"""
Repeated measures ANOVA
=======================

Based on [1]_.

"""
# Author: Christian Brodbeck <christianbrodbeck@nyu.edu>
from eelbrain import *

y = Var([7,  3,  6,  6,  5,  8,  6,  7,
         7, 11,  9, 11, 10, 10, 11, 11,
         8, 14, 10, 11, 12, 10, 11, 12],
        name='y')
a = Factor('abc', repeat=8, name='A')

###############################################################################
# Fixed effects ANOVA (independent measures, [1]_ p. 24):
print(test.ANOVA(y, a, title="Independent Measures"))

###############################################################################
# Repeated measures ANOVA ([1]_ p. 72): ``subject`` is defined as random effect
# and entered for model construction as completely crossed factor
subject = Factor(range(8), tile=3, name='subject', random=True)
print(test.ANOVA(y, a * subject, title="Repeated Measures"))

###############################################################################
# Two-way repeated measures ANOVA
# -------------------------------
y = Var([ 7,  3,  6,  6,  5,  8,  6,  7,
          7, 11,  9, 11, 10, 10, 11, 11,
          8, 14, 10, 11, 12, 10, 11, 12,
         16,  7, 11,  9, 10, 11,  8,  8,
         16, 10, 13, 10, 10, 14, 11, 12,
         24, 29, 10, 22, 25, 28, 22, 24])
a = Factor(['a0', 'a1'], repeat=3 * 8, name='A')
b = Factor(['b0', 'b1', 'b2'], tile=2, repeat=8, name='B')
subject = Factor(range(8), tile=6, name='subject', random=True)

print(test.ANOVA(y, a * b * subject, title="Repeated Measure:"))

###############################################################################
# Bar-plot with within-subject error bars and pairwise tests
plot.Barplot(y, a % b, match=subject)

###############################################################################
# References
# ----------
# .. [1] Rutherford, A. (2001). Introducing ANOVA and ANCOVA: A GLM Approach. Sage.