Statistics: Exercises and Solutions

A three-way Repeated Measures ANOVA

Exercise

Above you have seen how to conduct a two-way repeated measures ANOVA with this dataset from Zhou et al. (2020). But the data contains a third factor: congruency. First, run a three-way repeated measures ANOVA with target-match, distractor-match, and congruency as independent variables, and search accuracy as dependent variable. Next, plot the results in a two-panel plot, where the left subplot shows the effect of distractor and target match for congruent trials, while the right subplot shows this for incongruent trials.

Solution

from pandas import pivot_table
from datamatrix import io
from datamatrix import operations as ops
from statsmodels.stats.anova import AnovaRM
import seaborn as sns

# Read the data and pass it to AnovaRM
dm = io.readtxt('data/zhou_et_al_2020_exp1.csv')
aov = AnovaRM(
    dm,
    depvar='search_correct',
    subject='subject_nr',
    within=[
        'target_match',
        'distractor_match',
        'congruency'
    ],
    aggregate_func='mean'
).fit()
print(aov)
# Now plot the data!
dm_congruent, dm_incongruent = ops.split(dm.congruency, 1, 0)
plt.subplots_adjust(wspace=0.4)
plt.subplot(1, 2, 1)
plt.title('Congruent')
sns.pointplot(
    x='target_match',
    y='search_correct',
    hue='distractor_match',
    data=dm_congruent
)
plt.ylim(0.75, 1)
plt.xlabel('Target match')
plt.ylabel('Search accuracy (proportion)')
plt.legend(title='Distractor match')
plt.subplot(1, 2, 2)
plt.title('Incongruent')
sns.pointplot(
    x='target_match',
    y='search_correct',
    hue='distractor_match',
    data=dm_incongruent
)
plt.ylim(0.75, 1)
plt.xlabel('Target match')
plt.ylabel('Search accuracy (proportion)')
plt.legend(title='Distractor match')
plt.show()

Output:

                                Anova
======================================================================
                                         F Value Num DF  Den DF Pr > F
----------------------------------------------------------------------
target_match                              6.7339 1.0000 34.0000 0.0139
distractor_match                         13.9729 1.0000 34.0000 0.0007
congruency                               15.1063 1.0000 34.0000 0.0004
target_match:distractor_match             7.1687 1.0000 34.0000 0.0113
target_match:congruency                  16.2760 1.0000 34.0000 0.0003
distractor_match:congruency               2.9842 1.0000 34.0000 0.0932
target_match:distractor_match:congruency  1.2566 1.0000 34.0000 0.2702
======================================================================

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