Chapter 11.6-11.13

Symbol + Formula

100

This symbol represents the number of participants in each group or condition

n 

(small n)

200

This symbol represents the # of groups

And is this is your level or factor?

k!

Levels!

300

This symbol means the total of all scores in the study.

∑X_T

400

This symbol means the total score for one person across all conditions.

∑P

500

This symbol means all the scores are squared and then added together.

∑X²

Degrees of Freedom

100

In a one-way within-subjects ANOVA, the degrees of freedom between groups is found with this formula-->

df_{BG -->}

k−1

200

This formula gives the degrees of freedom between persons.

df_{BP -->}

n-1

300

df_E=

(k−1)(n−1)

400

df_Total=

(k)(n)−1

Also accepting: Adding dfBG, dfBP, dfe together

500

In a one-way within-subjects ANOVA, there are 6 treatment conditions and 9 participants in each.

What are the degrees of freedom for between groups, between persons, error, and total?

df_BG --> 5

df_BP --> 8

df_{E -->} 40

df_{Total -->} 53

// k = 6 // n = 9 //

df_BG=6−1=5

df_BP=9−1=8

df_{E -->} (6−1)(9−1)=5⋅8=40

df_Total = (6⋅9) - 1 = 53

Hypothesis + SS

100

Null Hypothosis for One-Way Within Subjects Anova:

σ²_μ = 0

[“population means do not vary” = which tells us the variance among the means is 0]

200

Alternative hypothesis -->

H1:σ²_μ > 0

[“population means vary” = which tells us the variance among the means is greater then 0]

300

In ANOVA, this effect size tells you the proportion of total variance explained by the treatment. 

Eta-quared

η²

400

For ANOVA, eta squared is computed with this formula:

What are the cut offs for small, medium, and large eta-squared? (EXTRA 400)

η²=SS_between/SS_total

• small = .01
• medium = .06
• large = .14

500

If an ANOVA has

 SS_between=18

SS_total=60

what is Eta-Squared? And what does that number look like in APA format (extra 500!)

0.30

The treatment effect was large, η² = .30.

F-Obt /MS

100

Reject H₀ — when Fobt ? Fcrit

≥

200

F_obt= 

[looking for the F-ratio formula]

MS_BG

_{______}

MS_E

300

MS_{E =}

SS_E

____

df_E

400

MS_BP =

SS_BP

_______

df_BP

500

MS_BG

SS_BG

_{________}

df_BG

BP + WG

100

WG means -

BP means - 

 within groups 

(variation inside the conditions rather than between conditions)

between persons 

(how people differ from each other overall)

200

A student who tends to get high testing scores in every condition, and another who tends to get low scores in every condition, create ____-____ _____. 

between-persons variation

300

In a repeated-measures ANOVA, this within-groups variation gets split into parts:

What are those (2) parts?

• between persons (_BP)
• error (_E)

400

SS_WG=

SS_BP + SS_E

500

This source of variation reflects consistent participant-to-participant differences across all treatment conditions and is removed from within-groups variation to isolate error.

SS_BP