docs/vignette-t-test.md
In mrzdcmps/changeofevidence: Change of Evidence
title: "Change of Evidence Vignette t-Test"
output:
html_document:
keep_md: true
self_contained: true
toc: true
Generate Sample Data
set.seed(9878)
exp=rbinom(100,20,0.52)
con=rbinom(100,20,0.5)
summary(exp)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 9.00 11.00 10.54 12.00 15.00
summary(con)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 8.75 10.00 9.96 12.00 15.00
df <- data.frame(condition = c(rep("exp", 100), rep("con", 100)),
value = c(exp, con))
Load library
library(changeofevidence)
Bayes Factor testing
Calculate Sequential Bayes Factors
# Undirectional one-sample t-tests with broad prior
bf.exp <- bfttest(exp, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 2.640455 (t=2.59456; p=0.01090879)
print(bf.exp)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=2.64; BF01=0.379
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=2.595; p=0.011
##
# Use exact=FALSE for a quicker test that doers not calculate every single BF
bf.con <- bfttest(con, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707, exact=FALSE)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 0.1123492 (t=-0.1732313; p=0.8628233)
print(bf.con)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=0.112; BF01=8.901
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=-0.173; p=0.863
##
# only the last 5 data points
bfttest(con, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707, nstart = length(con)-5)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 0.1123492 (t=-0.1732313; p=0.8628233)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=0.112; BF01=8.901
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=-0.173; p=0.863
##
# Directional paired samples t-test with narrow prior
bf.paired <- bfttest(exp, con, alternative = "greater", prior.loc = 0, prior.r = 0.1)
## Paired Samples test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 2.960334 (t=1.974355; p=0.02556375)
print(bf.paired)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: paired
## Sample size: 100
## Final Bayes Factor: BF10=2.96; BF01=0.338
## Parameter prior: Cauchy(0, 0.1)
## Directionality of H1 analysis prior: greater
## Orthodox Test: t-value=1.974; p=0.026
##
# Independent samples t-test with informed prior
bf.between <- bfttest(value ~ condition, data = df, alternative = "less", prior.loc = 0.1, prior.r = 0.1)
## Independent Samples test (N = 200 [100 + 100])
## Calculating Sequential Bayes Factors...
## First observation with two groups found at N = 101
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## Final Bayes Factor: 2.361634 (t=-1.865788; p=0.03177503)
print(bf.between)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: independent
## Sample size: 100, 100
## Final Bayes Factor: BF10=2.362; BF01=0.423
## Parameter prior: Cauchy(0.1, 0.1)
## Directionality of H1 analysis prior: less
## Orthodox Test: t-value=-1.866; p=0.032
##
Plot Seq BFs
# Plot seqbf object
plot(bf.paired)
# Plot multiple BFs
plotbf(list(exp=bf.exp$BF, con=bf.con$BF))
Robustness analyis
bf.paired.robust <- bfRobustness(bf.paired)
## Highest BF = 5.18 with prior: Cauchy(0.2, 0.05)
print(bf.paired.robust)
##
## Prior Robustness Analysis
## --------------------------------
## Test type: paired
## Sample size: 100
## Tested priors:
## -- distribution: Cauchy
## -- location: 0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1
## -- scale: 0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1
## Highest Bayes Factor: 5.181 with prior: Cauchy(0.2, 0.05)
## Lowest Bayes Factor: 0.045 with prior: Cauchy(1, 0.05)
## Median Bayes Factor: 0.894
##
plot(bf.paired.robust)
Simulations
Create simulations
# Indicate the amount of trials of one experimental run (e.g. 100 subjects * 20 trials)
# Specify the same test parameters as the test(s) you want to compare to (in this case the one-sample t-tests.)
sims <- simcreate(100*20, n.sims = 100, mean.scores = 10, use.files = F, alternative = "two.sided", prior.loc = 0, prior.r = 0.707)
## Lade nötiges Paket: foreach
## Lade nötiges Paket: doParallel
## Lade nötiges Paket: iterators
## Lade nötiges Paket: parallel
Plot BFs with simulation data
plot(bf.paired, sims.df = sims)
## [1] "Depending on the amount of simulations to be drawn, this might take a while!"
plotbf(list(exp=bf.exp$BF, con=bf.con$BF), sims.df = sims)
