In debruine/pipeline: Machine-Readable Studies

require(PoweR)
require(ggplot2)
require(car)
require(HLMdiag)
require(gtable)
require(gridExtra)
require(codebook)

source("effect_size_d_independent_function.R")

alldata <- read.table("data.txt", header=TRUE, dec=".") #read data

iv_labelstring <- "condition" #define variables to be used for axis (can be replaced by "Any Label")
dv_labelstring <- "answer (1-10)"  #define variables to be used for axis

alpha <- 0.05 #Set your alpha level 
conf_int <- 0.95 #Set your confidence interval

#Alternative hypothesis: specify "two.sided" (for x<>y), "less" (for x<y) or "greater" (for x>y)
H1 <- "two.sided"

############################################################
### Changed the information above? Then hit 'Knit Word' #####
#############################################################
#################### Know your way around R? ################ 
############ Feel free to change the script below ###########
#############################################################
options(scipen=20) #disable scientific notation 

alldata <- na.omit(alldata) #rows with missing data are removed
iv <- as.factor(alldata$iv)
xlabel <- levels(iv)[1] #name group 1 - needs to match the datafile (R is case-sensitive)!
ylabel <- levels(iv)[2] #name group 2 - needs to match the datafile (R is case-sensitive)!

factorlabel <- names(alldata)[3] #needs to match the datafile (R is case-sensitive)!
measurelabel <- names(alldata)[2]  #needs to match the datafile (R is case-sensitive)!

x.alldata <- subset(alldata, alldata[[factorlabel]]==xlabel)
y.alldata <- subset(alldata, alldata[[factorlabel]]==ylabel)
x <- x.alldata[[measurelabel]]
y <- y.alldata[[measurelabel]]

#######################################################################
#######################################################################
########### Calculate CI for within and between #######################
################ Scripts from Baguley, 2012 ###########################
#######################################################################
#######################################################################

# slightly adapted from: https://seriousstats.wordpress.com/2012/03/18/cis-for-anova/

bsci <- function(data.frame, group.var=match(factorlabel,names(alldata)), dv.var=match(measurelabel,names(alldata)), difference=FALSE, pooled.error=FALSE, conf.level=conf_int) {
  data <- subset(alldata, select=c(group.var, dv.var))
    fact <- factor(data[[1]], levels = c(xlabel,ylabel))
    dv <- data[[2]]
    J <- nlevels(fact)
    N <- length(dv)
    ci.mat <- matrix(,J,3, dimnames=list(levels(fact), c('lower', 'mean', 'upper')))
    ci.mat[,2] <- tapply(dv, fact, mean)
    n.per.group <- tapply(dv, fact, length)
    if(difference==TRUE) diff.factor= 2^0.5/2 else diff.factor=1
    if(pooled.error==TRUE) {
        for(i in 1:J) {
            moe <- summary(lm(dv ~ 0 + fact))$sigma/(n.per.group[[i]])^0.5 * qt(1-(1-conf.level)/2,N-J) * diff.factor
            ci.mat[i,1] <- ci.mat[i,2] - moe
            ci.mat[i,3] <- ci.mat[i,2] + moe
            }
        }
    if(pooled.error==FALSE) {
         for(i in 1:J) {
            group.dat <- subset(data, data[1]==levels(fact)[i])[[2]]
            moe <- sd(group.dat)/sqrt(n.per.group[[i]]) * qt(1-(1-conf.level)/2,n.per.group[[i]]-1) * diff.factor
            ci.mat[i,1] <- ci.mat[i,2] - moe
            ci.mat[i,3] <- ci.mat[i,2] + moe
        }
    }
    ci.mat
}

#change matrix output from functions to dataframe, add CI from between, add labels and means 
ci.sum<-as.data.frame(bsci(alldata, group.var=match(factorlabel,names(alldata)), dv.var=match(measurelabel,names(alldata)), difference=TRUE))
ci.sum[[factorlabel]] <- c(xlabel,ylabel)
ci.sum[[measurelabel]] <- c(mean(x),mean(y))

