Psycstat #3

Repeated-Measures Designs

Evaluates mean diff between two measurements from one sample

• AKA within-subject, related-samples, or dependent-samples dependent

• calculations done with sample of difference scores

Advantage of Repeated-Measures Designs

• fewer participants than independent measures design

• can see changes over time 

  • ex: learning or development 

disadvantages of repeated-measures designs

• testing effects

• floor & ceiling effects

testing effects

exposure to first condition may influence scores in second condition

• ex: practice on an IQ test in first condition may cause improved performance in second condition

floor effects

when individual’s score is so low in condition 1, they have nowhere to go but in condition 2

ceiling effects

when individual has such as high score in condition 1

repeated measures t-test Null Hypothesis

H₀: μ_D = 0

• two tailed 

• no consistent or systematic diff between two conditions

repeated measures t-test Alt. Hypothesis

H1: μD ≠ 0

• systematic diff. between conditions produces a non-zero mean diff.

differences scores (D)

D = X₂ -X₁

finding critical value using df

df = n - 1

calculating repeated-measures t-stat

hypothesis tests for repeated-measures design

cohen’s d

standardized mean diff. between treatments

r² 

percentage of variance accounted for 

effect of variance on measures of effect size (cohen’s d & r²)

• larger variance → smaller cohen’s d & r²

• sample size → no effect on cohen’s d & small influence on r²

SPSS output for repeated measures t-test

• sig. (p-val) < .05 , reject null hyp.

Repeated Measures vs. Independent Measures

repeated measures - one sample w/ same individuals in both treatments, fewer subjects, eliminates individual diff., higher liklihood of detecting real treatment effect

independent measures design - two separate samples (one in each treatment), more subjects, every score represents diff person

ANOVA

hypothesis testing procedure used to evaluate mean diff. between two or more populations

strength of ANOVA over multiple t-tests

• tests for 2+ groups at once

• avoids Type I error inflation (multiple t-tests)

F-ratio logic

F-ratio: ratio of sample’s systematic variance to its random variance

MS_between

• mean differences between samples (treatment effects)

• (Signal/Systematic variability)

• from effects of IV and/or chance/sampling error

• ex: diff mean levels

MS_within

• diff expected by chance (w/o treatment effects_

• (Noise/Random variability)

• from random chance or sampling

• ex: variability for people who got 5 hours of tutoring 

null hypothesis for one way ANOVA

H₀: μ1 = μ2 = μ3

• all groups are equal

• no diff between levels (AKA groups)

• F-ratio ~ 1.00

  • no significant effect of IV

alt. hypothesis for one-way ANOVA

H1: μ1 ≠ μ2

• at least one diff mean

• large F-ratio

  • reject null & conclude significance

all hypothesis in ANOVA are

non-directional

• can never have negative F

Critical region (One-Way ANOVA)

• df_between = k - 1

  • columns

• df_within = N - K

  • rows

F-ratio (One-way ANOVA)

SS_total

provided

G

grand mean

SS_within

ΣSS inside each condition

SS_between

SS_total - SS_within

SPSS output for ANOVA

if sig <.05 , proceed to hoc tests

making a decision for One-Way ANOVA

compare F-value to critical value, if F more extreme → reject H₀

ANOVA simply states that

a difference exists

• doesn’t indicate which levels are different

post-hoc tests

determine exactly which groups are diff. & which aren’t

• after ANOVA where H₀ rejected 

• compares treatments, two at a time, to test mean diff. while correcting for concerns about experiment-wise Type I error inflation

effect size

η² (eta squared)

two-factor ANOVA

examines effects of 2+ IV or quasi-IV on dependent variable

• separate Hyp tests for same data

• seperate F-ratios

main effect

mean diff. among levels of a factor

• ex: flashcards & age - Main effect of B: Do young students perform better than older students regardless of method?

interaction

“extra” mean diff. not explained by main effects

• occurs when mean diff. between cells (individual treatment) are diff. from predicted from overall main effects of factor

• non-parallel lines on graph 

• Combined impact of A and B

• ex: Does method effectiveness change by age group?

null hypothesis Two Factor ANOVA

h₀: no interaction between factors A & B.

• mean diff between treatment conditions explained by main effects of two factors

structure of two-factor ANOVA

alt. hypothesis Two-factor ANOVA

h₁: interaction between factors

• mean diff. between treatment conditions not predicted from overall main effects of two factors

SS_total

Σ(X - G)²

• will be provided

SS_within

ΣSS inside each condition (AKA cell)

SS_between

SS_total - SS_within

SS_A

SS_B

SS_AxB

SS_Between - SS_A - SS_B

• extent to which cells are diff. from total/grand

• higher if main effects don’t explain/predict cell means 

F-ratio (Two-Factor ANOVA)

Significant interaction (Two-Factor ANOVA)

main effect becomes meaningless

Non significant interaction (Two-Factor ANOVA)

interpret main effects as normally

Simple Main effects

impact of one factor on dependent variable at specific level of other factor

• specifics of interactions

• description - both of the IVs and DV

Reporting results of Two-Factor ANOVA (each test include)

F (df, p-value)

• F greater than critical value → p < alpha value (a = .05) → effect is significant (reject null hyp.)

interpreting results of two-factor ANOVA

• main effects of factor A & factor B & sig

  • significant if F > crit. val

• A x B interaction

  • significant if F > crit. val

• do indepdent effects (main effects) explain data → NO if sig.