docs/FactorialVignette.md

In cwendorf/easiOrigin: easiOrigin

Factorial Vignette

This vignette analyzes data from a two-factor between-subjects design.

• Data Management
• Data Entry
• Descriptive Statistics
• Analyses of the Means
• Confidence Intervals
• Significance Tests
• Analyses of the Effects
• Source Table
• Significance Test
• Effect Size

Data Management

Data Entry

FactorA <- c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2)
FactorB <- c(1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2)
Outcome <- c(0,0,3,5,4,7,4,9,9,6,4,9,3,6,8,3)
FactorA <- factor(FactorA,levels=c(1,2),labels=c("A1","A2"))
FactorB <- factor(FactorB,levels=c(1,2),labels=c("B1","B2"))
FactorialData <- data.frame(FactorA,FactorB,Outcome)
FactorialData

##    FactorA FactorB Outcome
## 1       A1      B1       0
## 2       A1      B1       0
## 3       A1      B1       3
## 4       A1      B1       5
## 5       A1      B2       4
## 6       A1      B2       7
## 7       A1      B2       4
## 8       A1      B2       9
## 9       A2      B1       9
## 10      A2      B1       6
## 11      A2      B1       4
## 12      A2      B1       9
## 13      A2      B2       3
## 14      A2      B2       6
## 15      A2      B2       8
## 16      A2      B2       3

Descriptive Statistics

descMeansBy(Outcome~FactorA,by=FactorB)

## $`Descriptive Statistics for the Data: B1`
##          N       M      SD
## A1   4.000   2.000   2.449
## A2   4.000   7.000   2.449
## 
## $`Descriptive Statistics for the Data: B2`
##          N       M      SD
## A1   4.000   6.000   2.449
## A2   4.000   5.000   2.449

Analyses of the Means

Confidence Intervals

ciMeansBy(Outcome~FactorA,by=FactorB)

## $`Confidence Intervals for the Means: B1`
##          M      SE      df      LL      UL
## A1   2.000   1.225   6.000  -0.997   4.997
## A2   7.000   1.225   6.000   4.003   9.997
## 
## $`Confidence Intervals for the Means: B2`
##          M      SE      df      LL      UL
## A1   6.000   1.225   6.000   3.003   8.997
## A2   5.000   1.225   6.000   2.003   7.997

ciMeansBy(Outcome~FactorA,by=FactorB,conf.level=.99)

## $`Confidence Intervals for the Means: B1`
##          M      SE      df      LL      UL
## A1   2.000   1.225   6.000  -2.541   6.541
## A2   7.000   1.225   6.000   2.459  11.541
## 
## $`Confidence Intervals for the Means: B2`
##          M      SE      df      LL      UL
## A1   6.000   1.225   6.000   1.459  10.541
## A2   5.000   1.225   6.000   0.459   9.541

Significance Tests

nhstMeansBy(Outcome~FactorA,by=FactorB)

## $`Hypothesis Tests for the Means: B1`
##       Diff      SE       t      df       p
## A1   2.000   1.225   1.633   6.000   0.154
## A2   7.000   1.225   5.715   6.000   0.001
## 
## $`Hypothesis Tests for the Means: B2`
##       Diff      SE       t      df       p
## A1   6.000   1.225   4.899   6.000   0.003
## A2   5.000   1.225   4.082   6.000   0.006

nhstMeansBy(Outcome~FactorA,by=FactorB,mu=5)

## $`Hypothesis Tests for the Means: B1`
##       Diff      SE       t      df       p
## A1  -3.000   1.225  -2.449   6.000   0.050
## A2   2.000   1.225   1.633   6.000   0.154
## 
## $`Hypothesis Tests for the Means: B2`
##       Diff      SE       t      df       p
## A1   1.000   1.225   0.816   6.000   0.445
## A2   0.000   1.225   0.000   6.000   1.000

Analyses of the Effects

Source Table

descMultifactor(Outcome~FactorA,by=FactorB)

## $`Source Table for the Effects: Between Subjects`
##                      SS      df      MS
## FactorA           4.000   1.000   4.000
## FactorB          16.000   1.000  16.000
## FactorA:FactorB  36.000   1.000  36.000
## Residuals        72.000  12.000   6.000

Significance Test

nhstMultifactor(Outcome~FactorA,by=FactorB)

## $`Hypothesis Tests for the Effects: Between Subjects`
##                       F      df       p
## FactorA           0.667   1.000   0.430
## FactorB           2.667   1.000   0.128
## FactorA:FactorB   6.000   1.000   0.031
## Residuals            NA  12.000      NA

Effect Size

pvaMultifactor(Outcome~FactorA,by=FactorB)

## $`Proportion of Variance Accounted for by the Effects: Between Subjects`
##                   EtaSq ParEtaSq
## FactorA           0.031    0.053
## FactorB           0.125    0.182
## FactorA:FactorB   0.281    0.333
## Residuals         0.563       NA

cwendorf/easiOrigin documentation built on Nov. 1, 2023, 10:57 a.m.