## [1] "Depending on the amount of simulations to be drawn, this might take a while!"
Change of evidence measures
CoE 1: Maximum BF
r.exp.maxbf <- maxbf(bf.exp, sims.df = sims)
## >> MAXIMUM BF <<
## Highest BF: 11.05546 ( at N = 89 )
## Sims with this or a higher BFs: 3 %
r.con.maxbf <- maxbf(bf.con, sims.df = sims)
## >> MAXIMUM BF <<
## Highest BF: 1.677659 ( at N = 24 )
## Sims with this or a higher BFs: 24 %
CoE 2: BF Energy
r.exp.nrg <- energybf(bf.exp, sims.df = sims)
## >> BF ENERGY <<
## Calculating Energy of sims...
##
## Energy of BF of data: 106.5228
## Sims Energy: M = -56.10375 , SD = 64.66779
## Sims with this or higher Energy: 2 %
r.con.nrg <- energybf(bf.con, sims.df = sims)
## >> BF ENERGY <<
## Calculating Energy of sims...
##
## Energy of BF of data: -67.026
## Sims Energy: M = -56.10375 , SD = 64.66779
## Sims with this or higher Energy: 32 %
Coe 3: FFT Amplitude Sum
# Create Fast Fourier Transforms of Sequential BFs
fft.exp <- fftcreate(bf.exp)
fft.con <- fftcreate(bf.con)
# Compare amplitude sums with simulations
r.exp.fft <- ffttest(fft.exp, sims.df = sims)
## >> FREQUENCY ANALYSIS <<
##
## Number of Frequencies: 50
## Sum of Amplitudes: 8.090708
## Sims Amplitude Sums: M = 1.774112 SD = 2.982413
## Simulations with this or higher amplitude sum: 3 %
r.con.fft <- ffttest(fft.con, sims.df = sims)
## >> FREQUENCY ANALYSIS <<
##
## Number of Frequencies: 50
## Sum of Amplitudes: 1.317572
## Sims Amplitude Sums: M = 1.774112 SD = 2.982413
## Simulations with this or higher amplitude sum: 26 %
# Plot FFTs
# Use parameter "coordy" to ensure a comparable coordinate system
plotfft(fft.exp, sims.df = sims)
plotfft(fft.con, sims.df = sims)
mrzdcmps/changeofevidence documentation built on Feb. 27, 2025, 3:10 a.m.
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title: "Change of Evidence Vignette t-Test" output: html_document: keep_md: true self_contained: true toc: true
Generate Sample Data
set.seed(9878)
exp=rbinom(100,20,0.52)
con=rbinom(100,20,0.5)
summary(exp)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 9.00 11.00 10.54 12.00 15.00
summary(con)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 8.75 10.00 9.96 12.00 15.00
df <- data.frame(condition = c(rep("exp", 100), rep("con", 100)),
value = c(exp, con))
Load library
library(changeofevidence)
Bayes Factor testing
Calculate Sequential Bayes Factors
# Undirectional one-sample t-tests with broad prior
bf.exp <- bfttest(exp, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 2.640455 (t=2.59456; p=0.01090879)
print(bf.exp)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=2.64; BF01=0.379
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=2.595; p=0.011
##
# Use exact=FALSE for a quicker test that doers not calculate every single BF
bf.con <- bfttest(con, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707, exact=FALSE)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 0.1123492 (t=-0.1732313; p=0.8628233)
print(bf.con)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=0.112; BF01=8.901
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=-0.173; p=0.863
##
# only the last 5 data points
bfttest(con, mu = 10, alternative = "two.sided", prior.loc = 0, prior.r = 0.707, nstart = length(con)-5)
## One Sample test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 0.1123492 (t=-0.1732313; p=0.8628233)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: one-sample
## Sample size: 100
## Final Bayes Factor: BF10=0.112; BF01=8.901
## Parameter prior: Cauchy(0, 0.707)
## Directionality of H1 analysis prior: two.sided
## Orthodox Test: t-value=-0.173; p=0.863
##
# Directional paired samples t-test with narrow prior
bf.paired <- bfttest(exp, con, alternative = "greater", prior.loc = 0, prior.r = 0.1)
## Paired Samples test (N = 100)
## Calculating Sequential Bayes Factors...
##
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## Final Bayes Factor: 2.960334 (t=1.974355; p=0.02556375)
print(bf.paired)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: paired
## Sample size: 100
## Final Bayes Factor: BF10=2.96; BF01=0.338
## Parameter prior: Cauchy(0, 0.1)
## Directionality of H1 analysis prior: greater
## Orthodox Test: t-value=1.974; p=0.026
##
# Independent samples t-test with informed prior
bf.between <- bfttest(value ~ condition, data = df, alternative = "less", prior.loc = 0.1, prior.r = 0.1)
