Extra Practice

2.12. Extra Practice#

This is meant to help you practise the same core skills you developed in the previous exercises. Completing these exercises are optional and only meant to provide a little extra practice if you want.

2.12.1. Set up Python Libraries#

As usual you will need to run this code block 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

2.12.2. 1. Does Lunch Improve Decision Making#

A behavioural scientist investigates whether being fed improves decision-making.

Participants complete a decision-making task twice on the same day:

  • Before lunch

  • After lunch

Scores reflect task performance (higher scores indicate better decisions).

a) Comment on the design of the study

< Comment here>

c) Load the data into a Pandas dataframe

decision = pd.read_csv("https://raw.githubusercontent.com/SageBoettcher/StatsCourseBook_2026/main/data/decision_making_lunch_study.csv")

decision
ParticipantID LunchOption BeforeLunchScore AfterLunchScore
0 1 Veg 57.1 59.200000
1 2 Veg 58.6 60.100000
2 3 Meat 63.4 67.100000
3 4 Meat 70.9 73.000000
4 5 Meat 67.0 71.000000
5 6 Veg 64.5 68.300000
6 7 Veg 57.1 62.900000
7 8 Veg 60.0 66.900000
8 9 Meat 63.8 67.300000
9 10 Veg 69.2 70.500000
10 11 Meat 51.4 67.200000
11 12 Meat 54.6 56.800000
12 13 Meat 61.9 63.500000
13 14 Veg 53.0 55.300000
14 15 Meat 65.3 68.700000
15 16 Meat 59.6 61.600000
16 17 Veg 58.5 68.200000
17 18 Veg 56.9 57.700000
18 19 Meat 56.8 63.300000
19 20 Veg 58.1 64.100000
20 21 Veg 57.9 62.700000
21 22 Veg 68.1 72.600000
22 23 Meat 62.8 65.800000
23 24 Meat 59.2 60.000000
24 25 Meat 58.8 61.300000
25 26 Veg 55.1 60.800000
26 27 Meat 64.5 66.400000
27 28 Meat 52.1 56.500000
28 29 Veg 63.9 64.800000
29 30 Veg 62.0 67.300000
30 31 Veg 47.6 68.000000
31 32 Veg 39.7 35.500000
32 33 Veg 42.7 45.300000
33 34 Veg 42.2 49.500000
34 35 Meat 42.4 36.400000
35 36 Veg 42.5 36.500000
36 37 Meat 50.8 58.500000
37 38 Meat 47.4 48.800000
38 39 Veg 53.1 58.100000
39 40 Meat 48.7 46.500000
40 41 Meat 49.3 50.200000
41 42 Veg 47.4 46.900000
42 43 Veg 53.6 47.600000
43 44 Veg 47.4 46.400000
44 45 Veg 50.8 56.500000
45 46 Meat 51.3 50.600000
46 47 Veg 71.6 72.200000
47 48 Veg 67.0 66.100000
48 49 Veg 67.3 66.100000
49 50 Meat 68.1 66.600000
50 51 Meat 66.7 66.400000
51 52 Veg 45.0 60.000000
52 53 Veg 47.4 61.292894
53 54 Veg 47.4 61.020410
54 55 Veg 47.6 68.000000

d) Plot the raw data for before and after lunch and plot the distribtuino of the differences. Comment on both.

Note you may need to add a Diff column to the dataset

#Code here

e) Conduct a suitable rank-based non-parametric test to assess whether lunch improves decision-making scores. For this you should:

  • State your hypotheses

  • State relevant descriptive statistics

  • Carry out the test using the built in function from scipy.stats with appropriate option choices

  • State your conclusions

#Code here

f) Conduct a suitable permutation test of VitalVit’s claim

  • State your hypotheses

  • State relevant descriptive statistics

  • Carry out the test using the built in function from scipy.stats with appropriate option choices

  • State your conclusions

#Code here

2.12.3. 2. Correlation#

The researcher was also interested in the reliability of the decision-making task. In particular, they wanted to know whether individuals who performed well before lunch also tended to perform well after lunch.

This can be assessed by examining the correlation of decision-making scores within individuals across the two testing sessions. A strong positive correlation would suggest that the task reliably captures stable individual differences in decision-making ability, even if overall performance changes after lunch.

a) Plot the data and comment on what an appropriate test would be then carry out this test

#Code here

< Comment here>

b) Now carry out the permuation version

3. Does Meat vs. Veg Lunch Matter#

The researcher also asked participants whether they went for the meat or the veg option. They are interested in whether this choice will affect their AfterLunchScore.

a) Plot the differences between the groups

#Code here

b) Conduct an appropriate rank-based non-parametric test of the decision making scores

  • State your hypotheses

  • State relevant descriptive statistics

  • Carry out the test using the built in function from scipy.stats with appropriate option choices

  • State your conclusions

#Code here

c) Conduct a permutation test of the same claim

  • State your hypotheses

  • State relevant descriptive statistics

  • Carry out the test using the built in function from scipy.stats with appropriate option choices

  • State your conclusions

#Code here
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