soci208 - module 1

SOCI208 Module 1 - Nature of Data

1. Data Sets

A data set is a collection of facts assembled for a particular purpose.

Exhibit: GRAD data set [m1001.htm]

A rectanguar data set is one where the information is organized in a element (unit) by variable format, where

a unit or element is a unit of observation; for example

in the GRAD data set units are states of the U.S.
in the GSS98 (General Social Survey) data set units are individual respondents to the survey
in the NOS (National Organizations Survey) elements are individual respondents to a survey together with the organization where they work

a variable is a characteristic of interest about an element; for example

in the GRAD data PWHI (the percent of the population white) is a variable
in GSS98 WORDSUM is a variable

a case is the information on all variables for one unit (corresponding to one row of the data set)
an observation is information about a single variable for a given element; for example

in the GRAD data the value 69.3 of the variable GRAD (= percent high school graduation rate) for NC is an observation

2. Levels of Measurement

1. Levels of Measurement

An influential typology due to <> distinguishes different types of data according to the level of measurement.

**Levels of Measurement (+ or - indicate presence or absence of property in corresponding column)**
	Exclusive & exhaustive set of attributes	Ordering of categories defined	Interval between categories defined	Absolute zero defined (so that ratios make sense)
A. *Categorical* (aka *nominal, qualitative, or classification*) variable	+	-	-	-
B. *Ordinal* variable	+	+	-	-
C. *Interval* variable	+	+	+	-
D. *Ratio* variable	+	+	+	+

Examples:

Categorical variables

sex or "gender"
religion (e.g., Protestant, Catholic, Jewish, Other)
region (of a state in the U.S.)

Ordinal variables

the Mohr scale of hardness - categories from graphite to diamond are ordered after the relation 'material 1 scratches material 2'
Likert scales, such as opinion questions with answer categories Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree
"How well do you speak Spanish?" with answer categories Very Well, Pretty Well, Well, Not Very Well, Not At All

Interval variables

temperature expressed in degrees Farenheit ^oF or Celsius ^oC; note that ^oF = 32 + 9/5 ^oC; Q - Can one say that 64 ^oF is "twice as warm" as 32 ^oF? (Hint: convert ^oF to ^oC and see if the ratio is the same.) Thus temperatures expressed in ^oF or ^oC are interval, but not ratio (see next), variables.
IQ; Q - How would one know that (1) IQ is an interval variable rather than an ordinal variable, and (2) that it is an interval but not a ratio variable? (This is actually a very subtle and interesting question.)

Ratio variables

income (of an individual) or GDP per capita (of a country)
percent of the labor force in agriculture (of a country or state)
age
counts (where the values are integers)

2. Implications of Levels of Measurement

The level of measurement has implications for the kinds of analysis that can be performed with a variable:

categorical variables are analyzed using contingency tables (tabular analysis)
interval and ratio variables can be analyzed using regression techniques such as scatterplots and multiple regression
ordinal variables are often treated either as categorical variables (with loss of the order information; ex: using YOUNG, ADULT, SENIOR age categories) or as interval variables (assuming equal intervals between categories, an assumption that may or may not be justified; ex: treating as an interval variable "How well do you speak Spanish?" coded from 1 to 5); there are also some advanced techniques that do use the order information of ordinal variables
the analyst may decide to treat a higher level variable as a lower level one for a number of reasons; ex: in studying the effect of education on income, an analyst chooses to measure education as categorical/ordinal "LT HS, HS, SOCO, CO, GRAD" rather than the ratio variable measuring years of education, to allow for non-linear effects of education due to a "credentialling" phenomenon
for most data analysis, one can simplify the four-fold typology of data into two types:

qualitative (categorical variables, and sometimes ordinal variables treated as categorical)
quantitative (interval & ratio, and sometimes ordinal variables treated as interval)

3. Data Sources

1. Experimental & Observational Studies

1. Experimental Studies

In experimental studies the analyst is able to manipulate the value of one or several variables of interest (the experimental treatment) to estimate their effects on the dependent variable, while using random assignment of subjects to treatments to control statistically for other factors that can affect the dependent variable. For example

psychologists at Duke recruit babies (3 to 5 months old) for experiments; while the baby sits on the mother's knees, he/she is shown a puppet theater stage where is shown a scene that is either physically possible (a hand appears that slides one object, say a yellow cone, away from another, say a blue cylinder) or physically impossible (when the hand slides the cone away, the blue cylinder comes with it with no appparent connection between the objects). The dependent variable is the length of time the baby stares at the scene (a measure of "surprise" or "perplexity" in infants); here the experimental treatment is the type of scene shown; subjects are randomly assigned to the "possible" or "impossible" scene. Q - What theory are these psychologists testing?

Experimental studies allow strong inferences about causal relations among variables.

2. Observational Studies

In observational studies the analyst cannot manipulate the values of the independent variable(s) of interest and cannot use randomization to control the effects of other factors. For example

to estimate the effect of family background (or "social class") on educational achievement of children, an observational study may interview a sample of students in high school and their parents, and collect additional data from school officials about grades and test results; the analyst must use statistical methods to try disentangling various factors that can affect achievement, besides the socio-economic level of the family.

It is more difficult to estimate causal relations with observaitonal than with experimental data, because there is always the possibility of omitting an important causal factor.

2. Individual & Aggregate Units

In the social sciences many studies are based either on individual data (where the elements are people) or on aggregate units each of which represents a group of individuals (such as an organization, country, electoral district, or other administrative unit). Common differences between these sources of data are

measures of association between variables are often stronger with aggregate units than with individual units. Q - Why is that?
it may be delicate to infer across levels, i.e. to conclude from an association at the aggregate level that a similar association exists at the individul level; this issue is sometimes called "the ecological fallacy" (which is itself a misleading term)

Last modified 21 Aug 2002