1. Measurement, matrices, and proximities

2. Measurement
Measurement is the rule based assignment of numbers to objects.
Examples of rules for nominal measurement:
(1) If someone looks to you like a woman, assign her a 1.
(2) Ask a person their gender. If they say “female” or “woman” then assign that person a 1.
Ask the class to think about rules for ordinal and interval measurement of the same variable

3. Matrices
There are two basic shapes of data matrices: rectangular and square.
The typical social science matrix is a rectangle.
Sociologists typically have tall, thin data rectangular matrices. They know some things about a lot of people.
Anthropologists typically have wide, flat rectangular matrices. They know a lot of things about some people.

4. Name
Age
Sex
Educ
etc
xxx

5. thing1
thing2
thing3
thing n
Informant 1
xxxx
Informa nt 2
Informant 3
Informant 4

6. Ways and modes These are 2-way, 2-mode matrices.
A 1-way matrix is an array or vector of numbers.
The rows and columns are the 2 ways; the fact that the rows are cases and the columns are variables means that the matrices are 2- mode.
Matrices in which the rows and columns represent the same objects are 2-way, 1-mode matrices.

7. Proximities
Proximity matrices are 2-way, 1-mode matrices that show the similarity or dissimilarity between all pairs of objects in a study.
Note that “objects” can be people in a village or kinds of grapes used in making wine or answers to questions in a survey about anything -- food preferences or reasons for risky sexual behavior.

8. Measuring proximity
If larger numbers mean that two things are closer together or more alike, then we are measuring similarity.
If larger numbers mean that two things are farther apart or less alike, then we are measuring dissimilarity.
Proximity can be measured directly or indirectly.

9. Direct measure of dissimilarity
This next slide shows the driving distance between all pairs of nine cities in the U.S.
It is a direct measure of dissimilarity.

11. Direct measure of similarity
The next slide shows the similarity among all pairs of 15 emotions.
These data come from triad tests, a direct measure of similarity.
The triad test of similarity between pairs of object. Triad tests have questions of this form:
Here are three emotions. Choose the one that is least like the other two:
HATE BORED ANGER

12. In row 14, column 2 we see that, when 30 people were given the opportunity to choose the odd emotion out, 95% kept hate and anger together. In contrast, in row 13, column 2, we see that, those same people kept bored and anger together just 4% of the time.
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
LOVE
ANGER
DISGUST
SHAME
FEAR
ANGUISH
ENVY
ANXIOUS
TIRED
HAPPY
SAD
LONELY
BORED
HATE
EXCITEMENT
---
LOVE
0.00
0.09
0.08
0.21
0.10
0.35
0.16
0.82
0.20
0.14
0.41
0.74
ANGER
0.85
0.19
0.59
0.64
0.46
0.32
0.17
0.40
0.04
0.95
0.11
DISGUST
0.76
0.66
0.55
0.63
0.38
0.70
0.13
SHAME
0.22
0.75
0.51
0.57
0.39
0.47
0.06
FEAR
0.71
0.05
0.86
ANGUISH
0.31
0.69
ENVY
0.44
0.30
0.28
ANXIOUS
0.29
TIRED
0.73
10 HAPPY
0.34
11 SAD
0.24
12 LONELY
13 BORED
14 HATE
15 EXCITEMENT
In row 14, column 2 we see that, when 30 people were given the opportunity to choose the odd emotion out, 95% kept hate and anger together. In contrast, in row 13, column 2, we see that, those same people kept bored and anger together just 4% of the time.