Quantitative Data Analysis

1
Quantitative Data Analysis
Edouard Manet In the Conservatory, 1879
2

• 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.

3

• 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.

4

• 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.

5

• 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.

6

• 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.

7

• 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.

8

• 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.

9

• 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.

10

• 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.

11

• 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.

12

• 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.

13

• 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.

14

• 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.

15

• 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).

16

• 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.

17

• 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.

18

• 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).

19

• 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.

20

• 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.

21

• 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.

22

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

23

• 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

24

• 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.

25

• 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.

26

• 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?

27

• 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).

28

• 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).

29

• 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.

30

• 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.

31

• 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.

32

• 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

33
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
34

• 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.

35

• 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.

36

• 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.

37

• 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.

38

• 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.

39
Questions?