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 

A. Oneway Analysis of Variance 
oneway analysis of variance: a statistical tool that
permits comparison of several means for one independent variable pooled variance (abbreviated s_{p}^{2}): the average of the variances within groups 
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 Tukey's HSD (abbreviation for John Tukey's Honestly Significant Difference test) used to make all possible comparisons when means are taken two at a time (the most powerful multiple comparison test for making pairwise comparisons) Scheffe's critical S: used to make complex comparisons of means 
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 
3.
Looking for Nonlinear Relationships 
trend analysis: a method to isolate the nature of
linear and nonlinear trends in effects identified as significant by analysis of variance mean square: a synonym for the variance as computed in analysis of variance (shorthand for "the mean of the squared differences of scores from their mean") 
Interval Estimation Methods: use of a range of values that capture population parameters; permits identification of differences among groups by looking for means that are outside the confidence interval around another mean 

C. Factorial Analysis of Variance 
variable factor: a variable broken down into levels or
groups factorial analysis of variance: a test of statistical significance that identifies main and interaction effects between independent variables main effects: dependent variable effects from independent variables separately interaction effects: dependent variable effects from independent variables taken together 
1.
Computing Factorial ANOVA 2. Examining Effect Patterns A Guide to Advanced Statistical Methods 
grand mean: the average of the means in a study 
Multiple
regression correlation 
multiple regression correlation (a.k.a. multiple
correlation): a correlation of multiple predictors with a single output variable beta weights: measures of the contribution made by each predictor to the overall correlation multicollinearity: the requirement that predictors be uncorrelated multiple discriminant analysis: a method to predict membership in particular groups from a knowledge of a number of predictor variables (measured on interval or ratio levels) loglinear analysis: extension of chi square testing for analysis of more than two variables measured on the nominal level 
Multivariate analyses 
multivariate analyses: analyses that deal with more
than one dependent variable at a time canonical correlation: an extension of multiple regression, correlating two sets of variables redundancy index: tells whether sets of variables should be interpreted differentially for additional canonical component roots MANOVA (Multivariate Analysis of Variance): extension of analysis of variance for multiple dependent variables test of sphericity: a measure of variation indicating the interrelationship of dependent variables multivariate multiple correlation: extension of multiple regression for many interrelated dependent measures multivariate analysis of covariance: extension of MANOVA to adapt analysis of covariance for multiple interrelated dependent variables Hotelling's T^{2}: t test for intercorrelated dependent variables 
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 LISREL (Linear Structural Relations): a computer program to isolate relationships by examining covariances among 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 
one assumption made for nonparametric tests: randomization 
B. Tests for Nominal Level Dependent Variables 
chi square test: designed to deal with "count" data 
1. The One Sample Chi Square Test 
one sample chi square test (a.k.a. the (goodness of
fit) "goodness of fit" test): a chi square test that allows a researcher to take
a single independent variable that is broken down into nominal categories and identify
whether the arrangement among the categories is greater than would have been expected by
chance equal probability hypothesis: a method to determine expected frequencies by presuming that the frequencies in each category are equal 
2. The Chi Square Test of Independence 
chi square test of independence: use of chi square to determine relationships between two or more variables; null hypothesis states that classification variables are independent of (unrelated to) each other 
factor analysis: a statistical method that helps the researcher discover and identify the unities or dimensions, called factors, behind many measures 

3. Determining Effect Sizes 
contingency coefficient: a method to compute effect sizes from the observed chi square value 