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 (λ)
Ordinal Variables
Gamma (γ)
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
Dependent Variable
Nominal
Ordinal
Interval/Ratio
Crosstabs
Chi-Square
Lambda
Gamma
Kendall’s tau
Sommers’ d
Means
t-test
ANOVA
Correlate
Pearson s
Regression (R)

11. Inferential Statistics
Univariate Inferences
Cautions about Making Inferences
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.

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
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.

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
ANSWER: D. 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
ANSWER: B. 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
ANSWER: C. A time-series analysis represents changes in a variable over time.