Practicals 10 – transformation and non-parametrics
1. Hair length was measured in two samples of ten randomly chosen male students doing their studies
at the faculty of science and the faculty of law.
The measured hair length (in cm) was
F. Sci.: 14, 17, 29, 14, 14, 11, 39, 23, 18, 8, 51, 36
F. Law: 6,8, 2, 3, 4,2,10,21, 5, 8, 3, 5
Does the hair length of guys significantly differ depending on which faculty they do their studies?
2. The number of vascular plant species was recorded in 10 countries. How does the number of species
depend on country area?
3. Aggressiveness of football fans was monitored at 20 football matches of different leagues (0 =
district league, 5 = Champions' league) on an ordinal scale (0 = calm fans, 1 = loud support to players,
2 = loud support + some fireworks, 3 = loud support + many fireworks, 4 = fireworks thrown on the
pitch, 5 = fans running on the pitch, 6 = fans running on the pitch and attacking the referee.
The resulting data were as follows:
match ID league aggressiveness
1 2 0
2 0 3
3 2 4
4 3 3
5 4 0
6 5 1
7 2 3
8 4 4
9 2 4
10 3 5
11 4 0
12 3 1
13 2 4
14 3 5
15 1 5
16 2 2
17 1 4
18 0 3
19 5 2
20 5 3
Is aggressivness of fans associated with league level?
4. During the finals of the pizza tasting competition, ten evaluators tasted pairs of pizza samples
prepared by cooks Francesco and Giacomo. Their evaluation (on a scale 1-5, 1 is best, 5 worst) was the
following:
Francesco: 1,2,1,1,3,1,1,2,1,2
Giacomo: 1,3,2,3,1,2,1,2,2,1
Is there any significant difference in the quality of pizza these guys make? Who will be the winner of
the competition?
5. Lettuce varieties were evaluated for their taste. They also differed in leaf color. The taste was ranked
on the scale (1=delightful, 2=very good, 3=acceptable, 4=bitter, not really good, 5=ugly disgusting).
The resulting values are summarized here:
red leaved varieties:
1,2,1,2,1,2,2,1,1,1,3,1,1,3,1,3,1,3,3,2,2,3,1,2,3,1,1,4,1,2,2,2,2,2,2,1,2,3,1,1,2,2,2,2,2,2,1,1,2,2,3,1,2,1,1,2,2,1,1,2
green leaved varieties:
4,2,2,1,2,2,1,3,2,1,2,4,3,3,3,3,2,3,2,1,4,2,2,3,2,2,1,1,5,3,3,2,3,2,1,3,3,2,2,1,2,2,3,3,3,1,1,3,2,3,3,3,2,1,2,3,2,2,3,1
Is there an association between leaf color and the taste of lettuce?
6. 24 people read 24 books (one each) written by four different authors (6 by each). After reading the
book, they were asked to rate the book on a scale: 1 – annoying, 2 – boring, 3 – mostly boring with
some enjoyable parts, 4 – enjoyable, and 5 – wonderful.
The resulting data are summarized below:
Ernest Hemingway: 4, 5, 4, 4, 3, 4
Charles Dickens: 2, 4, 5, 5, 2, 4
Alexander Pushkin: 3, 4, 5, 4, 3, 3
Lev Tolstoy: 2, 1, 3,2, 3, 2
Is there any significant difference in rating among these authors?
Which of them has the highest average rating?