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I'm measuring a particular property of worms (e.g. length, speed, ...). The worms are subdivided in 3 treatments (genetic strains) and each treatment group consists of 15 individuals. I replicated the experiment 3 times, by measuring the given property in each treatment for 3 days in a row. Please note that I did not measure the same individual multiple times, worms were thrown in the trash at the end of the day and fresh worms were used the next day.

According to my interpretation, since I measured each individual only once, I made 3 biological replicates and not 3 technical replicates. I continued by merging the data of the 3 replicates and went for one-way ANOVA with "genetic strain" as the only factor.

My supervisor, however, believes that merging replicates and not incorporating them into the ANOVA analysis will reduce the test's power. Therefore, I'm looking for a statistically well-supported answer to this issue. Should I continue by merging the replicates or should I incorporate them in the analysis?

P.S. I have the same question when doing a t-test (in that case, 3 replicates of 2 genetic strains).

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  • $\begingroup$ So you have 45 worms for each treatment, 15 measured on each day. What makes the 15 measured on each day more similar?, that is, why do you want to use days as blocks?Anyhow, you could use a nested model, so let the data itself decide. $\endgroup$ – kjetil b halvorsen Apr 12 '20 at 20:15
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    $\begingroup$ The reason for dividing the work over 3 days is that doing the actual measurements takes quite some time. So, measuring 135 worms in one day is not possible. $\endgroup$ – emacs Apr 13 '20 at 11:36
  • $\begingroup$ Can you please add that (así an edit) to the question, with sone info om the naturen og the measurements. Which instruments is used, and do om. Can instrument drift be a topic? Be influenced by temperaturen, humidity, which varies between saus ? ... $\endgroup$ – kjetil b halvorsen Apr 13 '20 at 12:37
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It seems you are treating days (within treatments) as blocks. There might well be reasons for doing that, even if you don't told us them. So just let the data decide if there really is block differences, and use a mixed model, with random intercepts for the blocks. In R this could be written something like

mod0 <- lme4::lmer(Y ~ treatment + (1 | day:treatment), data=your_data_frame)
summary(mod0)

then look at the estimated variance of the random effect to see if there is evidence for block effects.

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