1.11. Tutorial exercises#
We again use the wellbeing dataset, to practice running permutation tests.
1.11.1. Set up Python libraries#
As usual, run the code cell below to import the relevant Python libraries
# Set-up Python libraries - you need to run this but you don't need to change it
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import pandas as pd
import seaborn as sns
sns.set_theme(style='white')
import statsmodels.api as sm
import statsmodels.formula.api as smf
1.11.2. Import and view the data#
wb = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/WellbeingSample.csv')
wb
ID_code | College | Subject | Score_preVac | Score_postVac | |
---|---|---|---|---|---|
0 | 247610 | Lonsdale | PPE | 60 | 35 |
1 | 448590 | Lonsdale | PPE | 43 | 44 |
2 | 491100 | Lonsdale | engineering | 79 | 69 |
3 | 316150 | Lonsdale | PPE | 55 | 61 |
4 | 251870 | Lonsdale | engineering | 62 | 65 |
... | ... | ... | ... | ... | ... |
296 | 440570 | Beaufort | history | 75 | 70 |
297 | 826030 | Beaufort | maths | 52 | 49 |
298 | 856260 | Beaufort | Biology | 83 | 84 |
299 | 947060 | Beaufort | engineering | 62 | 65 |
300 | 165780 | Beaufort | PPE | 48 | 56 |
301 rows × 5 columns
1.11.3. Questions#
Test the following hypotheses:#
Wellbeing scores pre- and post-vac are correlated in engineering students
There is a difference in the wellbeing scores of PPE students between Beaufort or Lonsdale (before the vacation)?
Wellbeing over all students increases across the vacation
Slightly harder one:#
Wellbeing increases more across the vacation for Beaufort students than Lonsdale students
Detailed Instructions#
In each case 1-4, you will need to decide what to do, carry it out and and write it up:
a. Hypotheses
what is our null hypothesis
what is our alternative hypothesis?
Is it a paired or unpaired test for difference of means, or a correlation test?
therefore which
permutation_type
is needed,samples
,pairings
orindependent
?
Is it a one- or two-tailed test?
therefore which
alternative
hypothesis type is needed,two-sided
,greater
orless
?
What \(\alpha\) value will you use?
what value must \(p\) be smaller than, to reject the null hypothesis?
this is the experimenter’s choice but usually 0.05 is used (sometimes 0.001 or 0.001)
b. Test statistic and descriptive statistics
What is your test statistic?
Report appropriate descriptive statstics and plot the data (you should choose an appropriate plot type)
c. Carry out the permutation test
Carry out the test. Plot the null distribution. Report the \(p\)-value.
d. Report your conclusion
Will you reject the null hypothesis, or fail to reject it? What is your cnclusion in plain English?
e. Finally, write it up
In each case, include a final cell in which you write the test up as if for a journal article