The Practice of Social Research

Chapter 16 – Statistical Analysis

Chapter Outline Descriptive Statistics Inferential Statistics Other Multivariate Techniques Quick Quiz

Descriptive Statistics Descriptive Statistics – statistical computations

describing either the characteristics of a sample or the relationship among variables in a sample.

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.

Descriptive Statistics Nominal Variables

Lambda (λ)

Ordinal Variables Gamma (γ)

Interval and Ratio Variables Pearson (r)

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.

Descriptive Statistics Linear Regression

Regression Line

Unexplained Variation

Explained Variation

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.

Inferential Statistics Inferential Statistics – the body of statistical

computations relevant to making inferences from findings based on sample observations to some larger population.

Independent Variable

Dependent Variable

Nominal Ordinal Interval/Ratio

Nominal CrosstabsChi-SquareLambda

CrosstabsChi-SquareLambda

Ordinal CrosstabsChi-SquareLambda

CrosstabsChi-SquareLambdaGammaKendall’s tauSommers’ d

Interval/Ratio Meanst-testANOVA

Meanst-testANOVA

CorrelatePearson sRegression (R)

Inferential Statistics Univariate Inferences

Cautions about Making Inferences1. The sample must be drawn from the population about which

inferences are being made.

2. The inferential statistics assume several things: (a) simple random sampling, (b) sampling with replacement, (c) 100 percent completion rate

3. Inferential statistics are addressed to sampling error only, not nonsampling error.

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.

Inferential Statistics The Logic of Statistical Significance

1. Assumptions regarding the independence of two variables in the population study

2. Assumptions regarding the representativeness of samples selected through conventional probability-sampling procedures

3. The observed joint distribution of sample elements in terms of the two variables

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.

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

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.

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.

Other Multivariate Techniques Path Analysis – a form of multivariate analysis in

which the causal relationship among variables are presented in a graphic format.

Other Multivariate Techniques Time-Series Analysis – an analysis of changes in a

variable over time.

Other Multivariate Techniques Factor Analysis – a complex algebraic method for

determining the general dimensions of factors that exist within a set of concrete observations.

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.

Other Multivariate Techniques Discriminant Analysis – method of analysis similar to

multiple regression, except that the dependent variable can be nominal.

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.

Other Multivariate Techniques 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. Ex post facto hypothesizing

B. Tests of statistical significance

C. 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. Ex post facto hypothesizing

B. Tests of statistical significance

C. Disconfirmation

D. 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. Descriptive statistics

B. Inferential statistics

C. both of the above

D. 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. regression

B. bivariate

C. time-series

D. log-linear

Chapter 16 Quiz

ANSWER: C.

A time-series analysis represents changes in a variable over time.