Hypothesis test: can this be by chance?
The EDA and linear regression analysis is pretty conclusive. Nonetheless, you will top off the analysis of the zigzag effect by testing the hypothesis that lane assignment has nothing to do with the mean fractional difference between even and odd lanes using a permutation test. You will use the Pearson correlation coefficient, which you can compute with dcst.pearson_r()
as the test statistic. The variables lanes
and f_13
are already in your namespace.
This exercise is part of the course
Case Studies in Statistical Thinking
Exercise instructions
- Compute the observed Pearson correlation coefficient, storing it as
rho
. - Initialize an array to store the 10,000 permutation replicates of
rho
usingnp.empty()
. Name the arrayperm_reps_rho
. - Write a
for
loop to draw the permutation replicates.- Scramble the
lanes
array usingnp.random.permutation()
. - Compute the Pearson correlation coefficient between the scrambled
lanes
array andf_13
. Store the result inperm_reps_rho
.
- Scramble the
- Compute and print the p-value. Take "at least as extreme as" to be that the Pearson correlation coefficient is greater than or equal to what was observed.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Compute observed correlation: rho
rho = ____
# Initialize permutation reps: perm_reps_rho
perm_reps_rho = ____
# Make permutation reps
for i in range(10000):
# Scramble the lanes array: scrambled_lanes
scrambled_lanes = ____
# Compute the Pearson correlation coefficient
____[i] = ____
# Compute and print p-value
p_val = ____(____ >= ____) / 10000
print('p =', p_val)