Hello Sarah,

if I got you correctly you have two factors here: condition (with 4 levels) and time (with 3 levels). So the easiest way to handle your data is probably a two-way ANOVA.

Regarding the second question: it is common to indicate significant comparisons between to means within a figure with a '*', but you should always report the p-value.

Best,

Steffen

Hi Steffen,

Thanks for the answer.

Sorry I was probably unclear on the first point : my 3 replications were set on the same time (it's just 3 different growing boxes).

So I have only 1 factor here (substrate quality) and I went for One way ANOVA. What I don't understand is how do I use the replications that I have made statistically ?

Thanks !

Sarah

You have a classic nested anova. The following link has a good explanation, SAS code, and link to R code.

http://www.biostathandbook.com/nestedanova.html

In this example, each measurement is your larva, each rat is your replication, and each technician is your substrate.

As to your other question, the interpretation is that means sharing a letter are not significantly different. This is sometimes called a compact letter display (cld).

This is a compact way of presenting results from multiple comparisons, post-hoc test, or pairwise tests, such as TukeyHSD.

You can construct the cld mechanically by listing your means from highest to lowest, assigning an a to the highest, and then assigning a b to the first mean you get to that is significantly different, and so on. In some cases it can get unintuitive because means can have multiple letters, e.g. abc and bcd, and you also have to manually remove redundant letters.

There are some computer procedures to do this, such as in R, multcompView::multcompletters, rcompanion::cldList, and emmeans::cld.

Hi Salvatore, thanks !

I was not that far when intuitively using both ANOVA for the means of each one of the replications ; and another ANOVA for comparing variations between groups.

Thanks for sharing the link, however I feel like there is a sort of typo in it, as I am not getting the same results, or maybe I just did not get it right.

Anyway, they also state that whenever you have balanced design (equal samples sizes in each subgroups) you can also do just like I did...

As for the CLD (thanks I did not know how to call it), I had understood the idea, however I was wondering what happens in case X = Y (no significant difference), and Y = Z ; but X is greater (significant) than Z. Like, if you classify X as "a", than Y is also "a" (not significantly different), then Z would also be "a" as it is not significantly higher than Y. But Y and Z cannot be called both "a"...

I guess, in that situation you would put "a", "ab" and "b" ?

I can do it manually, just make sure that I put the p-value, right ?

(I am not using any software, just Excel...)

Yes, in your example the grouping letters would be a, ab, b.