Project 1- Test a Perceptual Phenomenon

Project summary - Congruent vs Incongruent

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

1)Independent variable:It can be be congruent or incongruent. 2)Dependent variable:It is time that takes for complete the task by the participant

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

The two-tailed t-test is the appropriate methods for this sample of data: The dataset does not include population μ and σ. Therefore, we cannot conduct a z-test. We can compare two means from 2 samples and calculate the standard deviation and confidence level 1)The null hypotheses is: The average time it takes to complete the incongruent test is less than or equal to the average time needed to complete the congruent test.

2)The alternative hypotheses is: The average time it takes to complete the incongruent test is more than the average time needed to complete the congruent test.

=>µx = incongruent condition population mean =>µy = congruent condition population =>µD = µx - µY =>H0: µD = 0 =>HA: µD ≠ 0 (two-tailed test)

import pandas as pd
import matplotlib.pyplot as plt
import math
df = pd.read_csv(r'stroopdata.csv')
df["p-id"]= df.index +1
df

	Congruent	Incongruent	p-id
0	12.079	19.278	1
1	16.791	18.741	2
2	9.564	21.214	3
3	8.630	15.687	4
4	14.669	22.803	5
5	12.238	20.878	6
6	14.692	24.572	7
7	8.987	17.394	8
8	9.401	20.762	9
9	14.480	26.282	10
10	22.328	24.524	11
11	15.298	18.644	12
12	15.073	17.510	13
13	16.929	20.330	14
14	18.200	35.255	15
15	12.130	22.158	16
16	18.495	25.139	17
17	10.639	20.429	18
18	11.344	17.425	19
19	12.369	34.288	20
20	12.944	23.894	21
21	14.233	17.960	22
22	19.710	22.058	23
23	16.004	21.157	24

The two-tailed t-test is the appropriate methods for this type of sample:

 a)We cannot conduct a z-test since the sample doesnot include population μ and σ. 
 b)Since we can calculate the means of congruent and uncongruent we can apply T test.

3)descriptive statistics regarding this dataset.

The below code will give stats like mean,std of Congruent and Incongruent timings

thereult = df.describe()
thereult[1:3]

	Congruent	Incongruent	p-id	time-diff
mean	14.051125	22.015917	12.500000	7.964792
std	3.559358	4.797057	7.071068	4.864827

The below code will give median value of Congurent

median_of_Congruent = df['Congruent'].median()
median_of_Congruent

14.3565

The below code will give median value of Incongruent

median_of_Incongruent = df['Incongruent'].median()
median_of_Incongruent

21.0175

1. 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.

plt.hist(df['time-diff'].values,bins=10)
plt.xlabel("Time-diff")
plt.ylabel("Frequency")
plt.title("Histogram of time difference ")
plt.xticks(range(0, 25, 2))
plt.show()

From the above graph we came to know that the time-difference is between 2 to 12 seconds and average time difference is around 7.5 to 8.3There are two outliers in this data in between 16-18 and 20-22

5) Statistical test & result

Confidence Interval=90% α=0.1 T−critical=+1.714,−1.714

y=df['Incongruent']
x=df['Congruent']
d=y-x
d

0      7.199
1      1.950
2     11.650
3      7.057
4      8.134
5      8.640
6      9.880
7      8.407
8     11.361
9     11.802
10     2.196
11     3.346
12     2.437
13     3.401
14    17.055
15    10.028
16     6.644
17     9.790
18     6.081
19    21.919
20    10.950
21     3.727
22     2.348
23     5.153
dtype: float64

mean_d=d.mean()
mean_d

7.9647916666666658

#standard error of the mean difference
sdd = d.std()/math.sqrt(24)
sdd

0.99302863477834058

t_statistic=mean_d/sdd
t_statistic

8.020706944109957

Result: We can regect null hypothesis since there is no much difference in responce time (t-statistic = 8.027 > t-critical = 1.714). The avg time that takes by the person to complete the test in an incongruent setting is longer than congruent setting test.