10.8. Tutorial exercises#

We again use the wellbeing dataset, to practice running permutation tests.

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 
import seaborn as sns

Colab users#

You need to use a more recent version of scipy.stats than the default. To do this run the following code block and after it has run, go to the menus at the top of colab and click runtime-->Restart Runtime

# Set-up Python libraries - you need to run this but you don't need to change it
!pip install scipy==1.10.0
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import pandas 
import seaborn as sns

Collecting scipy==1.10.0

  Using cached scipy-1.10.0-cp39-cp39-macosx_10_15_x86_64.whl (35.2 MB)

Requirement already satisfied: numpy<1.27.0,>=1.19.5 in /Users/joreilly/opt/anaconda3/lib/python3.9/site-packages (from scipy==1.10.0) (1.24.3)

Installing collected packages: scipy
  Attempting uninstall: scipy
    Found existing installation: scipy 1.9.3

    Uninstalling scipy-1.9.3:
      Successfully uninstalled scipy-1.9.3

ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
gensim 4.3.0 requires FuzzyTM>=0.4.0, which is not installed.
Successfully installed scipy-1.10.0

Import and view the data#

wb = pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/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

Questions#

In each case, you will need to decide:

  • 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 or independent?

Is it a one- or two-tailed test?

  • therefore which alternative hypothesis type is needed, two-sided, greater or less?

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)

Test the following hypotheses:#

  1. Wellbeing scores pre- and post-vac are correlated in engineering students

  2. There is a difference in the wellbeing scores of PPE students between Beaufort or Lonsdale (before the vacation)?

  3. Wellbeing over all students increases across the vacation

Slightly harder one:#

  1. Wellbeing increases more across the vacation for Beaufort students than Lonsdale students