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There are 2 independent variables - a congruent words condition, and an incongruent words condition.
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The dependent variable is time taken to name the ink colors in equally-sized Congruent & Incongruent lists.
(2) What is an appropriate set of hypotheses for this task? Specify your null and alternative hypotheses, and clearly define any notation used. Justify your choices.
In a dependent samples t-test, each subject or entity is measured twice, resulting in pairs of observations. Since same set of participants will go through and record time for same set of congruent & incongruent words, resulting in pairs of observations , mean time should be used to compare and dependent samples t-test should be performed. Here size of the dataset is 24 and selection of participants from general population is unknown. Assuming normal distribution for both congruent & Incongruent words condition.
Alternate Hypothesis H_1 - Mean time to read incongruent list is greater than mean time to read congruent list
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H_0 : μ_ic = μ_c
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H_1 : μic > μ_c
Where μ_ic is mean time taken to read words in incongruent condition and μ_c is mean time taken to read words in congruent condition
(3) Report some descriptive statistics regarding this dataset. Include at least one measure of central tendency and at least one measure of variability. The name of the data file is 'stroopdata.csv'.
import matplotlib
import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt# Import csv file
df=pd.read_csv('stroopdata.csv')print('Number of rows in dataset :: ',df.shape[0])
print('Number of columns in dataset :: ',df.shape[1])
#find no of columns and non-empty fields in dataset
print('dataset information :: ')
df.info()Number of rows in dataset :: 24
Number of columns in dataset :: 2
dataset information ::
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 24 entries, 0 to 23
Data columns (total 2 columns):
Congruent 24 non-null float64
Incongruent 24 non-null float64
dtypes: float64(2)
memory usage: 464.0 bytes
- There are 2 columns in given dataset: Congruent , Incongruent and It has 24 rows of data which means there are 24 individual participants .
- There are no non-null values which means Both columns are of equal size and no need to remove rows with at least one null value.
- Data type for storing Time taken to read Congruent & Incongruent lists is float.
df.head()| Congruent | Incongruent | |
|---|---|---|
| 0 | 12.079 | 19.278 |
| 1 | 16.791 | 18.741 |
| 2 | 9.564 | 21.214 |
| 3 | 8.630 | 15.687 |
| 4 | 14.669 | 22.803 |
- The mean, median and mode are used to measure central tendency of data set
- The Standard deviation, quantile Range and variance are used to measures variability of data set
Congruent_data = df['Congruent']
Incongruent_data = df['Incongruent']
C_Mean=np.mean(Congruent_data)
IC_Mean=np.mean(Incongruent_data)
C_Median=np.median(Congruent_data)
IC_Median=np.median(Incongruent_data)
C_Mode=stats.mode(Congruent_data)[0]
IC_Mode=stats.mode(Incongruent_data)[0]
C_Std_dev=np.std(Congruent_data)
IC_Std_dev=np.std(Incongruent_data)
C_Variance=Congruent_data.var()
IC_Variance=Incongruent_data.var()
print('Congruent Mean :: ',C_Mean,' Incongruent Mean ::',IC_Mean)
print('Congruent Median :: ',C_Median,' Incongruent Median ::',IC_Median)
print('Congruent Mode :: ',C_Mode,' Incongruent Mode :: ',IC_Mode)
print('\nCongruent Standard Deviation :: ',C_Std_dev,' Incongruent Standard Deviation ::',IC_Std_dev)
print('\nQuantile Range :: ')
print(df.quantile([.25, .5, .75]))
print('\nCongruent Variance :: ',C_Variance,' Incongruent Variance :: ',IC_Variance)Congruent Mean :: 14.051125000000004 Incongruent Mean :: 22.01591666666667
Congruent Median :: 14.3565 Incongruent Median :: 21.0175
Congruent Mode :: [8.63] Incongruent Mode :: [15.687]
Congruent Standard Deviation :: 3.4844157127666326 Incongruent Standard Deviation :: 4.696055134513317
Quantile Range ::
Congruent Incongruent
0.25 11.89525 18.71675
0.50 14.35650 21.01750
0.75 16.20075 24.05150
Congruent Variance :: 12.669029070652174 Incongruent Variance :: 23.011757036231884
(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.
# Build the visualizations here
plt.figure(figsize=(15,7))
plt.hist([Congruent_data, Incongruent_data], color=['blue', 'red'])
legend = ['Congruent', 'Incongruent']
plt.xlabel('Time to read List (seconds)')
plt.ylabel('Frequency')
plt.xticks(range(0,35))
plt.legend(legend)
plt.title('Frequency chart of Time taken to read Congruent & Incongruent Lists')
plt.show()
- From above figure we can see that both plots are skewed. Incongruent list is taking more time than Congruent list
- Congruent List read time is centered in between 14 to 15.5 seconds
- Incongruent List read time is centered in between 18 to 19 seconds
- Least frequency for Congruent list is around 20 seconds
- Least frequency for Incongruent list is around 16 seconds
(5) Now, perform the statistical test and report your results. What is your confidence level or Type I error associated with your test? What is your conclusion regarding the hypotheses you set up? Did the results match up with your expectations? Hint: Think about what is being measured on each individual, and what statistic best captures how an individual reacts in each environment.
Calculate Mean Difference of Congruent & Incongruent List
# Perform the statistical test here
Mean_Diff= IC_Mean - C_Mean
print('Mean Difference :: ',Mean_Diff)Mean Difference :: 7.964791666666665
Calculate Standard deviation Difference of Congruent & Incongruent List
# Perform the statistical test here
Std_Dev_Diff=(Incongruent_data-Congruent_data).std()
print('Standard Deviation Difference :: ',Std_Dev_Diff)Standard Deviation Difference :: 4.864826910359056
t_statistic is (Mean difference)/(Standard Deviation difference/square root of Dataset length))
t_statistic=Mean_Diff/(Std_Dev_Diff/np.sqrt(len(df)))
print('t_statistic :: ',t_statistic)t_statistic :: 8.020706944109955
t_critical value for a 90% confidence level and (no of participants-1) d.f.
stats.t.ppf(.90, len(df)-1)1.3194602391408932
From above analysis we can say that t_statistic > t_critical . So we can reject the Null Hypothesis H_0 that there is no difference in mean time taken to read congruent and incongruent list
(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!
- I think it takes more time to read list in incongruent words condition compared to congruent words condition because mismatch of name of the color and color of the word can cause high probability of errors compared to words of same name and color.
- A similar task would be comparing time taken to complete a marathon without training and with training.with training anyone would perform slightly better than without training