Test a Perceptual Phenomenon¶
Ques1. What is our independent variable? What is our dependent variable?
Ans1. Time to complete each test or the 'reaction time' is the dependent variable and the independent variable is whether the word is congruent or not. There are a few other variables like color choices, font and size, length of the word, number of words in the list etc which we need to control. For this experiment, we are making an assumption that the lurking variables are controlled
Ques2. What is an appropriate set of hypotheses for this task? What kind of statistical test do you expect to perform? Justify your choices.
Ans2. Null hypotheses or H0 is that both the congruent and the incongruent word conditions will take the same time(µc = µi) where µc is the estimated mean of congruent population and µi is the mean of incongruent population. The alternate hypotheses or HA is that they are statistically different(µc ≠µi). We will perform dependent Two-Tailed t-test for dependent samples since both tests are performed with same participants. Paired t-test tests whether the mean of the differences between dependent or paired observations is equal to a target value. We are using t-test as the sample size is less than 30 and we do not know the population mean and standard deviation.
H0: µc = µi at α = 0.05,
HA: µc ≠µi at α = 0.05, where α is the t-critical at which the probability is .05 and µc and µi are population means for congruent and incongruent group respectively.Ques3. Report some descriptive statistics regarding this dataset. Include at least one measure of central tendency and at least one measure of variability.
import numpy as np
import pandas as pd
from scipy import stats, integrate
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(color_codes=True)
import plotly as py
dt = pd.read_csv('Stroop.csv')
dt.describe()
Ans3. Measure of central tendency: Mean for congruent set is 14.051125 and incongruent set is 22.015917, Differences in mean is 7.96479
Measure of variability: Standard Deviation for congruent set is 3.559358 and incongruent set is 4.797057, Variance is 12.66902907 and 23.01175704 respectively
Ques4. Provide one or two visualizations that show the distribution of the sample data. Write one or two sentences noting what you observe about the plot or plots.
%pylab inline
sns.distplot(dt.Congruent, kde=False, fit=stats.gamma);
sns.distplot(dt.Incongruent, kde=False, fit=stats.gamma);
The blue histogram is for congruent and the green is for incongruent response times. The spread of incongruent is more than that of congruent. Congruent has its mode around 12 sec and incongruent around 20. The distribution is mildly normal.
dt2 = pd.read_csv('Stroop_2.csv')
For categorical analysis, I have summarized the data in single column: Response_Time and identified each one of them as 'Congruent' or 'Incongruent'. I also added X column with values 1 to 48 for indexing. It is the same data, just transformed so that we can make box plots and scatter plots by condition
dt2.head()
sns.set(style="ticks", palette="muted", color_codes=True)
ax = sns.boxplot(x="Response_Time", y="Condition", data=dt2,
whis=np.inf, color="c")
# Add in points to show each observation
sns.stripplot(x="Response_Time", y="Condition", data=dt2,
jitter=True, size=3, color=".3", linewidth=0)
sns.despine(trim=True)
Box plot of Congruent has tighter distribution than Incongruent test mainly due to high fliers around 35 sec for Incongruent condition. Median for Congruent condition is around 14.5 and for Incongruent, its at 21. We have already calculated means for the two conditions and it is supported by this chart that congruent has mean a lot lower than incongruent
g = sns.lmplot(x= "X", y="Response_Time", col="Condition", data=dt2);
g.set(xlim=(0, 45), ylim=(0, 45))
Next is the scatter plot for the the Response_Times for both the conditions, Incongruent condition shows higher response times and steeper slope than Congruent
g = sns.lmplot(x= "X", y="Response_Time", hue="Condition", data=dt2);
g.set(xlim=(0, 45), ylim=(0, 45))
Here I plotted both of them on the same chart to show slope comparison
Ques5. Now, perform the statistical test and report your results. What is your confidence level and your critical statistic value? Do you reject the null hypothesis or fail to reject it? Come to a conclusion in terms of the experiment task. Did the results match up with your expectations?
from scipy import stats
paired_sample = stats.ttest_rel(dt.Congruent, dt.Incongruent)
print ("t-statistic: %.3f and p-value : %.9f." % paired_sample)
Ans5
t-Test:
t-critical: 2.069
Avg Mean Difference between the two conditions: -7.964791667
Standard error: 0.993028635
t-statistic: -8.021
p-value: 4.1E-08
Confidence Interval: (-10.01, -5.90548)
Conclusion: Reject the null!
Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the difference between congruence and incongruence response time difference is statistically significant. The results matched up with my expectations as I spent more time reading the incongruent words than congruent and in other words, observed stroop effect
Ques6. Optional: What do you think is responsible for the effects observed? Can you think of an alternative or similar task that would result in a similar effect? Some research about the problem will be helpful for thinking about these two questions!
The stroop effect occurs because our brain reads effortlessly and identifying color requires more cognitive effort. It would be easier for a child who can not read and does not know meaningfulness of words. Some Stroop effect tests that might produce similar effect would be: rotate words, or arrange the letters in a clockwise or counterclockwise pattern, scramble the letters
References:
Stroop effect - Wikipedia