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A Brief Quiz
Inferential Statistics II
Determining if Variances are Equal
ANOVA with SPSS
ANOVA with Excel

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 sp2): 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