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Chapter 9
Principles of Analysis
and Interpretation
Principles of Analysis and Interpretation
• Data, as used in behavioral research, means
research results from which inferences are
drawn: usually numerical results, like scores of
tests and statistics such as means, percentages,
and correlation coefficients.
• Analysis means the categorizing, ordering,
manipulating, and summarizing of data to obtain
answers to research questions.
• Interpretation takes the results of analysis,
makes inferences pertinent to the research
relations studied, and draws conclusions about
these relations.
Frequencies and Continuous
Measures
• Quantitative data come in two general
forms: frequencies and continuous
measures.
• f={(x,y); where x is a member of the set X,
and y is either 1 or 0 depending on x’s
possessing or not possessing M}
• f={(x,y); x is an object, and y= any numeral}
Rules of Categorization
• The first setup in any analysis is categorization.
• The five rules of categorization are as follows:
• 1.Categories are set up according to the
research problem and purpose.
• 2.The categories are exhaustive.
• 3.The categories are mutually exclusive and
independent.
• 4.Each category (variable) is derived from one
classification principle.
• 5.Any categorization scheme must be on one
level of discourse
Kinds of Statistical Analysis
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Frequency Distributions
Graphs and Graphing
Measures of Central Tendency and Variability
Measures of Relations
Analysis of Differences
Analysis of Variance and Related Methods
Profile Analysis
Multivariate Analysis
Graphs and Graphing
• A graph is a two-dimension representation
of a relation or relations.
• Figure 9.1, 9.2, 9.3
• Interaction means that the relation of an
independent variable to a dependent
variable differs in different groups or at
different levels of another independent
variable..
Frequency Distributions
• Although frequency distributions are used
primarily for descriptive purposes, they
can also be used for other research
purposes.
• Observed distributions can also be
compared to theoretical distributions
(normal distributions).
Measures of Central Tendency and
Variability
• Mean, median, mode
• Standard deviation, range
Measures of Relations
• Ideally, any analysis of research data
should include both kinds of indices:
measures of the significance of a relation
and measures of the magnitude of the
relation.
Analysis of Differences
• 1.it is by no means confined to the
differences between measures of central
tendency.
• 2.All analyses of differences are intended
for the purpose of studying relation.
Conversely, the greater the differences the
higher the correlation, all other things
being equal.
Analysis of Variance and Related
Methods
• A method of identifying, breaking down,
and testing for statistical significance
variances that come from different sources
of variation. That is, a dependent variable
has a total amount of variance, some of
which is due to the experimental treatment,
some to error, and some to other causes.
• Figure 9.5, 9.6
Profile Analysis
• Profile analysis is basically the
assessment of the similarities of the
profiles of individuals or groups. A profile is
a set of different measures of an individual
or group, each of which is expressed in
the same unit of measure.
Multivariate Analysis
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Multiple regression
Canonical correlation
Discriminant analysis
Factor analysis
Path analysis
Analysis of covariance structures
Log-linear models
Indices
• Index can be defined in two related ways:
• 1.An index is an observable phenomenon
that is substituted for a less-observable
phenomenon. For example, test scores
indicate achievement levels, verbal
aptitudes, degrees of anxiety, and so on.
• 2.An index is a number that is a composite
of two or more numbers. For example, all
sums and averages, coefficients of
correlation.
Indices
• Indices are most important in research
because they simplify comparisons. The
percentage is a good example. Percentages
transform raw numbers into comparable form.
• Indices generally take the form of quotients:
ratios and proportions.
Social Indicators
• Indicators, although closely related to indices—
indeed, they are frequently indices as defined
above—form a special class of variables.
• Variables like income, life expectancy, fertility,
quality of life, educational level (of people), and
environment can be called social indicators. Social
indicators are both variables and statistics.
• Unfortunately, it is difficult to define “social
indicators.” In this book we are interested in social
indicators as a class of sociological and
psychological variables that in the future may be
useful in developing and testing scientific theories
of the relations among social and psychological
phenomena.
The Interpretation of Research
Data
• Adequacy of Research Design,
Methodology, Measurement, and Analysis
• Negative and Inconclusive Results
• Unhypothesized Relations and
Unanticipated Findings
• Proof, Probability, and Interpretation
Adequacy of Research Design, Methodology,
Measurement, and Analysis
• Most important, the design, methods of
observation, measurement, and statistical
analysis must all be appropriate to the
research problem.
Negative and Inconclusive Results
• When results are positive, when the data
support the hypotheses, one interprets the data
along the lines of the theory and the reasoning
behind the hypotheses. If we can repeat the feat,
the n the evidence of adequacy is even more
convincing.
• If we can be fairly sure that the methodology, the
measurement, and the analysis are adequate,
then negative results can be definite
contributions to scientific advancement.
Unhypothesized Relations and
Unanticipated Findings
• The unpredicted relation may be an important
key to a deeper understanding of the theory. For
example, positive reinforcement strengthens
response tendencies.
• Unpredicted and unexpected findings must be
treated with more suspicion than predicted and
expected findings. Before being accepted, they
should be substantiated in independent research
in which they are specially predicted and tested.
Proof, Probability, and Interpretation
• Let us flatly assert that nothing can be “proved”
scientifically. All one can do is to bring evidence
to bear that such-and such a proposition is true.
• Proof is a deductive matter. Experimental
methods of inquiry are not methods of proof,
they are controlled methods of bringing evidence
to bear on the probable truth or falsity of
relational propositions.
• In short, no single scientific investigation ever
proves anything. Thus the interpretation of the
analysis of research data should never use the
word proof.