Udacity Data Analyst Nanodegree

P1: Test a Perceptual Phenomenon

Author: Ioannis Karakasoglou Breier
Date: March 23, 2017

Background Information

In a Stroop task, participants are presented with a list of words, with each word displayed in a color of ink. The participant’s task is to say out loud the color of the ink in which the word is printed. The task has two conditions: a congruent words condition, and an incongruent words condition. In the congruent words condition, the words being displayed are color words whose names match the colors in which they are printed: for example RED, BLUE. In the incongruent words condition, the words displayed are color words whose names do not match the colors in which they are printed: for example PURPLE, ORANGE. In each case, we measure the time it takes to name the ink colors in equally-sized lists. Each participant will go through and record a time from each condition.

Questions For Investigation

1. What is our independent variable? What is our dependent variable?
  • The independent variable is the type of task (word-color congruency condition)
  • The dependent variable is the performance of each individual - response time measured in seconds - on the task.

Each row of the dataset we will use contains the performance for one participant, with the first number their results on the congruent task and the second number their performance on the incongruent task.

2. What is an appropriate set of hypotheses for this task? What kind of statistical test do you expect to perform? Justify your choices.

We want to evaluate the effect size of the task type on the performance of the students and assess whether the difference in our sample is because of the fact the congruent and incongruent populations are significantly different.

$\mu_{C}$: The congruent population's response time mean
$\mu_{I}$: The incongruent population's response time mean

We will test the following hypotheses:

$H_0$: The null hypothesis, that the congruent and incongruent populations are not significantly different $\rightarrow \mu_{C} - \mu_{I} = 0$

$H_A$: The alternative hypothesis, that the congruent and incongruent populations are significantly different $\rightarrow \mu_{C} - \mu_{I} \neq 0$

In this case:

  • The sample size is below 30
  • We don't know the population's standard deviation
  • The same subject is assigned two conditions

Therefore, we will conduct a Dependent t-test for Paired Samples.

3. Report some descriptive statistics regarding this dataset. Include at least one measure of central tendency and at least one measure of variability.
Summary Descriptive Statistics
Congruent Incongruent
Sample Size n 24.000 24.000
Mean - X 14.051 22.016
Std. Deviation S 3.559 4.797
Min 8.630 15.687
25% Qt 11.895 18.717
Median 14.356 21.018
75% Qt 16.201 24.052
Max 22.328 35.255
  • The congruent task sample has a mean of $\bar x_{C} =$ 14.051 seconds and a standard deviation $S_{C} = $ 3.559 seconds.
  • The incongruent task sample has a mean of $\bar x_{I} =$ 22.016 seconds and a standard deviation $S_{I} =$ 4.797 seconds.
4. 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.
  • In the density histogram below we observe that both samples look normally distributed with a similar variance.The incongruent task distribution of performance times seems to have a small bimodal peak around 35 seconds
  • In both the histogram and the boxplot it is obvious the the mean , the median and the IQR of measured times for the incongruent task is higher than those of the congruent task.

5. 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?

Two-tailed Dependent t-Test for Paired Samples with a 99% Confidence level

Degrees of Freedom : df = 23
Alpha- level : a = .01
t-critical values : $t_c$ = (-2.81 , +2.81)
t-Statistic(df) : t(23) = -8.02
p-Value : p < 0.0001

We observe the the t-Statistic is clearly smaller the the negative t-critical value and in the critical region with a p-value < 0.0001 and therefore we reject the Null Hypothesis with a 99% Confidence level and conclude that there is a significant difference in the scores for congruent and incongruent tasks.

The results confirmed our observations and expectations that there is indeed a statistically significant difference(increase)) in the response time to perform the incongruent tasks compared to the congruent tasks.

6. 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 interference between what the words say and the color of the words seem to confuse the brain. There are two theories that may explain the Stroop effect:

  • Speed of Processing Theory: the interference occurs because words are read faster than colors are named.
  • Selective Attention Theory: the interference occurs because naming colors requires more attention than reading words.

Alternative tasks to try:

  • Use non-color words such as "dog" or "house."
  • Use emotional words such as "sad" or "happy" or "depressed" or "angry."

Sources

Appendix

Code used for calculations and visualizations

In [ ]:
import math
import statistics as stat
import pandas as pd
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
import seaborn as sns

%matplotlib inline
%config InlineBackend.figure_format = 'retina'
plt.style.use('seaborn-notebook')

#get the data
st = pd.read_csv('stroopdata.csv')

#Get the summary statistics
var = st.describe()

#Change the index labels and round the values reported
var.index = ['Sample Size n', 'Mean - X', 'Std. Deviation S', 'Min', '25% Qt', 'Median',\
               '75% Qt', 'Max']
var = var.round(decimals=3)

#Get the values from the stats table
nC = int(var.iloc[0,0]); xC = round(float(var.iloc[1,0]),3)
SC = round(float(var.iloc[2,0]),3)

nI = var.iloc[0,1] ; xI = round(float(var.iloc[1,1]),3)
SI = round(float(var.iloc[2,1]),3)

#plot the density histogram
fig = plt.figure('1')
ax1 = fig.add_subplot(111)
plt.title('Tasks Histogram and KDE Plot')
plt.xlabel('Seconds')
plt.ylabel('Density')
sns.distplot(st[[0]],ax=ax1)
sns.distplot(st[[1]],ax=ax1, color='red')
plt.text(x=10, y=0.04, s= "Congruent",color='blue' )
plt.text(x=20, y=0.04, s= "Incongruent", color='red');

#plot the boxplot
st.plot(kind='box', vert=False)
plt.title('Tasks Box-Plot')
plt.xlabel('Seconds')
plt.xlim(0,45);

# get the critical t values for a one tailed positive test
dof = int(nC-1)
a= 0.01 # 
tails =  2

t_crit = round(float(stats.t.isf([a/tails], dof)[0]),2)

#Calculate the t-statistc
t = round(float(stats.ttest_rel(a = st[[0]],
                b = st[[1]])[0][0]),2)
In [ ]:
!jupyter nbconvert --template=nbextensions --to=html Project.ipynb