PSY4111 notes

Seite 1

MATCHED-PAIRS DESIGN

Design in which the participants matched for some particularly similarity undergo different treatments

• Find two participants who are as similar as possible [for when it is not appropriate to use the same person twice]

• Each member of the pair is randomly assigned to one of the two different conditions

Two main subtypes:

• Experimental

• Natural

REPEATED MEASURES DESIGN

Within-subject design

•Two basic types: simultaneous and successive

The successive repeated-measures experiment has two major subtypes:

• The before-after design: Usually requires a control group to draw valid conclusions

• The counterbalanced design: Does not always eliminate effects due to the order of conditions

• Repeated-measures should not be used when there are differential carryover effects

Anova

Controls the experimentwise Type I error rate while simultaneously allowing a test of the equality of multiple population means

• Analysis of variance

o One-Way: Only one independent variable

Advantages:

• Allows the experimenter to determine how the dependent variable changes with several different levels of the independent variable (which allows a lawful relationship to emerge if one exists)

• [When the experimenter is unsure of what single level might be effective] using several levels increases the possibility of a positive result occurring from the experiment

BETWEEN-GROUPS VARIATION (SSB)

The influence on variance due to the independent variable or treatment, plus error due to the random process of group assignment

WITHIN-GROUPS VARIATION (SSW)

The influence on variance due to error (chance factors like individual differences), which is presumed to be the same within each group

TOTAL VARIATION (SST)

The total variation in a data set = the within-group variation + between-group variation

F DISTRIBUTION

Is a family of distributions that tend to be positively skewed and to have a mean near 1.0

The exact shape of the F distribution is determined by both the df for the numerator and the df for the denominator

F RATIO

• Follows the F distribution when the null hypothesis (that all means are equal) is true

• Gets larger as the separation of the group means gets larger relative to the variability within groups

MEAN SQUARES

Pooled variance (measure of the average variability)

Computed by dividing each SS estimate (SSW or SSB) by their respective df (N-K or K-1)

Understand why conducting multiple t tests on a set of data with 3 or more groups is not appropriate

• Performing multiple t tests across multiple groups in a single study increases the likelihood of at least one Type I error occurring across the "family" of comparisons

o The chance of making a Type I error increases as more pairs of means are tested

Experimentwise (familywise) Type I error rate = 1- (1-alpha)^c

• c = number of independent t tests to be conducted

WHY?

• Alpha of .05 implies that, by chance, there will be one Type I error in every 20 tests (1/20 = 0.05).

• This means that, by chance the null hypothesis will be incorrectly rejected once in every 20 tests

• As the number of tests increases, the probability of finding a significant result by chance increases

Understand how the one-way ANOVA controls the Type I error probability

• Using the F test allows us to make one overall comparison that tells us whether there is a significant difference between the means of the groups

o It avoids the problem of an increased probability of Type I error that occurs when assessing many t values

• If the significance level is set at alpha, the probability of a Type I error for the ANOVA F-test = alpha regardless of the number of groups being compared

• The ANOVA can find a significant difference among several group means even when no two of the means are significantly different from each other

Understand the assumptions that should be met within the ANOVA and the consequences of violating these assumptions

1. Independent, random samples [in order to be representative of the populations from which they were drawn]

2. The population distributions from which our samples were drawn are normal, which implies that our dependent variable is normally distributed

3. Homogeneity of variance--The variances of our population distributions are equal

4. Generally speaking, the ANOVA is robust to minor violations of the normality and variance assumptions, except for cases in which heterogeneity is coupled with unequal sample sizes

Eta-squared

Measure of association

Approximate percentage of the variance in the DV that can be attributed to the IV

• Comparable to R2 in regression

• Upwardly biased—it overpredicts the population eta-squared

PLANNED COMPARISONS

• Comparisons done a priori/planned in advance

• Do not involve the same risk of a high αEW as post hoc comparisons

•

• Almost always well-grounded in theory and/or previous research

o Planned comparisons = less appropriate when the research is of an exploratory rather than confirmatory nature (just like a one-tailed test)

o Because such comparisons are usually done with a particular theoretical outcome in mind, they are typically not as conservative as post hoc comparisons (greater power)

• ADVANTAGE: You can use a smaller critical value (similar to advantage of using a one-tailed over a two-tailed test)

o Validity depends on a promise that the researcher truly planned the stated comparison and no others

FISHER'S PROTECTED t TEST

• Most liberal (and for that reason the most powerful) way to conduct post hoc comparisons (other than unprotected t tests)

o More powerful because it allows αEW to build up

• Should only be used following a significant F test and for no more than 3 groups

o Fisher's procedure allows a buildup of αEW when there are more than 3 groups and the complete null hypothesis is not true

o With more than 3 groups, more than 1 partial null could be true therefore you have the chance of committing multiple Type I errors

• The one case in which Fisher's procedure gives adequate protection even if the complete null hypothesis is not true is when there are only 3 groups

o Only one possible partial null hypothesis→ two of the population means are equal and one population mean is different

• Protects against Type I error inflation with only 3 groups:

o If the complete null hypothesis is true (H0: μ1 = μ2 = μ3):

• If the overall F is significant, you have already committed a Type I error and any more of them don't contribute further to αEW

• This is the case no matter how many groups are in the experiment

o If the partial null hypothesis is true (H0: μ1 = μ2 ≠ μ3):

• If the overall F is significant, it was not a Type I error

• Only one real chance of a Type I error when the partial null is true

• WHY? Because with only 3 groups there is only one possible partial null hypothesis→ two of the population means are equal and one population mean is different (H0: μ1 = μ2 ≠ μ3)

o Therefore: αEW was never in any danger of being more than .05

• PROBLEM: Fisher's protected t procedure keeps αEW down to .05 (or whatever the alpha level is) only for experiments in which the complete null hypothesis (the null that involves the equality of all the population means represented in the experiment) is true

o If the null is only partially true:

• The protection involved in Fisher's procedure is removed

• Allows the αEW to rise above the value that had been set for the overall ANOVA

• Fisher's protected t tests require:

o Independent random samples

o Homogeneity of variance

o Significant ANOVA

o That no partial null hypotheses are tested (to keep αEW at .05)

LSD

Fisher's LSD (least significant difference) test is a simplified procedure for Fisher's protected t when all the sample sizes equal

• When you are performing protected t tests and all of your samples are the same size, the denominator will be the same for every pair of sample means

o Leads to a shortcut—multiplying the common denominator of all the t tests by the critical value of t for your chosen alpha yields LSD (the least significant difference of sample means)

• Any pair of means whose difference is larger than LSD will differ significantly