Chapter 14
Inferential Statistics II:
Beyond Two Means
Outline 
Concepts 
I. Selecting an Appropriate Statistical Test 

II. Comparisons of More Than Two Means: Analysis of Variance 
analysis of variance: a test of statistical significance that compares the means of two or more groups. pooled variance (abbreviated s_{p}^{2}): the mean of the variances of subgroups involved in comparisons using analysis of variance (weighted for sample sizes in the case of unequal sample sizes). 
A. Oneway Analysis of Variance 
oneway analysis of variance: a statistical tool that permits comparison of several means for one independent variable 
B. What to Do after Finding Statistical Significance 

1. Multiple Comparison Tests 
multiple
comparison tests:
tests completed to identify locations of differences among means
identified as significant with analysis of variance 
2. Determining Effect Sizes 
Eta (h) (also known as the "correlation ratio"): directly interpreted as a correlation and used to compute effect sizes following analysis of variance or F. Eta may also be used to identify nonlinear as well as linear effects. Eta squared (η^{2}): a coefficient of determination computed from eta 
3. Looking for Nonlinear Relationships 
trend
analysis:
a method to isolate the nature of linear and nonlinear trends in effects
identified as statistically significant by analysis of variance 
Interval Estimation Methods: use of a range of values that
capture population parameters; permits identification of 

C. Factorial Analysis of Variance 
variable
factor:
(also called factor) a variable that has been divided into levels or
groups
main effects:
dependent variable effects from independent variables separately 
1.
Computing Factorial ANOVA 
grand mean: in factorial analysis of variance, the average of the mean conditions from predictor variables within groups variance: in analysis of variance, the pooled variance (s_{p}^{2}) residual. error variance: another name for “within groups variance” or “residual variance.” 
Main effects can be interpreted as if a simple oneway analysis of variance had been completed. If an interaction effect is shown to be a crossed interaction (disordinal), then the researcher should not interpret main effects for variables involved, since such information would be misleading.
Yet, if
the interaction effect is A Guide to Advanced Statistical Methods 

Multiple regression correlation 
multiple
regression correlation
(a.k.a.
multiple correlation): a correlation of multiple predictors with a
single output variable 
Multivariate analyses 
multivariate
analyses:
analyses that deal with more than one dependent variable at a time 
Modeling Methods 
path models:
use of correlational tools to interpret relationships to identify causal
models with exogenous (input variable) sources, endogenous (mediating)
variables, and dependent (output or criterion) variables 
III. Nonparametric Testing 

A. The Nature of Nonparametric Tests 
nonparametric tests: statistical methods that do not make assumptions about population distributions or population parameters (sometimes called "distributionfree" statistics) 
The Randomization Assumption: 

B. Tests for Nominal Level Dependent Variables 
chisquare test: designed to deal with "count" data; tests that permit examining observed frequencies of events with expected frequencies 
1. The One Sample ChiSquare Test 
one sample chisquare test (a.k.a. the (goodness of fit) "goodness of fit" test): a test of statistical significance for nominal level variables for which frequency data are obtained chisquare (c^{2}) distribution: a probability distribution of squared differences of scores. equal probability hypothesis: a method of determining expected frequencies for the onesample chisquare test assuming an equal proportion of events in each category 
2. The ChiSquare Test of Independence 
Chisquare test of independence: and adaptation of chisquare to the analysis of contingency tables 

factor
analysis: a statistical method that 
3. Determining Effect Sizes 
contingency coefficient: a method to compute effect sizes from the observed chisquare value 