January 28, 2019

## Concepts to Measurement:

### Variable(s)

• measurable properties of cases that map onto a concept

### Measure(s)

• procedure to find the values variables take for specific cases

## Concepts to Measurement:

### variable(s):

A measurable property of a case (phenomena, group, or individual) that corresponds to a concept or one of the concept's dimensions and can potentially take on different values across cases and time (it varies) across units.

• Derived to capture a concept
• Variables take on values for each case at a specific point in time
• Variation across cases or over time.
• General (e.g., "number of deaths in a civil war", not "number of deaths in the Syrian Civil War between 2011 and today")

## Concepts to Measurement:

### Measure(s)

A procedure for determining the value of a variable for specific cases based on observation.

• Measures are proposed to determine the value a variable takes for some cases
• They are always for some specific cases want to know about

## A Trivial Example:

### We need to:

• define a the concept of "height"
• create a variable that captures "height" and is measurable
• develop a measure to obtain values of that variable for West Lion and Seymour

## Concept to Measurement:

### Concept: Height (of a mountain)

Elevation of peak from the earth's surface

### Measure:

Use difference in barometric pressure to calculate difference in elevation

## A Trivial Example:

Are you going to climb the mountain? Prominence might be a better concept of height.

## A Less Trivial Example

### Descriptive Claim:

"Societies that are ethnically diverse are less likely to be democracies"

## A Less Trivial Example

"Societies that are ethnically diverse are less likely to be democracies"

### Let's move from concept to measure with "ethnically diverse"

• What is the concept of "ethnic diversity"?
• what is it to be "ethnically diverse"
• observable traits?
• traits/dimensions linked to causal story?

## A Less Trivial Example

"Societies that are ethnically diverse are less likely to be democracies"

## A Less Trivial Example

### Ethnic diversity: a concept

• Presence of many different ethnic groups?
• Presence of many distinct and large ethnic groups?

## A Less Trivial Example

### Ethnic diversity: a variable:

Propose a variable that could map onto the concept of "ethnic diversity"

## A Less Trivial Example

### Ethnic diversity: a variable

#### Probability that any two random individuals belong to different ethnic groups

"Ethno-linguistic fractionalization": "ELF"

### $ELF = 1 - \sum_{i=1}^{n} s_i^2$

Where $$s_i$$ is fraction of population for group $$i \in \lbrace 1 \ldots n \rbrace$$

## A Less Trivial Example

### Ethnic diversity: a measure

Propose a measure that would assign a value for "Ethno-linguistic fractionalization" in a specific country

## A Less Trivial Example

### Ethnic diversity: a measure

Measure size of ethnic groups using Atlas Narodov Mira:

Soviet anthropological text from 1964

• lists ethnic groups in each country
• lists the size of these groups

## Ethnic diversity: problems

### Concept:

• Different dimensions of ethnicity (e.g. language, religion, race, caste, tribe)
• Maybe political relevance matters (maybe differences between Greek, Italian, German, Irish, Scottish immigrant descendants in Canada are not relevant today)

### Variable:

• Country A: Group 1 50%, Group 2 50%
• $$ELF = 0.5$$
• Country B: Group 1 66.6%, Group 2 16.6%, Group 3 16.6%
• $$ELF = 0.5$$

## Ethnic diversity: revisions

### Measure:

Soviet anthropologists:

• Are group sizes from 1964 correct?
• Distinct ethnic groups treated as the same, unified ethnic groups treated as different
• Rwanda: Hutus and Tutsis coded as one ethnic group.

## Variables

We defined variables above… but it is important to note that

### In practice:

Variables take on values for each specific case at a specific point in time

• "Annual number of hate crimes"
• Case is a country/province/city, time is a year
• Can vary between countries/provinces/cities in year
• Can vary across years within a country/province/city

## Number of Hate Crimes

This is a variable. What values does it take?

• Numeric values
• Range: 0 to ?

Variations:

• Hate Crimes Per Capita
• Hate Crime Victimization Rate (number of hate crimes against a group $$g$$ per persons in group $$g$$)

## Language spoken:

This is a variable: what values does it take?

• Categories
• No numeric range
• One language is not "higher"/"lower" than another.