Docstoc

tTests and ANOVAs

Document Sample
tTests and ANOVAs Powered By Docstoc
					                         Overview        of
            t-Tests,        ANOVAs,       &   ANCOVAs

t-Test
     The most basic statistical test that measures group differences
is the t test, which analyzes significant differences between two
group means. Consequently, a t test is appropriate when the IV is
defined as having two categories and the DV is quantitative, (e.g.,
What is the difference between males and females [IV] with respect to
SAT scores [DV]? Is this difference statistically significant?). There
are two variations of t-tests: an independent-samples t-test and a
repeated-measures t-test.
     When to use a t test?
            1 IV (2 categories)             Group differences
            1 DV (quantitative)

One-Way Analysis of Variance
     One-way analysis of variance (ANOVA) tests the significance of
group differences between two or more means as it analyzes variation
between and within each group. ANOVA is appropriate when the IV is
defined as having three or more categories and the DV is quantitative,
(e.g., Do preschoolers of low, middle, and high socio-economic status
[IV] have different literacy test scores [DV]? If so, which groups are
significantly different?). Since ANOVA only determines the
significance of group differences and does not identify which groups
are significantly different, post hoc tests are usually conducted in
conjunction with ANOVA.
     When to use a one-way ANOVA?
            1 IV (2+ categories)                 Group differences
            1 DV (quantitative)

One-Way Analysis of Covariance
     One-way analysis of covariance (ANCOVA) is similar to ANOVA in
that two or more groups are being compared on the mean of some DV, but
ANCOVA additionally controls for a variable (covariate) that may
influence the DV (e.g., Do preschoolers of low, middle, and high
socio-economic status [IV] have different literacy test scores [DV]
after adjusting for family type [covariate]?) Many times the
covariate may be pretreatment differences, in which groups are equated
in terms of the covariate(s). In general, ANCOVA is appropriate when
the IV is defined as having two or more categories, the DV is
quantitative, and the effects of one or more covariates needs to be
removed.
     When to use a one-way ANCOVA?
            1 IV (2+ categories)                 Group differences
            1 DV (quantitative)
            1+ covariate


Source:

Mertler, C. A., & Vannatta, R. A. (2005). Advanced and
    multivariate statistical methods: Practical application and
    interpretation (3rd ed.). Los Angeles, CA: Pyrczak.

t-Test
I.       Research Questions…
        Generically-Stated Research Questions:
             Independent-samples: What is the difference between Group 1
              and Group 2 on Variable A? Is this difference statistically
              significant?
             Repeated-measures: What is the difference between Measure 1
              (i.e., Var. 1) and Measure 2 (i.e., Var. 2) for this sample?
              Is this difference statistically significant?
        Examples of Appropriately-Stated Research Questions:
             What is the difference between males and females with respect
              to SAT scores? Is this difference statistically significant?
             What is the difference between pretest and posttest scores for
              high school sophomores following an OGT prep course? Is this
              difference statistically significant? [ALT: How effective is
              an OGT prep course for high school sophomores?]
        Examples of Inappropriately-Stated Research Questions:
             What is the relationship between gender and SAT scores?
             Is there a difference between pretest and posttest scores for
              high school sophomores following an OGT prep course?
II.      Sampling & Data…
        Samples should always be selected randomly (probability samples)
             Allows for generalization of results to larger population,
              especially using any inferential statistical test
        Data must be quantitative
             Scale of measurement (i.e., nominal, ordinal, interval, ratio)
              – grouping variable is nominal (categorical); actual measures
              must be interval or ratio
III.         Data Analysis & Interpretation…
        Analysis involves the calculation and interpretation of a t-
         statistic (& its associated statistical significance)
        Sample output from SPSS…
                                                           Descriptive
                                                           statistics
                                                           for the two
                                                             groups




                                                                         Tests Ho that
                                                                              the
                                                                         variances of
                                                                             the 2
                                                                          populations
                                                                           are equal




                    t-statistic &
                    significance
                     (p-value);
                   if < .05, then
                     difference
                  between 2 groups
                   is significant
One-Way Analysis of              Variance
I. Research Questions…
      Generically-Stated Research Question:
           What is the difference between Groups 1, 2, & 3 on Variable A?
            Which, if any, groups are significantly different?
      Examples of Appropriately-Stated Research Questions:
           Do preschoolers of low, middle, and high socio-economic status
            have different literacy test scores? If so, which groups are
            significantly different?
           How do teachers’ assessment practices differ based on school
            district rating? Which of these differences, if any, are
            statistically significant?
      Examples of Inappropriately-Stated Research Questions:
           Similar to those for t-test…
II.    Sampling & Data…
      Samples should always be selected randomly (probability samples)
           Allows for generalization of results to larger population,
            especially using any inferential statistical test
      Data must be quantitative
           Scale of measurement (i.e., nominal, ordinal, interval, ratio)
            – grouping variable is nominal (categorical); actual measures
            must be interval or ratio
III.       Data Analysis & Interpretation…
      Analysis involves the calculation and interpretation of an F-
       statistic or F-ratio (& its associated significance)
      Sample output from SPSS…
                                                                      Descriptive
                                                                      statistics
                                                                     for the five
                                                                        groups




                                                          Value of
                                                           F-ratio




                                                             P-value; p <
                                                            .05, so there
                                                                 are
                                                             significant
                                                            differences…bu
                                                              t where???

                                                              Also, note
                                                              about the
                                                            value of .000!
                                                                These are
                                                                 pairwise
                                                               comparisons;
                                                                every pair
                                                             appears twice in
                                                                the table




                                                         Any value < .05
                                                           indicates a
                                                           significant
                                                       difference between
                                                       these 2 particular
                                                             groups


One-Way Analysis of              Covariance
I. Research Questions…
      Generically-Stated Research Question:
           What are the differences between Groups 1, 2, & 3 on Variable
            A, after controlling for the effects of Variable B? Which, if
            any, groups are significantly different?
      Examples of Appropriately-Stated Research Questions:
           Do preschoolers of low, middle, and high socio-economic status
            have different literacy test scores after adjusting for family
            type?
           How do teachers’ assessment practices differ based on school
            district rating, controlling for years of teaching experience?
            Which of these differences, if any, are statistically
            significant?
      Examples of Inappropriately-Stated Research Questions:
           Similar to those for t-test…
II.    Sampling & Data…
      Samples should always be selected randomly (probability samples)
           Allows for generalization of results to larger population,
            especially using any inferential statistical test
      Data must be quantitative
           Scale of measurement (i.e., nominal, ordinal, interval, ratio)
            – grouping variable is nominal (categorical); actual measures
            must be interval or ratio (including covariate)
III.       Data Analysis & Interpretation…
      Analysis involves the calculation and interpretation of an F-
       statistic or F-ratio (& its associated significance)
   Sample output from SPSS…




                               Significance
     “District                      of
     Rating” is                 covariate &
       the DV                    of group
                                differences
                                  (after
                                controlling
     “Years of                    for the
     Experience                 covariate)
      ” is the
     covariate

				
DOCUMENT INFO