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

Chapter 14

Inferential Statistics II:

Beyond Two Means

I.  Selecting an Appropriate
    Statistical Test
II.  Comparisons of More
     Than Two Means:
     Analysis of Variance
     A. Oneway Analysis of
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
          1. Multiple
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
--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
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
      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
          2.  Examining
               Effect Patterns
      --A Guide to Advanced
        Statistical Methods
grand mean: the average of the means in a study
         Multiple regression
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
--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: 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
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: statistical methods that do not make assumptions about population distributions or population parameters (sometimes called "distribution-free" statistics)
            --The Randomization
one assumption made for nonparametric tests: randomization
      B.  Tests for Nominal
            Level Dependent
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
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