docs/BetweenSubjectsVignette.md

In cwendorf/easi-dev: Estimation Approach to Statistical Inference

title: "Estimation Approach to Statistical Inference" author: "Craig A. Wendorf" date: "2020-10-18" output: rmarkdown::html_vignette: keep_md: TRUE vignette: > %\VignetteIndexEntry{Between Subjects Vignette} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8}

Estimation Approach to Statistical Inference

Between Subjects Vignette

Three Group Example Data

Group <- c(rep(1,3),rep(2,3),rep(3,3))
Outcome <- c(3,4,5,7,8,9,8,9,10)
Group <- factor(Group,levels=c(1,2,3),labels=c("Group1","Group2","Group3"))

BetweenData <- data.frame(Group,Outcome)
BetweenData

##    Group Outcome
## 1 Group1       3
## 2 Group1       4
## 3 Group1       5
## 4 Group2       7
## 5 Group2       8
## 6 Group2       9
## 7 Group3       8
## 8 Group3       9
## 9 Group3      10

Analyses of Multiple Groups

Confidence Intervals for the Means

ciMeans(Outcome~Group)

##        N M SD    SE    LL     UL
## Group1 3 4  1 0.577 1.516  6.484
## Group2 3 8  1 0.577 5.516 10.484
## Group3 3 9  1 0.577 6.516 11.484

ciMeans(Outcome~Group,conf.level=.99)

##        N M SD    SE    LL    UL
## Group1 3 4  1 0.577 -1.73  9.73
## Group2 3 8  1 0.577  2.27 13.73
## Group3 3 9  1 0.577  3.27 14.73

Plot of the Confidence Intervals for the Means

cipMeans(Outcome~Group)

cipMeans(Outcome~Group,conf.level=.99,mu=5)

Significance Tests for the Means

nhstMeans(Outcome~Group)

##        Diff    SE      t df     p
## Group1    4 0.577  6.928  2 0.020
## Group2    8 0.577 13.856  2 0.005
## Group3    9 0.577 15.588  2 0.004

nhstMeans(Outcome~Group,mu=5)

##        Diff    SE      t df     p
## Group1   -1 0.577 -1.732  2 0.225
## Group2    3 0.577  5.196  2 0.035
## Group3    4 0.577  6.928  2 0.020

Analyses of a Group Comparison

Confidence Interval for a Mean Difference

Comparison=factor(Group,c("Group1","Group2"))
ciDifference(Outcome~Comparison)

##   Diff     SE     df     LL     UL 
## -4.000  0.816  4.000 -6.267 -1.733

ciDifference(Outcome~Comparison,conf.level=.99)

##   Diff     SE     df     LL     UL 
## -4.000  0.816  4.000 -6.267 -1.733

Comparison=factor(Group,c("Group3","Group1"))
ciDifference(Outcome~Comparison)

##  Diff    SE    df    LL    UL 
## 5.000 0.816 4.000 2.733 7.267

Plot of the Confidence Interval for the Mean Difference

Comparison=factor(Group,c("Group1","Group2"))
cipDifference(Outcome~Comparison)

cipDifference(Outcome~Comparison,conf.level=.99)

Significance Test of the Mean Difference

nhstDifference(Outcome~Comparison)

##   Diff     SE      t     df      p 
## -4.000  0.816 -4.899  4.000  0.008

nhstDifference(Outcome~Comparison,mu=2)

##   Diff     SE      t     df      p 
## -6.000  0.816 -7.348  4.000  0.002

Analyses of Pairwise Comparisons

Confidence Intervals for the Pairwise Comparisons

ciPairwise(Outcome~Group)

##                 Diff    SE df     LL     UL
## Group1 v Group2   -4 0.816  4 -6.267 -1.733
## Group1 v Group3   -5 0.816  4 -7.267 -2.733
## Group2 v Group3   -1 0.816  4 -3.267  1.267

ciPairwise(Outcome~Group,conf.level=.99)

##                 Diff    SE df     LL     UL
## Group1 v Group2   -4 0.816  4 -7.759 -0.241
## Group1 v Group3   -5 0.816  4 -8.759 -1.241
## Group2 v Group3   -1 0.816  4 -4.759  2.759

Plot of the Confidence Intervals for the Pairwise Comparisons

cipPairwise(Outcome~Group)

cipPairwise(Outcome~Group,mu=-2,conf.level=.99)

