The Practice of Social Research
Chapter 16 – Statistical Analysis
Chapter Outline
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Descriptive Statistics
Inferential Statistics
Other Multivariate Techniques
Quick Quiz
Descriptive Statistics
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Descriptive Statistics – statistical computations
describing either the characteristics of a sample or
the relationship among variables in a sample.
Descriptive Statistics
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Measures of Association
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Proportionate Reduction of Error (PRE) – a logical model
for assessing the strength of a relationship by asking how
much knowing values on one variable would reduce our
errors in guessing values on another variable.
Descriptive Statistics
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Nominal Variables
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Ordinal Variables
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Lambda (λ)
Gamma (γ)
Interval and Ratio Variables
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Pearson (r)
Descriptive Statistics
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Regression Analysis – a method of data analysis in
which the relationships among variables are
represented in the form of an equation, called a
regression equation.
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Linear Regression Analysis – a form of statistical analysis
that seeks the equation for the straight line that best
describes the relationship between two ratio variables.
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Multiple Regression Analysis – a form of statistical
analysis that seeks the equation representing the impact
of two or more independent variables on a single
dependent variable.
Descriptive Statistics
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Linear Regression
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Regression Line
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Unexplained Variation
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Explained Variation
Descriptive Statistics
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Multiple Regression
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Partial Regression Analysis – a form of regression
analysis in which the effects of one or more variables are
held constant, similar to the logic of the elaboration
model.
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Curvilinear Regression Analysis – a form of regression
analysis that allows relationships among variables to be
expressed with curved geometric lines instead of straight
ones.
Inferential Statistics
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Inferential Statistics – the body of statistical
computations relevant to making inferences from
findings based on sample observations to some
larger population.
Independent Variable
Nominal
Ordinal
Nominal
Crosstabs
Chi-Square
Lambda
Crosstabs
Chi-Square
Lambda
Ordinal
Crosstabs
Chi-Square
Lambda
Crosstabs
Chi-Square
Lambda
Gamma
Kendall’s tau
Sommers’ d
Interval/Ratio
Means
t-test
ANOVA
Means
t-test
ANOVA
Dependent
Variable
Interval/Ratio
Correlate
Pearson s
Regression (R)
Inferential Statistics
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Univariate Inferences
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Cautions about Making Inferences
1.
2.
3.
The sample must be drawn from the population about which
inferences are being made.
The inferential statistics assume several things: (a) simple
random sampling, (b) sampling with replacement, (c) 100
percent completion rate
Inferential statistics are addressed to sampling error only, not
nonsampling error.
Inferential Statistics
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Tests of Statistical Significance
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Statistical Significance – a general term referring to the
likelihood that the relationship observed in a sample could
be attributed to sampling error alone.
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Tests of Statistical Significance – a class of statistical
computations that indicate the likelihood that the
relationship observed between variables in a sample can
be attributed to sampling error alone.
Inferential Statistics
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The Logic of Statistical Significance
1.
2.
3.
Assumptions regarding the independence of two
variables in the population study
Assumptions regarding the representativeness of
samples selected through conventional probabilitysampling procedures
The observed joint distribution of sample elements in
terms of the two variables
Inferential Statistics
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Level of Significance – in the context of tests of statistical
significance, the degree of likelihood that an observed,
empirical relationship could be attributed to sampling
error.
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A relationship is significant at the .05 level if the likelihood of its
being only a function of sampling error is no greater than 5 out
of 100.
Inferential Statistics
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Chi-Square
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Based on the null hypothesis.
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Computation:
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For each cell in the table, subtract the expected frequency for
that cell from the observed frequency.
Square the quantity.
Divide the squared difference by the expected frequency.
Chi-Square Table
Inferential Statistics
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t-Test
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Measure for judging the statistical significance of
differences in group means.
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Logic:
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The value of t will increase with the size of the differences
between means.
The value of t will also increase with the size of the sample
involved.
The value of t will be larger when variations of values within
each group are smaller.
Inferential Statistics
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Caution…
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There are no objective tests of substantive significance
(only objective significance).
Statistical significance is only appropriate for samples,
and not for whole populations.
Tests of significance are based on the same sampling
assumptions used to compute confidence intervals.
Other Multivariate Techniques
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Path Analysis – a form of multivariate analysis in
which the causal relationship among variables are
presented in a graphic format.
Other Multivariate Techniques
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Time-Series Analysis – an analysis of changes in a
variable over time.
Other Multivariate Techniques
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Factor Analysis – a complex algebraic method for
determining the general dimensions of factors that
exist within a set of concrete observations.
Other Multivariate Techniques
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Analysis of Variance (ANOVA) – method of analysis
in which cases under study are combined into
groups representing an independent variable, and
the extent to which the groups diff from one another
is analyzed in terms of some dependent variable.
Then, the extent to which the groups differ is
compared with the standard of random distribution.
Other Multivariate Techniques
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Discriminant Analysis – method of analysis similar to
multiple regression, except that the dependent
variable can be nominal.
Other Multivariate Techniques
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Log-Linear Models – data analysis technique based
on specifying models that describe the
interrelationships among variables and then
comparing expected and observed table-cell
frequencies.
Other Multivariate Techniques
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Geographic Information Systems (GIS) – analytic
technique in which researchers map quantitative
data that describe geographic units for a graphic
display.
Quick Quiz
Chapter 16 Quiz
1. _____ indicate the likelihood that the relationship
observed between variables in a sample can be
attributed to sampling error only.
A.
B.
C.
Ex post facto hypothesizing
Tests of statistical significance
Disconfirmation
Chapter 16 Quiz
ANSWER: B.
Tests of statistical significance indicate the likelihood
that the relationship observed between variables in a
sample can be attributed to sampling error only.
Chapter 16 Quiz
2. _____ is a causal model for understanding
relationships between variables.
A.
B.
C.
D.
Ex post facto hypothesizing
Tests of statistical significance
Disconfirmation
Path analysis
Chapter 16 Quiz
ANSWER: D.
Path analysis is a causal model for understanding
relationships between variables
Chapter 16 Quiz
3. _____ are statistical measures used for making
inferences from findings based on sample
observations to a larger population.
A.
B.
C.
D.
Descriptive statistics
Inferential statistics
both of the above
none of the above
Chapter 16 Quiz
ANSWER: B.
Inferential statistic are statistical measures used for
making inferences from findings based on sample
observations to a larger population.
Chapter 16 Quiz
4. A _____ analysis represents changes in a variable
over time.
A.
B.
C.
D.
regression
bivariate
time-series
log-linear
Chapter 16 Quiz
ANSWER: C.
A time-series analysis represents changes in a
variable over time.