chapter 12 Flashcards
(15 cards)
problem with multiple tests
When an experiment has more than two conditions, it is no longer appropriate to use a t-test to analyze the differences between condition means
When one t-test is conducted, the probability of making a Type I error is only 5%. However, when several t-tests are conducted, the overall probability of making a Type I is much higher.
preventing type I error
Bonferroni adjustment
Bonferroni adjustment
divide the desired alpha-level (0.05) by the number of statistical tests that will be conducted
- The overall likelihood of making a Type I error across all tests is 0.05.
- However, by decreasing the alpha-level for each particular test, the probability of making a Type II error increases
- Aka fishing (for a significant finding)
ANOVA
analysis of variance
used to analyze data from designs that involve more than two conditions and, thus, more than two means
- Analyzes the differences between all condition means simultaneously
- Holds the alpha level at 0.05 regardless of the number of means being tested
- “Is there variation between these groups” – using anova
f-test
ANOVA uses this statistic
the ratio of the variance among conditions (between groups) to the variance within conditions (within groups)
F = (MS between group) / (MS within group)
- The larger this ratio, the larger the calculated value of F, and the less likely that the differences among the means are due to error variance
- Compare this calculated value of F to the critical value of F based on the alpha-level and the degrees of freedom
- If the calculated value of F exceeds the critical value of F, then we conclude that at least one of the means differs significantly from the others
Total Sums of Squares
ANOVA partitions the total sum of squares (i.e., the total variability) into two parts:
- Sums of squares between-groups is systematic variance that reflects differences between the experimental groups
- Sums of squares within-group is error variance
Factorial Designs
Sums of squares between-groups (SSbg) can be broken down to test for each main effects and interactions
In a two-way factorial (A x B), the total variance is composed of four parts:
- Main effect of A
- Main effect of B
- A x B interaction
- Error variance
Follow-Up Tests
If an F-test is significant, we know that at least one group means differences from another
- However we do not know which means differ
Follow-up tests are needed to determine which means differs
Follow-Up to a Main Effect
Post hoc tests or multiple comparisons
If the F-test is not significant, follow-up tests are not conducted because the independent variable has no effect
Post hoc tests or multiple comparisons
(only if you have two categories in IV) are used to determine which means differ significantly:
- Least significant differences (LSD) test
- Tukey’s test
- Scheffe’s test
- Newman-Keuls test
Follow-Up Tests to ANOVA
Main effect for IV with two levels
- Multiple comparisons (just compare the means, similar to t-tests)
Main effects for independent variables with more than two levels
- Commonly used post hoc tests
- Use of post hoc tests
Interactions
- Testing simple main effects
Follow-up to an interaction
If the F-test shows that an interaction effect is significant, tests of simple main effects are conducted
- Shows us precisely which condition means within the interaction differ from each other
Simple main effect
simple main effects
an effect of one independent variable at a particular level of another independent variable
For a two-way interaction of AxB:
Simple main effect of A at B1
Simple main effect of A at B2
Simple main effect of B at A1
Simple main effect of B at A2
Analyses of Within-Subjects Designs
Paired t-test
Within-subjects ANOVA
Error variance in within-subject designs
Power in within-subjects designs
Multivariate Analysis of Variance
Conceptually Related Dependent Variables
- How is MANOVA useful when the researcher has several dependent variables?
Inflation of Type I Error
- How is MANOVA useful when the researcher wants to reduce the probability of Type I error?
How MANOVA works
- Canonical variate
- Multivariate version of the F-test