Significance Tests of the Pairwise Comparisons

nhstPairwise(Outcome~Group)

##                 Diff    SE      t df     p
## Group1 v Group2   -4 0.816 -4.899  4 0.008
## Group1 v Group3   -5 0.816 -6.124  4 0.004
## Group2 v Group3   -1 0.816 -1.225  4 0.288

nhstPairwise(Outcome~Group,mu=-2)

##                 Diff    SE      t df     p
## Group1 v Group2   -2 0.816 -2.449  4 0.070
## Group1 v Group3   -3 0.816 -3.674  4 0.021
## Group2 v Group3    1 0.816  1.225  4 0.288

Analyses of a Set of Contrasts

Confidence Intervals for the Set of Contrasts

ciContrasts(Outcome~Group,contrasts=contr.sum)

##             Est    SE     LL     UL
## (Intercept)   7 0.333  6.184  7.816
## x1           -3 0.471 -4.153 -1.847
## x2            1 0.471 -0.153  2.153

ciContrasts(Outcome~Group,contrasts=contr.sum,conf.level=.99)

##             Est    SE     LL     UL
## (Intercept)   7 0.333  5.764  8.236
## x1           -3 0.471 -4.748 -1.252
## x2            1 0.471 -0.748  2.748

ciContrasts(Outcome~Group,contrasts=contr.treatment)

##             Est    SE    LL    UL
## (Intercept)   4 0.577 2.587 5.413
## x2            4 0.816 2.002 5.998
## x3            5 0.816 3.002 6.998

ciContrasts(Outcome~Group,contrasts=contr.poly)

##                Est    SE     LL    UL
## (Intercept)  7.000 0.333  6.184 7.816
## x.L          3.536 0.577  2.123 4.948
## x.Q         -1.225 0.577 -2.637 0.188

ciContrasts(Outcome~Group,contrasts=contr.helmert)

##             Est    SE    LL    UL
## (Intercept)   7 0.333 6.184 7.816
## x1            2 0.408 1.001 2.999
## x2            1 0.236 0.423 1.577

ciContrasts(Outcome~Group,contrasts=contr.SAS)

##             Est    SE     LL     UL
## (Intercept)   9 0.577  7.587 10.413
## x1           -5 0.816 -6.998 -3.002
## x2           -1 0.816 -2.998  0.998

Plot of the Confidence Intervals for the Set of Contrasts

cipContrasts(Outcome~Group,contrasts=contr.sum)

cipContrasts(Outcome~Group,contrasts=contr.sum,conf.level=.99)

cipContrasts(Outcome~Group,contrasts=contr.treatment)

cipContrasts(Outcome~Group,contrasts=contr.poly)

cipContrasts(Outcome~Group,contrasts=contr.helmert)

cipContrasts(Outcome~Group,contrasts=contr.SAS)

Significance Tests of the Set of Contrasts

nhstContrasts(Outcome~Group,contrasts=contr.sum)

##             Diff    SE      t     p
## (Intercept)    7 0.333 21.000 0.000
## x1            -3 0.471 -6.364 0.001
## x2             1 0.471  2.121 0.078

nhstContrasts(Outcome~Group,contrasts=contr.treatment)

##             Diff    SE     t     p
## (Intercept)    4 0.577 6.928 0.000
## x2             4 0.816 4.899 0.003
## x3             5 0.816 6.124 0.001

nhstContrasts(Outcome~Group,contrasts=contr.poly)

##               Diff    SE      t     p
## (Intercept)  7.000 0.333 21.000 0.000
## x.L          3.536 0.577  6.124 0.001
## x.Q         -1.225 0.577 -2.121 0.078

nhstContrasts(Outcome~Group,contrasts=contr.helmert)

##             Diff    SE      t     p
## (Intercept)    7 0.333 21.000 0.000
## x1             2 0.408  4.899 0.003
## x2             1 0.236  4.243 0.005

nhstContrasts(Outcome~Group,contrasts=contr.SAS)

##             Diff    SE      t     p
## (Intercept)    9 0.577 15.588 0.000
## x1            -5 0.816 -6.124 0.001
## x2            -1 0.816 -1.225 0.267

cwendorf/easi-dev documentation built on Oct. 23, 2020, 4:28 p.m.