title: “Compute the CLR transformation” output: html_notebook

# Assuming you have two vectors of proportions for the two groups: prop1 and prop2

# Step 1: Collect the data

# Step 2: Compute the CLR transformation
clr1 <- log(prop1) - mean(log(prop1))
clr2 <- log(prop2) - mean(log(prop2))

# Step 3: Calculate the t-statistic
mean1 <- mean(clr1)
mean2 <- mean(clr2)
sd1 <- sd(clr1)
sd2 <- sd(clr2)
n1 <- length(clr1)
n2 <- length(clr2)
t_stat <- (mean1 - mean2) / sqrt((sd1^2 / n1) + (sd2^2 / n2))

# Step 4: Determine the degrees of freedom
df <- ((sd1^2 / n1 + sd2^2 / n2)^2) / (((sd1^2 / n1)^2) / (n1 - 1) + ((sd2^2 / n2)^2) / (n2 - 1))

# Step 5: Determine the p-value
p_value <- 2 * pt(abs(t_stat), df = df, lower.tail = FALSE)

# Step 6: Interpret the results
if (p_value < 0.05) {
  cat("The difference in the means of CLR-transformed proportions is statistically significant.\n")
} else {
  cat("The difference in the means of CLR-transformed proportions is not statistically significant.\n")
}