be conducted?
Is there an equivalent non-parametric test (in the case of non-normal distribution and heteroscedastic sample)?
I hope I was more clear.
 

Karabiner

TS Contributor
#4
First of all, thank you for your reply.
In the first part, I understood that, in addition to normal distribution, homoscedasticity of the variances must also be checked.
Heteroscedascity is an issue, if two groups of different sizes are compered.
For repeated-measures analyses, there are additional specific assumptions.
2 materials of different composition will be subjected to a substance that will cause demineralization of their structure. Then, they will be submitted to 5 different substances to verify if one of them is capable of promoting remineralization (n=8 for each experimental condition).
Each specimen will have its mechanical strength measured at 3 times: 1) before undergoing demineralization (initial measure); 2) after demineralization; 3) after remineralization treatment with each substance tested.
Ok, I asked for your research question, but seemingly you want us to guess. From this description I understand that you do not want to compare between the two materials, and that you do not measure after each of 5 remineralizations, but only after all 5 reminalizations were performed. So you could use a repeated-measures analysis of variance with 1 factor (3 levels), or maybe better a Friedman test. The importance of the baseline was not explained here, though - maybe it is not important, and you just do a pre-post comparison (t-test or Wilcoxon signed rank test).

Is there an equivalent non-parametric test (in the case of non-normal distribution and heteroscedastic sample)?
No.

With kind regards

Karabiner
 

fed2

Active Member
#6
Well, normal distribution of "data" (sample data) is irrelevant.
actually it is because it tells you about whether the population it was sampled from is normal. try drawing a box plot