Chaptr14

*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_p²): 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) log-linear 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 T²: 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 "distribution-free" 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