Psych Stats Exam 3

The Correlational Method

Two or more variables are systematically measured and the relationship between them is systematically assessed.

• Mask wearing = Predictor Variable

• COVID = Dependent Variable

Correlations

• Positive Correlation

• Negative Correlation

• Zero Correlation

3 Types of Dependent-Sample Designs

• Repeated Measures Design

• Matched-Subjects Design

• Matched-Pairs Investigations

Repeated Measures Design

A study which observations are measured on the same subject under two (or more) conditions

• Ex) Measure symptoms of schizophrenia before and after treatment

Matched-Subjects Design

A study in which subjects from two (or more) samples are paired by the experimenter on a variable

• Ex) First pair of subjects may weight 180 and the next pair may weight 160

Matched-Pairs Investigations

A study in which subjects from two groups are naturally paired

• Ex) Natural pairings like twins

Standard Error of the Difference between Two Dependent Means

O & P are known (population and covariance)

Estimated Standard Error of the Difference between Two Dependent Means

O & P are unknown (population and covariance)

Degrees of Freedom for two related (Dependent) groups

Only use n for 1 group (n-1)

Order Effects

Exposure to treatment condition assigned first, changes performance on the treatment condition assigned second

• Ex) Have 2 depression treatments. The first treatment will probably have an effect on the second

Regression Effects

When subjects are selected because of their extreme scores on some measure, measurement on the same variable yields scores closer to the mean

• Ex) only selected extremely depressed people during pre-measure

Effects of Dependent measures

• Error - decrease

• Power - increases

• Homogeneity of variance- the assumption is not necessary for two dependent means

Analysis of Variance (ANOVA)

A statistical procedure used to compare simultaneously the means of two or more samples, populations, or groups

One-Way Anova

An analysis of variance study with only one independent variable’ a single factor design

• May be two or more treatment conditions

Treatment Conditions

Different values or level of the independent variable

• Symbolized by “K”

H0 is often called the…

Omnibus Hypothesis

Within-groups Variation

Variation of scores around the mean in a single treatment condition "(“error”)

• Variation is due to chance only

• (Error variance) does not depend on whether H0 is true

Between-groups Variation

Variation among the means of the different treatment conditions

• Variation is due to chance and the treatment effect (Independent variable)

• It does depend on whether H0 is true

Partition of the Sum of Squares

When comparing 2 or more populations, the mean of all scores is called the grand mean.

• Signified by 2 bar X

• From the total sample, we obtain 3 different (SS) Total, Within, and Between

Within-Groups Variance Estimate

An estimate of inherent variance only

• Symbolized as S²w

• estimates o² (the inherent variance, also called error variance)

Between-Groups Variance Estimate

An estimate of inherent variance plus the treatment effect

• Symbolized as S²bet

• Estimated O² plus the treatment effect

F ratio

• H0 is true F should be close to 1

• H0 is false F must be > 1

• F distribution family of curves depending on degrees of freedom

Characteristics of the F distribution

• Positively Skewed

• If the numerator is larger than the denominator, the F ratio may be much larger than 1

• If S²bet is smaller than S²w then F will be less than 1, but not less than zero

• The F test is still not directional

Assumptions of ANOVA

Same as Independent Samples t-test

• Populations are normally distributed

• Homogeneity of population variances

• Independent sampling (scores in each group are independent of scores in other groups)

• Random sampling with replacement

Proportion of Variance accounted for (R²)

Proportion of the total variance of scores from the grand mean that is accounted for by the variation between the means of the groups

• also known at n² or “eta squared”

Effect size

Conventions/Rule of thumb

.01 = small

.06 = medium

.14 = large

Planned Comparisons

Statistical tests performed after obtaining a value of F that indicate which means are significantly different

• More rigorous

Factorial Research Design

A way of organizing a study in which the effects of 2 or more IVs are examined by making groupings of each combination of the IVs

Two-way ANOVA

4 sources of variation

• Main effect of A

• Main effect of B

• Interaction of A & B

• Error

Interaction effect

The difference in the effect of one factor across levels of the other factor

Main effects

Compare row mean or column means

• means of one factor collapsing across levels of the other factor

• mean of row or column cell means if equal n

Orthogonal

Two main effects (independent, uncorrelated) sources of variance

• can tell by multiplying contrast weights and adding

• If they sum to zero, contrasts are orthogonal

Interaction

Is a lack of parallelism in graph of means

Independent Variable

Variable that is changes or manipulated

Test (Interactions)

One or more independent variables might influence the strength or direction of other independent variables