Test a Perceptual Phenomenon

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.

Data Overview

The data contain originally two columns, Congruent and Incongruent, I’ll add a third column paired_differences which account for difference between these two.

TEST

Questions For Investigation

1. What is our independent variable? What is our dependent variable?

Independent: Words types (Congruent/Incongruent).

Dependent: Time to response (seconds).

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

Hypotheses

\(\mu_{\Delta}\): The mean of paired differences.

\(Ho\): \(\mu_{\Delta} = 0\), There is no significant reading time difference between Congruent and Incongruent readings.

\(H_{A}\):\(\mu_{\Delta}\neq 0\), There is a significant reading time difference between Congruent and Incongruent readings.

Test Selection

To select the right statistical test we need to verify the following:-

  • Data Type:
    • Independent: 2 Categories (Congruent/Incongruent).
    • Dependent: Continuous (Seconds).
  • Samples
    • Paired samples.
  • Sample size \(> 30\).
    • FALSE, We have 24 paired points.
  • The data following normal distribution.
    • To be checked graphically and statistically.

Graphical Exploration

Statisitcal Exploration

Shapiro-Wilk normality test can be conducted to verivy the data normallity.


    Shapiro-Wilk normality test

data:  stroopdata$paired_differences
W = 0.91042, p-value = 0.03602

\(p-value = 0.03602 < \alpha:0.05\) The test indicate that our data is not normal.

Since the test is biased to sample size, we’ll conduct normal Q-Q plot to verify.

From the last three tests we can conculde that our data is not normal, hence we can’t perform parametric test and an altrentaive non-parametric test is needed, in this case we ’ll use Wilcoxon Signed Rank test.

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

   Congruent        Incongruent      paired_differences
 "Min.   : 8.63  " "Min.   :15.69  " "Min.   : 1.950  "
 "1st Qu.:11.90  " "1st Qu.:18.72  " "1st Qu.: 3.646  "
 "Median :14.36  " "Median :21.02  " "Median : 7.667  "
 "Mean   :14.05  " "Mean   :22.02  " "Mean   : 7.965  "
 "3rd Qu.:16.20  " "3rd Qu.:24.05  " "3rd Qu.:10.258  "
 "Max.   :22.33  " "Max.   :35.26  " "Max.   :21.919  "
 "SD     :3.5594"  "SD     :4.7971"  "SD     :4.8648"

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.

Please refer to Graphical Exploration

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?


    Wilcoxon signed rank test

data:  stroopdata$Congruent and stroopdata$Incongruent
V = 0, p-value = 1.192e-07
alternative hypothesis: true location shift is not equal to 0

\(p-value = 1.192e-07 < 0.05\)

We reject the null hypothesis, changing the word type from Congruent to Incongruent have significant on the response time.

Ammar Al-Khaldi

08 September, 2017