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# TwoSampleHero.r
# Statypus Academy: The Signal and the Noise
# Course Resources: r.statypus.org
##################################################################

# --- STAGE 1: INDEPENDENT SIGNALS (Setosa vs. Versicolor) ---

# We return to our two distinct species.
# Last block, we saw two separate hills. Now we ask:
# Is the gap between them a "True Signal" or just environmental noise?

seto <- iris$Sepal.Length[iris$Species == "setosa"]
vers <- iris$Sepal.Length[iris$Species == "versicolor"]

# The Universal Lens (Independent t-test)
# We assume the groups are unrelated populations.
independent_study <- t.test(seto, vers)

# VIEW THE FIELD REPORT
print(independent_study)

# SEARCH THE OUTPUT:
# 1. Find the "mean in group setosa" and "mean in group versicolor".
# 2. Find the p-value. If this is < 0.05, the signal is clear.


# --- STAGE 2: PAIRED SIGNALS (Growth over Time) ---

# Now we look at the SAME individuals measured twice.
# Because the "Morning" and "Evening" measurements are linked,
# we can cancel out the "noise" unique to each individual plant.

set.seed(45)
morning <- iris$Sepal.Length[iris$Species == "setosa"]
evening <- morning + rnorm(50, mean=0.3, sd=0.1)

# We used the set.seed function to ensure that the random growth we added is the
# same each time you run this code. This way, everyone will see the same results
# when they run the paired t-test. However, if you want to see how the results
# change with different random growth, you can remove or change the set.seed line.

# The Universal Lens (Paired t-test)
# We must tell the lens to focus on the relationship (paired = TRUE).
paired_study <- t.test(evening, morning, paired = TRUE)

# VIEW THE FIELD REPORT
print(paired_study)

# SEARCH THE OUTPUT:
# 1. Find the "mean of the differences". This is the average growth.
# 2. Find the 95 percent confidence interval.
#    This is our "Detection Range." If 0 is outside this range,
#    the growth signal is confirmed.