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## The Practice of Social Research

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### Title: The Practice of Social Research Author: Aurea K Osgood Last modified by: T.L. Warburton Created Date: 9/11/2008 2:35:26 PM Document presentation format – PowerPoint PPT presentation

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Title: The Practice of Social Research

1
The Practice of Social Research
• Chapter 16 Statistical Analysis

2
Chapter Outline
• Descriptive Statistics
• Inferential Statistics
• Other Multivariate Techniques
• Quick Quiz

3
Descriptive Statistics
• Descriptive Statistics statistical computations
describing either the characteristics of a sample
or the relationship among variables in a sample.

4
Descriptive Statistics
• Measures of Association
• 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.

5
Descriptive Statistics
• Nominal Variables
• Lambda (?)
• Ordinal Variables
• Gamma (?)
• Interval and Ratio Variables
• Pearson (r)

6
Descriptive Statistics
• 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.
• 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.
• 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.

7
Descriptive Statistics
• Linear Regression
• Regression Line
• Unexplained Variation
• Explained Variation

8
Descriptive Statistics
• Multiple Regression
• 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.
• Curvilinear Regression Analysis a form of
regression analysis that allows relationships
among variables to be expressed with curved
geometric lines instead of straight ones.

9
Inferential Statistics
• Inferential Statistics the body of statistical
computations relevant to making inferences from
findings based on sample observations to some
larger population.

10
Independent Variable Independent Variable Independent Variable
Dependent Variable Nominal Ordinal Interval/Ratio
Dependent Variable Nominal Crosstabs Chi-Square Lambda Crosstabs Chi-Square Lambda
Dependent Variable Ordinal Crosstabs Chi-Square Lambda Crosstabs Chi-Square Lambda Gamma Kendalls tau Sommers d
Dependent Variable Interval/Ratio Means t-test ANOVA Means t-test ANOVA Correlate Pearson s Regression (R)
11
Inferential Statistics
• Univariate Inferences
• The sample must be drawn from the population
• 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.

12
Inferential Statistics
• Tests of Statistical Significance
• Statistical Significance a general term
referring to the likelihood that the relationship
observed in a sample could be attributed to
sampling error alone.
• 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.

13
Inferential Statistics
• The Logic of Statistical Significance
• Assumptions regarding the independence of two
variables in the population study
• Assumptions regarding the representativeness of
samples selected through conventional
probability-sampling procedures
• The observed joint distribution of sample
elements in terms of the two variables

14
Inferential Statistics
• 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.
• 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.

15
Inferential Statistics
• Chi-Square
• Based on the null hypothesis.
• Computation
• 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

16
Inferential Statistics
• t-Test
• Measure for judging the statistical significance
of differences in group means.
• Logic
• 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.

17
Inferential Statistics
• Caution
• 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.

18
Other Multivariate Techniques
• Path Analysis a form of multivariate analysis
in which the causal relationship among variables
are presented in a graphic format.

19
Other Multivariate Techniques
• Time-Series Analysis an analysis of changes in
a variable over time.

20
Other Multivariate Techniques
• Factor Analysis a complex algebraic method for
determining the general dimensions of factors
that exist within a set of concrete observations.

21
Other Multivariate Techniques
• 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.

22
Other Multivariate Techniques
• Discriminant Analysis method of analysis
similar to multiple regression, except that the
dependent variable can be nominal.

23
Other Multivariate Techniques
• 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.

24
Other Multivariate Techniques
• Geographic Information Systems (GIS) analytic
technique in which researchers map quantitative
data that describe geographic units for a graphic
display.

25
Quick Quiz
26
Chapter 16 Quiz
• 1. _____ indicate the likelihood that the
relationship observed between variables in a
sample can be attributed to sampling error only.
• Ex post facto hypothesizing
• Tests of statistical significance
• Disconfirmation

27
Chapter 16 Quiz
• Tests of statistical significance indicate the
likelihood that the relationship observed between
variables in a sample can be attributed to
sampling error only.

28
Chapter 16 Quiz
• 2. _____ is a causal model for understanding
relationships between variables.
• Ex post facto hypothesizing
• Tests of statistical significance
• Disconfirmation
• Path analysis

29
Chapter 16 Quiz
• Path analysis is a causal model for understanding
relationships between variables

30
Chapter 16 Quiz
• 3. _____ are statistical measures used for making
inferences from findings based on sample
observations to a larger population.
• Descriptive statistics
• Inferential statistics
• both of the above
• none of the above

31
Chapter 16 Quiz
• Inferential statistic are statistical measures
used for making inferences from findings based on
sample observations to a larger population.

32
Chapter 16 Quiz
• 4. A _____ analysis represents changes in a
variable over time.
• regression
• bivariate
• time-series
• log-linear

33
Chapter 16 Quiz