January 28, 2019

Evaluating Descriptive Claims

Plan for Today:

(1) Recap: Concepts, Variables, Measures

(2) Levels of Measurement

(3) Problems with Variables

Recap

Concepts, Variables, Measures.

Concepts to Measurement:

Concept (and dimensions)

\(\xrightarrow{}\)

Variable(s)

  • measurable properties of cases that map onto a concept

\(\xrightarrow{}\)

Measure(s)

  • procedure to find the values variables take for specific cases

\(\xrightarrow{}\)

"Answer"

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

Concepts to Measurement:

Question/Claim

\(\not\xrightarrow{}\) Concepts not scientific/irrelevant

Concept (and dimensions)

\(\not\xrightarrow{}\) Variable does not map onto concept

Variable(s)

\(\not\xrightarrow{}\) Procedure does not produce the true value

Measure(s)

"Answer"

A Trivial Example:

A descriptive question:

"Is West Lion taller than Seymour?"

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

\(\xrightarrow{}\)

Variable: Vertical distance from sea level to the top of the peak

\(\xrightarrow{}\)

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"

What do we need to know to evaluate this claim?

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

Anything wrong here?

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

Variables

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

variables take on values for each case.

variables take different kinds of values

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 \(g\))

Number of Hate Crimes

Languages

Language spoken:

This is a variable: what values does it take?

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

But what if we counted the fraction of people?

Another example: