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Measuring Complex Phenomena: The Role of Indexes and Scales in Sociology, Lecture notes of Social Statistics and Data Analysis

An introduction to indexes and scales, their importance in modern society and personal success, and the process of constructing and evaluating them. It covers the concept of measurement levels, reliability, and validity, as well as methods for evaluating reliability and validity. The document also touches upon the importance of indexes in social research and their role in statistics and data analysis.

Typology: Lecture notes

2011/2012

Uploaded on 01/26/2012

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Indexes, Reliability & Validity
Modern society “runs” on a growing
number of indexes (e.g., CPI, TSX, S & P
500, NASDAQ, Uniform Crime Reports,
etc.,)
Personal success also increasingly turns
on how well we do on testing scales or
indexes (e.g., LSAT, GRE, GMAT, MCAT,
personnel and job testing, etc.,).
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Indexes, Reliability & Validity

 Modern society “runs” on a growing

number of indexes (e.g., CPI, TSX, S & P

500, NASDAQ, Uniform Crime Reports,

etc.,)

 Personal success also increasingly turns

on how well we do on testing scales or

indexes (e.g., LSAT, GRE, GMAT, MCAT,

personnel and job testing, etc.,).

 With measurement assign numbers to

“map” social phenomena. Four levels or

types of measurement: nominal, ordinal,

interval, ratio.

 Indexes & scales provide an interval/ratio

measure of some complex individual or

social attribute (e.g., intelligence, aptitude,

alienation, power, religiosity).

 Indexes & scales measure the different

aspects or components of any complex

phenomenon.

Why use scales and indexes?

 Summarize several indicators into a single index score.

 With an index we can assume we have achieved a higher level of measurement (e.g., add up a series of nominal responses to form an ordinal or interval index). This allows us to use more powerful statistics in analysis.

 Indexes & scales almost always provide a more reliable and valid measure of a phenomenon than a single indicator or question.

 With scales we are more concerned about

reliability & validity with indexes.

 Most scales assume unidimensionality ….the

scale is measuring only one concept.

 Sociology is concerned with developing

interesting & useful indexes to test research hypotheses. Ad hoc indexes are common in social research.

Reliability

 Reliability is the consistency of an index

(e.g., a reliable IQ test will produce similar

IQ scores when applied to the same

sample of people at two different times).

 A reliable index is accurate and is

measuring something with very little error.

 Reliability measures the error in our

measurement!

Evaluating Reliability:

Parallel Forms Reliability (two similar versions of an index should produce similar index scores).

Test-Retest Reliablity (same index administered to same group at 2 different times should produce similar index scores).

Split-Half Reliability (Randomly split questions that form index into 2 sub- indexes…scores on the 2 sub-indexes should be similar for a given respondent).

Cronbach’s Alpha (A statistical measure of reliablity…the closer the alpha coefficient is to 0 the lower your reliability, the closer it is to 1 the higher the reliability of your index.

Types of Validity:

 Content Validity: researcher makes

informed judgment that a question appears

to be measuring the phenomenon.

 “Do you feel social rules are irrelevant?” is

a content valid indicator of anomie. “Do

you feel that carrots prevent cancer?” is

not.

 Clear conceptual definitions allow for

stronger content validity.

 Criterion Validity: researcher measures

congruence between index & something

else measuring the concept (the criterion).

 LSAT scores should be strongly related to

Law School GPAs. If so, LSAT has strong

criterion validity. Job satisfaction index

scores should be strongly related to other

measures of job satisfaction (productivity,

absenteeism). If so, job satisfaction index

has strong criterion validity.

 Concurrent & Predictive Criterion Validity.

“Jury opinion validity” ….a variant of

content validity.

“Known groups validity”… a variant of

criterion validity.

Indexes do not require the level of

validity (or reliability) scales require.

How to succeed at Statistics & Data

Analysis:

 Avoid chatting, dozing off, text messaging, net surfing, etc., during lectures & labs…this can be tough given the subject matter but try to remain quiet, attentive and awake!

 Study statistics regularly! Massed or crammed studying of stats is a recipe for disaster.

Do not fall behind…schedule a weekly review!

 Work out problems using a calculator to build intuitive understanding & confidence.

Use computer labs wisely…plan ahead so you can complete as much of the Assignment during our labs as possible!!!

TABLE 1.1: RESPONSES OF REMOVAL OF A TOY BY SEX OF CHILD. RESPONSE OF CHILD SEX OF CHILD MALE FEMALE

Cry 25 28 Express Anger 15 3

Withdraw from Play 5 4 Play with Alternative Toy 5 15

N= 50 50

Standardizing Frequency Distributions

 We can facilitate comparisons of groups of different sizes by using proportions or percentages.

 We convert a frequency into a proportion by dividing the number of cases in a category by the total number of cases.

p = f / N where f is the number of cases in a category and N is the total number of cases. (e.g., 15 girls out of 50 girls found an alternative toy so the proportion is 15 / 50 = .30; the proportion of boys who found an alternative toy was 5 / 15 = .10)

SEX OF STUDENTS MAJORING IN ENGINEERING AT UNIVERSITIES “A” AND “B”.

ENGINEERING MAJORS SEX UNIVERSITY “A” UNIVERSITY “B” f f Male 1,082 146

Female 270 37

Total 1,352 183

SEX OF STUDENTS MAJORING IN ENGINEERING AT UNIVERSITIES “A” AND “B”.

ENGINEERING MAJORS SEX UNIVERSITY “A” UNIVERSITY “B” f f Male 1, 80%

146 80% Female 270 20%

37 20% Total 1,352 183