PS395 - Analysis of Variance Midterm

Content: Paired t-test, RM one-way ANOVA

Paired t-test

A parametric statistical test that uses the t-distribution to explore differences in mean dependent variable scores across two within-group conditions across a single group.

other names: related, dependent

• continuous IV with 2 categorical levels — “type of IV/condition/level”

• continuous DV — “amount of DV reported”

benefits: reduces unsystematic variance compared to an independent t-test

• participants are their own control — there is no unsystematic variance across conditions, therefore reduced error (i.e., we need fewer people to detect an effect)

H₀: no difference; average pairwise difference = 0

H_A: difference; average pairwise difference ≠ 0

assumptions:

• DV is continuous

• paired observations (2 measurements per subject)

• differences between pairs are normally distributed

parameters:

• t= statistic

• Dbar= average pairwise difference/mean difference

• sd= standard deviation

• N=number of participants

SPSS: analyze — compare means — paired sample t-test

Within-subjects Design

The same participants are exposed to all levels of the IV — measurements of the DV are being measured twice, but within each subject

other names: repeated measures design

conceptual formula: (observed pairwise difference)/(estimate of SE of the pairwise difference)

• requires less participants, may introduce order effects (e.g., practice, fatigue)

• reduces individual differences

Between-groups Design

Compares different groups of participants, where each group experiences only one level of the independent variable (IV)

other names: independent measures design

• requires more participants

• eliminates carryover effects — influences from previous conditions

Power

The probability of detecting a real effect, if there is a real effect

Repeated Measures One-way ANOVA

A parametric statistical test that examines variance in a single dependent variable, in respect of one within-group independent variable.

• tests whether three or more related groups have significantly different means

• used when we have the sam subjects being measured under 3+ conditions (e.g., drug dosage levels)

• used when we want to repeat measurements over time (e.g., pre-test, mid-test, post-test)

assumptions:

• DV is continuous

• repeated measurements on the same subjects

• sphericity

• each group’s differences should be normally distributed

Sphericity

A term usually applied to within-group studies to measure equality of variance across pairs of conditions.

• tested using Mauchly’s test

Mauchly’s Test

A statistical measure that examines sphericity of within-group variance across pairs of conditions in repeated-measures ANOVA — the assumption of equal variances is violated if the outcome (Mauchly’s W) is significant; if it is violated, an adjustment is needed (use Greenhouse-Geisser)

F = (variance between conditions, effect)/(variance within subjects, error)

SPSS: analyze — general linear model — repeated measures