5. Comparing Two or Several Means Flashcards
If you use a paired samples t-test:
- There ought to be less unsystematic variance compared to the independent t-test.
- The same participants take part in both experimental conditions.
- Other things being equal, you do not need as many participants as you would for an independent samples design.
Shape of the t-distribution
- As the degrees of freedom increase, the distribution becomes closer to normal.
- it is symmetrical
- in small samples it is wider than the normal distribution
- It has a similar bell-shape to the normal distribution
Which t-test has more power to find an effect given that everything else is equal?
Repeated measures
vs
indepependent measures
Repeated measures has more power to find an effect
- When the same participants are used across conditions the unsystematic variance (often called the error variance) is reduced dramatically, making it easier to detect any systematic variance
Which statistical test is almost identical to ANOVA
regression
A researcher testing the effects of two treatments for anxiety computed a 95% confidence interval for the difference between the mean of treatment 1 and the mean of treatment 2. If this confidence interval includes the value of zero, then she she cannot conclude that there is a significant difference in the treatment means: true or false
True
- If the confidence interval contains zero, it means that the difference between the two population means could be zero (i.e., they are the same). In this situation, we would accept the null hypothesis that there is no difference between the population means
If the F-ratio is large enough to be statistically significant, then we know only that
one or more of the differences between means are statistically significant
When the between-groups variance is a lot larger than the within-groups variance, the F-value is ____ and the likelihood of such a result occurring because of sampling error is _____
large; low
- If the differences between group means are large enough, then the resulting model will be a better fit of the data than the grand mean
Conducting multiple t-tests increases the familywise error rate, so if you are going to do this, it is important to divide the accepted probability level (.05) by
the number of t-tests you conduct
- Alternatively, you could run post hoc tests, which control the familywise error rate
Assumptions of repeated measures t-test
The sampling distribution is normally distributed:
- In the dependent t-test this means that the sampling distribution of the differences between scores should be normal, not the scores themselves.
- Data is measured at least at the interval level
Assumptions of independent measures t-test
The sampling distribution is normally distributed:
- In the dependent t-test this means that the sampling distribution of the differences between scores should be normal, not the scores themselves.
- Data is measured at least at the interval level
The independent t-test, because it is used to test different groups of people, also assumes:
- Variances in these populations are roughly equal (homogeneity of variance).
- Scores in different treatment conditions are independent (because they come from different people).
What does ANOVA tell us?
- It tests for an overall difference between groups - Tests for ANY DIFFERENCE between groups
- It tells us that the group means are different
- It DOES NOT tell us exactly which means differ
Theory of ANOVA:
If the experiment is successful, then the model will explain…
more variance than it can’t
What are the assumptons of ANOVA?
Normal distribution:
- fairly robust for equal sample sizes and larg(ish) N
Homogeneity of variance:
- fairly robust for equal sample sizes
(Between groups design) independence of scores:
- one data point must not influence the other
Two-way ANOVA is basically the same as one-way ANOVA, except that:
The model sum of squares is partitioned into three parts.
- The model sum of squares is partitioned into the effect of each of the independent variables and the effect of how these variables interact
What are the two main reasons for including covariates in ANOVA?
- To reduce within-group error variance
- Elimination of confounds
Conducting an ANCOVA reduces error variance and adjusts the means on the covariate so that the mean covariate score is the same for all groups
If we were to run a four-way between-groups ANOVA, how many sources of variance would there be?
16
- 4 main effects
- 11 interaction effects
- 1 error term
Advantages of an ANCOVA
Reduces Error Variance:
- By explaining some of the unexplained variance (SSR) the error variance in the model can be reduced
Elimination of systematic bias:
- The relationship between questionnaire responses and business performance, controlling for pre-existing differences in business performance.
Greater Experimental Control:
- By controlling known extraneous variables, we gain greater insight into the effect of the predictor variable(s).
What is a factorial ANOVA?
A factorial ANOVA compares means across two or more independent variables
What are the benefits of a factorial design?
We can look at how variables Interact:
- Interactions show how the effects of one IV might depend on the effects of another
- Interactions are often more interesting than main effects
The assumption of homogeneity of variance is not relevant when conducting a _______ ANOVA
repeated-measures
- The assumption of homogeneity of variance (the assumption that the variances between groups are roughly equal) is relevant for between-groups ANOVA and not for repeated-measures ANOVA
Sphericity is met when
Sphericity is the condition where the variances of the differences between all combinations of related groups (levels) are equal.
Violation of sphericity is when the variances of the differences between all combinations of related groups are not equal.
One advantage of repeated measures designs over independent designs is that we are able to calculate a degree of error for each effect, whereas in an independent design we are able to calculate only one degree of error: true or false?
True
Advantages of repeated measures ANOVA/design
Sensitivity:
- Unsystematic variance is reduced
- More sensitive to experimental effects
Economy:
- Less participants are needed
Disadvantages of repeated measures ANOVA/design
- Fatigue
- Carryover (order) fx
- practice fx
solution = counterbalancing
What are the assumptions of a mixed ANOVA
- Homogeneity of variance for independent or between group ANOVA
- Sphericity for repeated of within group ANOVA
