Summary comments on the nature of ANALYSIS OF
- The technique tests for significant differences
between the means of k groups based on two
different estimates of population VARIANCE.
- One estimate is based on the variance
within each of k samples.
- The other is based on the variance between
(among) the sample means.
- The F test is simply a ratio between these two
estimate of variance based on BETWEEN mean
estimate of variance based on WITHIN group
- If this ratio is small, then the two estimates tend
to agree, and we conclude that the observed differences
in means reflect differences allowable by drawing random
samples from the same population.
- If the ratio is "large," however, we conclude
that the differences among our groups do not simply
reflect random error in sampling.
Interpretation of the F ratio:
- An F ratio less than 1 is never signficant for
rejecting the null hypothesis.
- That would show more variation within groups
than between groups, and thus the groups would
explain no variation at all in X.
- Ratios larger than 1 may be significant:
one must find out by checking the table of the F
distribution corresponding to the chosen alpha
- Degrees of freedom (df) for the "between"
estimate (the larger) run along the top of the F
- df for the "within" estimate run down the
- An observed value larger than the one in the table
means the difference is significant at that alpha
- Relationship of F to t:
- Conceptually: F is a generalization of
T-test for two groups
- When there are two groups (and thus df BSS =
- t = square root of F (or t2 =
Analysis of variance with SPSS:
- SPSS Programs for analysis of variance
- Under the Analyze Menu, choose Compare
- Then select One-Way ANOVA
- Press the "Options" button and check
"Descriptive" and "Means plot"
- Transfer your dependent variable
into the "Dependent List"
- Transfer your independent
(discrete) variable into the
- One-way analysis of variance programs follow a common
form, reading from right to left:
Analysis of variance in research: a simple
- Lacy, "Political Knowledge of College Activist
Groups: SDS, YAF, and YD"
- Intellectual Problem: previous research has
shown that liberal students were better informed than
- But this research compared activist and
- The conservative activist students need to be
- Existing studies suggest no difference in
intelligence between these two groups
- Lacy's Research Design and Data Analysis
- Studied 15 YAF, 39 SDS, and 33 YD at University of
- Compared them on test of political knowledge
- Analysis of variance for knowledge of American
government showed no significant differences among the