## Independent Samples test (N = 200 [100 + 100])
## Calculating Sequential Bayes Factors...
## First observation with two groups found at N = 101
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## Final Bayes Factor: 2.361634 (t=-1.865788; p=0.03177503)
print(bf.between)
##
## Sequential Bayesian Testing
## --------------------------------
## Test type: independent
## Sample size: 100, 100
## Final Bayes Factor: BF10=2.362; BF01=0.423
## Parameter prior: Cauchy(0.1, 0.1)
## Directionality of H1 analysis prior: less
## Orthodox Test: t-value=-1.866; p=0.032
##
Plot Seq BFs
# Plot seqbf object
plot(bf.paired)
# Plot multiple BFs
plotbf(list(exp=bf.exp$BF, con=bf.con$BF))
Robustness analyis
bf.paired.robust <- bfRobustness(bf.paired)
## Highest BF = 5.18 with prior: Cauchy(0.2, 0.05)
print(bf.paired.robust)
##
## Prior Robustness Analysis
## --------------------------------
## Test type: paired
## Sample size: 100
## Tested priors:
## -- distribution: Cauchy
## -- location: 0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1
## -- scale: 0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1
## Highest Bayes Factor: 5.181 with prior: Cauchy(0.2, 0.05)
## Lowest Bayes Factor: 0.045 with prior: Cauchy(1, 0.05)
## Median Bayes Factor: 0.894
##
plot(bf.paired.robust)
Simulations
Create simulations
# Indicate the amount of trials of one experimental run (e.g. 100 subjects * 20 trials)
# Specify the same test parameters as the test(s) you want to compare to (in this case the one-sample t-tests.)
sims <- simcreate(100*20, n.sims = 100, mean.scores = 10, use.files = F, alternative = "two.sided", prior.loc = 0, prior.r = 0.707)
## Lade nötiges Paket: foreach
## Lade nötiges Paket: doParallel
## Lade nötiges Paket: iterators
## Lade nötiges Paket: parallel
Plot BFs with simulation data
plot(bf.paired, sims.df = sims)
## [1] "Depending on the amount of simulations to be drawn, this might take a while!"
plotbf(list(exp=bf.exp$BF, con=bf.con$BF), sims.df = sims)
## [1] "Depending on the amount of simulations to be drawn, this might take a while!"
Change of evidence measures
CoE 1: Maximum BF
r.exp.maxbf <- maxbf(bf.exp, sims.df = sims)
## >> MAXIMUM BF <<
## Highest BF: 11.05546 ( at N = 89 )
## Sims with this or a higher BFs: 3 %
r.con.maxbf <- maxbf(bf.con, sims.df = sims)
## >> MAXIMUM BF <<
## Highest BF: 1.677659 ( at N = 24 )
## Sims with this or a higher BFs: 24 %
CoE 2: BF Energy
r.exp.nrg <- energybf(bf.exp, sims.df = sims)
## >> BF ENERGY <<
## Calculating Energy of sims...
##
## Energy of BF of data: 106.5228
## Sims Energy: M = -56.10375 , SD = 64.66779
## Sims with this or higher Energy: 2 %
r.con.nrg <- energybf(bf.con, sims.df = sims)
## >> BF ENERGY <<
## Calculating Energy of sims...
##
## Energy of BF of data: -67.026
## Sims Energy: M = -56.10375 , SD = 64.66779
## Sims with this or higher Energy: 32 %
Coe 3: FFT Amplitude Sum
# Create Fast Fourier Transforms of Sequential BFs
fft.exp <- fftcreate(bf.exp)
fft.con <- fftcreate(bf.con)
# Compare amplitude sums with simulations
r.exp.fft <- ffttest(fft.exp, sims.df = sims)
## >> FREQUENCY ANALYSIS <<
##
## Number of Frequencies: 50
## Sum of Amplitudes: 8.090708
## Sims Amplitude Sums: M = 1.774112 SD = 2.982413
## Simulations with this or higher amplitude sum: 3 %
r.con.fft <- ffttest(fft.con, sims.df = sims)
## >> FREQUENCY ANALYSIS <<
##
## Number of Frequencies: 50
## Sum of Amplitudes: 1.317572
## Sims Amplitude Sums: M = 1.774112 SD = 2.982413
## Simulations with this or higher amplitude sum: 26 %
# Plot FFTs
# Use parameter "coordy" to ensure a comparable coordinate system
plotfft(fft.exp, sims.df = sims)
plotfft(fft.con, sims.df = sims)
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