Is ANOVA right for me?

#1
Hi there!

So I am relatively new to the statistical side of biological data and want to know the best test for my data. The experiment was looking at the concentration of a hormone over time between two treatments with multiple replicates.
something like this:

Treatment A:
Rep 1:
Times: 0, 1, 5 hours
# of samples at each time: 5
Rep 2:
Times: 0, 1, 5 hours
# of samples at each time: 5
Treatment B:
Rep 1:
Times: 0, 1, 5 hours
# of samples at each time: 5
Rep 2:
Times: 0, 1, 5 hours
# of samples at each time: 5

Basically I want to run two test without loosing too much statistical power.
1. If my replicated for each treatment are statistically different?
if not, I will group the samples together
2. If my treatment are statistically different?

I know that I can run an one-way ANOVA to answer question 1 and then run a second one-way ANOVA for question two, however I do not know how much power I will be losing from this process. in my research I have also been pointed at running a mixed ANOVA to encompass both questions, however my samples are not repeating so I am not sure if that would work.

Anyway I would love some advise on different statistical methods that could tackle this data format. Thanks!!!!!!
 

staassis

Active Member
#2
Your experiment is a case of Repeated Measures ANOVA if the residuals are normally distributed. The normality can be verified using Kolmogorov-Smirnov, Shapiro-Wilk or another test. If the residuals are not normally distributed, you should use a nonparametric version of Repeated Measures ANOVA, but this is still ANOVA.
 

Karabiner

TS Contributor
#3
I beg to differ. You cannot verify that the population's distribution follows a certain shape.
You only can reject the hypothesis that the underlying distribution follows a certain shape.

But non-significance does not mean that the population is normally distributed. In case of small
samples, you can for example test for a normal distribution and lognormal distribution and
beta distribrtution at the same time and receive three non-significant results. That would not
mean that the underlying distribution has 3 different shapes at the same time.

In the present case, with just n=20 and therefore low statistical power, it can be expected that
even medium-to-large deviations from normality (in the population) will result in a non-signficant
result

@FishStats
You say that you do not have repeated measures here. Do you mean that, for example, in
Treatment A and Rep 1, the n=5 at hour 0 and the n=5 at hour 1 are two independent samples?
I am not sure about the nomenclature, i.e. whether "replicate" may mean the same entities.

With kind regards

Karabiner
 
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