# Unsure of statistics needed while working with replicates

I apologize if the question is considered too broad, but I'm hoping to get at least a basic starting point as I'm somewhat stuck with how to approach this. I am working with community ecological data-counts of species collected. The main goal of the project is to see if there is a difference between diversity across hot and cold years. Alpha diversity and ordinations are calculated on top of this but I need to show that there is no likely effect due to sites where data was collected.

For each temp. type(warm or cold) there are four years/type being used(so total of 8 communities). For each year, there are 6 different sites where species were collected. I am keeping months separated-so within a month, two trips were taken per site(these are replicates).

Essentially I have {Temp Type:(Cold vs Warm)-->4 Years/type-->6 sites/year-->and 2 replicates/site}

So main factors are site, replicate within site, and temp. type. response is species counts for each given year. I need to test to make sure there is no significant effect of sites and replicates within sites. I assume a nested anova may be appropriate?

Not very neat to do by hand, but multi-way ANOVA is completely possible here and runs easily in R or other languages. Consider the following example data set:

temp <- c("Warm", "Cold")
year <- paste("Year", 1:4)
site <- paste("Site", LETTERS[1:6])
reps <- 1:2

data_df <- expand.grid(reps, factor(year), factor(temp), factor(site))[,4:1]
colnames(data_df) <- c("Site", "Temperature", "Year", "Replicate")
set.seed(1)
data_df$$Measurement <- round( 15 + 1.5 * (data_df$$Temperature == "Warm") +
0.1*(as.numeric(data_df$$Site)-3.5) + rnorm(nrow(data_df), 0.4 * (as.numeric(data_df$$Year)-2.5), 1) +
rnorm(nrow(data_df), 0, 4)
)


I need to test to make sure there is no significant effect of sites and replicates within sites

Then you simply run

anova_model <- aov(Measurement ~ Site * Replicate, data = data_df)
summary(anova_model)


Notice the * operator that gives us the interaction term. The results are

               Df Sum Sq Mean Sq F value Pr(>F)
Site            5  146.4  29.285   1.950 0.0946 .
Replicate       1    0.1   0.094   0.006 0.9372
Site:Replicate  5   58.3  11.669   0.777 0.5690
Residuals      84 1261.4  15.016
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Now this is obviously fabricated data and hence a complete rubbish, but once you put your measurements in, you will get your answers.

• Not sure if count data will meet the assumptions of traditional ANOVA. Nov 5, 2023 at 11:51
• It might be the best shot, possibly later adding a Poisson VST. Also, consider the essence of the question - this shouldn't provide predictions but rather estimate the effects of Size and Replicate Nov 5, 2023 at 12:25