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Quantitative Data Analysis

Edouard Manet In the Conservatory, 1879

- Quantification of Data
- Introduction
- To conduct quantitative analysis, responses to

open-ended questions in survey research and the

raw data collected using qualitative methods must

be coded numerically.

- Quantification of Data
- Introduction (Continued)
- Most responses to survey research questions

already are recorded in numerical format. - In mailed and face-to-face surveys, responses are

keypunched into a data file. - In telephone and internet surveys, responses are

automatically recorded in numerical format.

- Quantification of Data
- Developing Code Categories
- Coding qualitative data can use an existing

scheme or one developed by examining the data. - Coding qualitative data into numerical categories

sometimes can be a straightforward process. - Coding occupation, for example, can rely upon

numerical categories defined by the Bureau of the

Census.

- Quantification of Data
- Developing Code Categories (Continued)
- Coding most forms of qualitative data, however,

requires much effort. - This coding typically requires using an iterative

procedure of trial and error. - Consider, for example, coding responses to the

question, What is the biggest problem in

attending college today. - The researcher must develop a set of codes that

are - exhaustive of the full range of responses.
- mutually exclusive (mostly) of one another.

- Quantification of Data
- Developing Code Categories (Continued)
- In coding responses to the question, What is the

biggest problem in attending college today, the

researcher might begin, for example, with a list

of 5 categories, then realize that 8 would be

better, then realize that it would be better to

combine categories 1 and 5 into a single category

and use a total of 7 categories. - Each time the researcher makes a change in the

coding scheme, it is necessary to restart the

coding process to code all responses using the

same scheme.

- Quantification of Data
- Developing Code Categories (Continued)
- Suppose one wanted to code more complex

qualitative data (e.g., videotape of an

interaction between husband and wife) into

numerical categories. - How does one code the many statements, facial

expressions, and body language inherent in such

an interaction? - One can realize from this example that coding

schemes can become highly complex.

- Quantification of Data
- Developing Code Categories (Continued)
- Complex coding schemes can take many attempts to

develop. - Once developed, they undergo continuing

evaluation. - Major revisions, however, are unlikely.
- Rather, new coders are required to learn the

existing coding scheme and undergo continuing

evaluation for their ability to correctly apply

the scheme.

- Quantification of Data
- Codebook Construction
- The end product of developing a coding scheme is

the codebook. - This document describes in detail the procedures

for transforming qualitative data into numerical

responses. - The codebook should include notes that describe

the process used to create codes, detailed

descriptions of codes, and guidelines to use when

uncertainty exists about how to code responses.

- Quantification of Data
- Data Entry
- Data recorded in numerical format can be entered

by keypunching or the use of sophisticated

optical scanners. - Typically, responses to internet and telephone

surveys are entered directly into a numerical

data base. - Cleaning Data
- Logical errors in responses must be reconciled.
- Errors of entry must be corrected.

- Univariate Analysis
- Distributions
- Data analysis begins by examining distributions.
- One might begin, for example, by examining the

distribution of responses to a question about

formal education, where responses are recorded

within six categories. - A frequency distribution will show the number and

percent of responses in each category of a

variable.

- Univariate Analysis
- Central Tendency
- A common measure of central tendency is the

average, or mean, of the responses. - The median is the value of the middle case when

all responses are rank-ordered. - The mode is the most common response.
- When data are highly skewed, meaning heavily

balanced toward one end of the distribution, the

median or mode might better represent the most

common or centered response.

- Univariate Analysis
- Central Tendency (Continued)
- Consider this distribution of respondent ages
- 18, 19, 19, 19, 20, 20, 21, 22, 85
- The mean equals 27. But this number does not

adequately represent the common respondent

because the one person who is 85 skews the

distribution toward the high end. - The median equals 20.
- This measure of central tendency gives a more

accurate portrayal of the middle of the

distribution.

- Univariate Analysis
- Dispersion
- Dispersion refers to the way the values are

distributed around some central value, typically

the mean. - The range is the distance separating the lowest

and highest values (e.g., the range of the ages

listed previously equals 18-85). - The standard deviation is an index of the amount

of variability in a set of data.

