Introduction

We may all experienced the same situation when we read a colored word describe a color: we tend to spend more time to recognize the color of the word if it is different with what it describes.This phenomenon is called Stroop Effect. As a course project for Udacity Data Analyst Nano Degree, this project will use basic statistics tools to analyze a dataset from a Stroop Effect Experiment.

Study Questions

Question 1

What is our independent variable? What is our dependent variable?

Our independent variable is the condition when we read the words, which has two values-congruent words condition and incongruent words condition Our dependent variable is the time used to read the words in second.

Question 2

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

Let the congruent population response time mean be μC, and the incongruent population response time mean be μI. Our hypotheses are: H0 : μC − μI ≥ 0 Ha : μC − μI < 0 The null hypothesis (H0) is that the congruent population response time mean is not significantly less than the incongruent population response time mean. The alternative hypothesis (Ha) is that the congruent population response time mean is significantly less than the incongruent population response time mean.

Since the data were collected from the same participant under two conditions, I would use a one-way paired-t test to test my hypotheses. However, this method should only be used under the assumption that the data are normally distributed. We will talk about it in later section.

Question 3

Report some descriptive statistics regarding this dataset. Include at least one measure of central tendency and at least one measure of variability.

Use stat.desc function from the pastecs package in R, we can get following descriptive statistic about the stroop study dataset. The most common measure of central tendency is mean. From R output, the average time used under congruent and incongruent conditions are 14.051s and 22.016s respectively. Standard deviation is a measure of variability. For this dataset, the standard deviations for the two conditions are 3.559 and 4.797.

##    Congruent      Incongruent   
##  Min.   : 8.63   Min.   :15.69  
##  1st Qu.:11.90   1st Qu.:18.72  
##  Median :14.36   Median :21.02  
##  Mean   :14.05   Mean   :22.02  
##  3rd Qu.:16.20   3rd Qu.:24.05  
##  Max.   :22.33   Max.   :35.26

Question 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

Boxplot is an useful visualization to show the distribution of the data, it is also helpful for detecting outliers! From the Boxplot, we found that in general the congruent group used less time than the incongruent group. We also found that there are two outliers in the incongruent data.

Histogram is another useful plot help us to visualize the distribution of a data. From following histogram plot, we found that the Congruent group used less time than the Incongruent group. The distribution of the Congruent data is normal, while the Incongruent data is right skewed because of the outliers.

Question 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?

The result from the one-way pairted-t test is as below: my confidence level is α = 0.05, the critical statistic value is t = −8.0207. Because the P-value is less than 0.05, we successfully rejected our Null hypothesis and conclude that we are 95 confident that it takes a longer time to read words under incongruent condition than under congruent condition. The result matched up with my expectation because when I did the experiment I spent almost twice of the time to read words under incongruent condition.

## 
##  Paired t-test
## 
## data:  Congruent and Incongruent
## t = -8.0207, df = 23, p-value = 2.052e-08
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##       -Inf -6.262868
## sample estimates:
## mean of the differences 
##               -7.964792

Question 6

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?

One possible explanation can be when we see a word we can read it directly. However, when we see a color we need to first name the color then read it, which takes longer reaction time.

Some similar tasks may include: uppercase the word, turn the words upside down et al.

Reference

https://faculty.washington.edu/chudler/java/ready.html

https://en.wikipedia.org/wiki/Stroop_effect

https://faculty.washington.edu/chudler/words.html

http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/hypothesis-tests/tests-of-means/why-use-paired-t/