The Stroop effect is a demonstration of interference in the reaction time of a task.

The task has two conditions:

• Congruent words condition
• 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.

Questions for Investigation

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

• Independent Variable
  • Words that match color
  • Words that don't match color

• Dependent Variable
  • Time it take to read the words
  • Time it takes to name the color of ink

2.a What is an appropriate set of hypotheses for this task?

Null Hypothesis and Alternative Hypothesis:

$$H_0:\mu_c-\mu_i\geq0$$

$$H_a:\mu_c-\mu_i<0$$

The null hypothesis $(H_0)$ is that the mean of the population reaction time of the task under the incongruent words condition is not significantly longer than that of the congruent words condition. The alternative hypothesis $(H_a)$ is that the mean of the population reaction time of the task under the incongruent words condition is significantly longer than that of the congruent words condition.

2.b What kind of statistical test do you expect to perform?

Each subject is tested under two conditions hence we will be performing 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.

Descriptive Statistics is calculated using Google Sheets.

The average time taken under congruent condition: $\overline{x}_c$ = 14.051125
The average time taken under incongruent condition: $\overline{x}_i$ = 22.01591667

The point estimate for the sample is:
$\overline{x}_c - \overline{x}_i$ = -7.964791667

Standard Deviation(SD) of the difference between two conditions in time: 4.86482691

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.

import pandas as pd
import seaborn as sns

stroop_data = pd.read_csv("C:/Users/Vinay/Desktop/stroop_data.csv") 
sns.boxplot(data=stroop_data)

The plot above and below visualizes the distribution of the sample data using boxplot and distplot from seaborn library respectively. Based on the plot, the reaction time of the task under incongruent words condition appears to be longer than that of the congruent words condition.

data = pd.DataFrame(stroop_data, columns=['Congruent', 'Incongruent'])
sns.distplot(data['Congruent'])
sns.distplot(data['Incongruent'])

5. 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?

t-statistic:

$$t = \frac{\overline{x}_c - \overline{x}_i}{\frac{SD}{\sqrt{n}}}$$

$$t = \frac{-7.964791667}{\frac{4.86482691}{\sqrt{24}}}$$

$$t = -8.023$$

t-critical:

For $\alpha$-level of 0.05 on one side (negative tail)

$$t_{critical} = -1.714$$

P - Value:

The two-tailed P value is less than 0.0001
By conventional criteria, this difference is considered to be extremely statistically significant.

Confidence Interval(CI) for mean population difference at 95%:

$$CI = M_D - t_{critical}(\frac{SD}{\sqrt{n}})$$

$$CI = -7.964791667 - (-1.714)(\frac{4.86482691}{\sqrt{24}})$$

$$CI = -6.2627$$

Conclusion:
Since t-statistic is past the t-critical value we will reject the null hypothesis, which means participants took more time under incongruent condition.
Indeed my result match up with the outcome of this test.

Stroop Effect interferes people reaction time significantly.