- Univariate Analysis
- Dispersion (Continued)
- The standard deviation represents dispersion with

respect to the normal (bell-shaped) curve. - Assuming a set of numbers is normally

distributed, then each standard deviation equals

a certain distance from the mean. - Each standard deviation (1, 2, etc.) is the

same distance from each other on the bell-shaped

curve, but represents a declining percentage of

responses because of the shape of the curve (see

Chapter 7).

- Univariate Analysis
- Dispersion (Continued)
- For example, the first standard deviation

accounts for 34.1 of the values below and above

the mean. - The figure 34.1 is derived from probability

theory and the shape of the curve. - Thus, approximately 68 of all responses fall

within one standard deviation of the mean. - The second standard deviation accounts for the

next 13.6 of the responses from the mean (27.2

of all responses), and so on.

- Univariate Analysis
- Dispersion (Continued)
- If the responses are distributed approximately

normal and the range of responses is lowmeaning

that most responses fall close to the meanthen

the standard deviation will be small. - The standard deviation of professional golfers

scores on a golf course will be low. - The standard deviation of amateur golfers scores

on a golf course will be high.

- Univariate Analysis
- Continuous and Discrete Variables
- Continuous variables have responses that form a

steady progression (e.g., age, income). - Discrete (i.e., categorical) variables have

responses that are considered to be separate from

one another (i.e., sex of respondent, religious

affiliation).

- Univariate Analysis
- Continuous and Discrete Variables
- Sometimes, it is a matter of debate within the

community of scholars about whether a measured

variable is continuous or discrete. - This issue is important because the statistical

procedures appropriate for continuous-level data

are more powerful, easier to use, and easier to

interpret than those for discrete-level data,

especially as related to the measurement of the

dependent variable.

- Univariate Analysis
- Continuous and Discrete Variables (Continued)
- Example Suppose one measures amount of formal

education within five categories less than hs,

hs, 2-years vocational/college, college,

post-college). - Is this measure continuous (i.e., 1-5) or

discrete? - In practice, five categories seems to be a cutoff

point for considering a variable as continuous. - Using a seven-point response scale will give the

researcher a greater chance of deeming a variable

to be continuous.

- Subgroup Comparisons
- Collapsing Response Categories
- Sometimes the researcher might want to analyze a

variable by using fewer response categories than

were used to measure it. - In these instances, the researcher might want to

collapse one or more categories into a single

category. - The researcher might want to collapse categories

to simplify the presentation of the results or

because few observations exist within some

categories.

- Subgroup Comparisons
- Collapsing Response Categories Example
- Response Frequency
- Strongly disagree 2
- Disagree 22
- Neither agree nor disagree 45
- Agree 31
- Strongly Agree 1

- Subgroup Comparisons
- Collapsing Response Categories Example
- One might want to collapse the extreme responses

and work with just three categories - Response Frequency
- Disagree 24
- Neither agree nor disagree 45
- Agree 32

- Subgroup Comparisons
- Handling Dont Knows
- When asking about knowledge of factual

information (Does your teenager drink alcohol?)

or opinions on a topic the subject might not know

much about (Do school officials do enough to

discourage teenagers from drinking alcohol?), it

is wise to include a dont know category as a

possible response. - Analyzing dont know responses, however, can be

a difficult task.

- Subgroup Comparisons
- Handling Dont Knows (Continued)
- The research-on-research literature regarding

this issue is complex and without clear-cut

guidelines for decision-making. - The decisions about whether to use dont know

response categories and how to code and analyze

them tends to be idiosyncratic to the research

and the researcher.

- Bivariate Analysis
- Introduction
- Bivariate analysis refers to an examination of

the relationship between two variables. - We might ask these questions about the

relationship between two variables - Do they seem to vary in relation to one another?

That is, as one variable increases in size does

the other variable increase or decrease in size? - What is the strength of the relationship between

the variables?

- Bivariate Analysis
- Bivariate Tables
- Divide the cases into groups according to the

attributes of the independent variable (e.g., men

and women). - Describe each subgroup in terms of attributes of

the dependent variable (e.g., what percent of men

approve of sexual equality and what percent of

women approve of sexual equality).

- Bivariate Analysis
- Bivariate Tables (Continued)
- Read the table by comparing the independent

variable subgroups with one another in terms of a

given attribute of the dependent variable (e.g.,

compare the percentages of men and women who

approve of sexual equality). - Bivariate analysis gives an indication of how the

dependent variable differs across levels or

categories of an independent variable. - This relationship does not necessarily indicate

causality (see Chapter 15).

- Bivariate Analysis
- Contingency Tables
- Tables that compare responses to a dependent

variable across levels/categories of an

independent variable are called contingency

tables (or sometimes, crosstabs). - When writing a research report, it is common

practice, even when conducting highly

sophisticated statistical analysis, to present

contingency tables also to give readers a sense

of the distributions and bivariate relationships

among variables.

- Bivariate Analysis
- Contingency Tables (Continued)
- A table should have a title that succinctly

describes what is contained in the table. - If a table lists information about a scale or

index, then it or a prior table should list the

statements used to measure the scale or index. - The attributes of each variable should be clearly

indicated. - The base of percentages should be reported.
- Notes should be provided about missing data.

- Multivariate Analysis
- Introduction
- Although informative, bivariate analysis can

mislead the researcher regarding cause and

effect. - Multivariate analysis (see Ch. 15-16) often is

needed to gain a better understanding of cause

and effect among variables. - Multivariate analysis can involve the

introduction of a third variable into a

contingency table, or it can involve more

sophisticated analysis and presentation of

relationships among variables.

- Multivariate Techniques
- Factor Analysis
- Factor analysis indicates the extent to which a

set of variables measures the same underlying

concept. - This procedure assesses the extent to which

variables are highly correlated with one another

compared with other sets of variables. - Consider the table of correlations (i.e., a

correlation matrix) on the following slide

Multivariate Techniques Factor Analysis

(Continued) X1 X2 X3 X4 X5 X6 X1 1 .52 .60 .21

.15 .09 X2 .52 1 .59 .12 .13 .11 X3 .60 .59 1 .08

.10 .10 X4 .21 .12 .08 1 .72 .70 X5 .15 .13 .10 .7

2 .68 .73 X6 .09 .11 .10 .70 .73 1

- Multivariate Techniques
- Factor Analysis (Continued)
- Note that variables X1-X3 are moderately

correlated with one another, but have weak

correlations with variables X4-X6. - Similarly, variables X4-X6 are moderately

correlated with one another, but have weak

correlations with variables X1-X3. - The figures in this table indicate that variables

X1-X3 go together and variables X4-X6 go

together.

- Multivariate Techniques
- Factor Analysis (Continued)
- Factor analysis would separate variables X1-X3

into Factor 1 and variables X4-X6 into Factor

2. - Suppose variables X1-X3 were designed by the

researcher to measure self-esteem and variables

X4-X6 were designed to measure marital

satisfaction.

- Multivariate Techniques
- Factor Analysis (Continued)
- The researcher could use the results of factor

analysis, including the statistics produced by

it, to evaluate the construct validity of using

X1-X3 to measure self-esteem and using X4-X6 to

measure marital satisfaction. - Thus, factor analysis can be a useful tool for

confirming the validity of measures of latent

variables.

- Multivariate Techniques
- Factor Analysis (Continued)
- Factor analysis can be used also for exploring

groupings of variables. - Suppose a researcher has a list of 20 statements

that measure different opinions about same-sex

marriage. - The researcher might wonder if the 20 opinions

might reflect a fewer number of basic opinions.

- Multivariate Techniques
- Factor Analysis (Continued)
- Factor analysis of responses to these statements

might indicate, for example, that they can be

reduced into three latent variables, related to

religious beliefs, beliefs about civil rights,

and beliefs about sexuality. - Then, the researcher can create scales of the

grouped variables to measure religious beliefs,

civil beliefs, and beliefs about sexuality to

examine support for same-sex marriage.

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