######## PLOT DATA AND CHECK FOR OUTLIERS AND NORMALITY ##########

#Test normality 
normality_rejections_x <- (statcompute(21, x, levels = c(0.05))$decision + statcompute(6, x, levels = c(0.05))$decision + statcompute(2, x, levels = c(0.05))$decision + statcompute(7, x, levels = c(0.05))$decision)

normality_rejections_y <- (statcompute(21, y, levels = c(0.05))$decision + statcompute(6, y, levels = c(0.05))$decision + statcompute(2, y, levels = c(0.05))$decision + statcompute(7, y, levels = c(0.05))$decision)

#Testing equality of variances
pvalue_levene <- leveneTest(alldata[[measurelabel]] ~ as.factor(alldata[[factorlabel]]))$"Pr(>F)"[1:1]
if (pvalue_levene < 0.05){equalvar <- "the assumption that variances are equal is rejected (consider reporting robust statistics)."}
if (pvalue_levene >= 0.05){equalvar <- "the assumption that variances are equal is not rejected."}

###       Perform t-test, calculate ES (Cohen's d)   ####

t_test_res <- effect_size_d(x, y, conf.level = conf_int)

m_diff = t_test_res$m_diff
ci_l_m_diff = t_test_res$ci_l_m_diff
ci_u_m_diff = t_test_res$ci_u_m_diff
d = t_test_res$d
d_unb = t_test_res$d_unb
sd_pooled = t_test_res$sd_pooled
ci_l_d = t_test_res$ci_l_d
ci_u_d = t_test_res$ci_u_d
ci_l_d_unb = t_test_res$ci_l_d_unb
ci_u_d_unb = t_test_res$ci_u_d_unb
n1 = t_test_res$n1
n2 = t_test_res$n2
m1 = t_test_res$m1
m2 = t_test_res$m2
sd1 = t_test_res$sd1
sd2 = t_test_res$sd2
cor = t_test_res$cor
t_value = t_test_res$t_value
df = t_test_res$df
ncp = t_test_res$ncp
p_value = t_test_res$p_value
CL = t_test_res$CL

#Specify direction of difference
if(mean(x) > mean(y)){direction <- "greater than"}
if(mean(x) < mean(y)){direction <- "smaller than"}
if(p_value < alpha){surprising <- "surprising"}
if(p_value >= alpha){surprising <- " not surprising"}

#Interpret size of effect (last resort - use only if effect size cannot be compared to other relevant effects in the literature)
if (abs(d) < 0.2){effectsize <- "tiny"}
if (0.2 <= abs(d) && abs(d) < 0.5){effectsize <- "small"}
if (0.5 <= abs(d) && abs(d) < 0.8){effectsize <- "medium"}
if (abs(d) >= 0.8){effectsize <- "large"}

This document summarizes a comparison between two independent groups, comparing r dv_labelstring between the r xlabel and r ylabel conditions. This script can help to facilitate the analysis of data, and the word-output might prevent copy-paste errors when transferring results to a manuscript.

Checking for outliers, normality, equality of variances.

Outliers

Boxplots can be used to identify outliers. Boxplots give the median (thick line), and 25% of the data above and below the median (box). End of whiskers are the maximum and minimum value when excluding outliers (whih are indicated by dots).

ggplot(alldata, aes(factor(eval(parse(text=paste(factorlabel)))), eval(parse(text=paste(measurelabel))))) +
  geom_boxplot()+
  ylab(dv_labelstring)  + xlab(iv_labelstring) + theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank())

Normality assumption

The independent t-test assumes that scores in both groups (r xlabel and r ylabel) are normally distributed. If the normality assumption is violated, the Type 1 error rate of the test is no longer controlled, and can substantially increase beyond the chosen significance level. Formally, a normality test based on the data is incorrect, and the normality assumption should be tested on additional (e.g., pilot) data. Nevertheless, a two-step procedure (testing the data for normality, and using alternatives for the traditional t-test if normality is violated, seems to work well (see Rochon, Gondan, & Kieser, 2012).

Tests for normality

Four tests for normality are reported below for both groups. Yap and Sim (2011, p. 2153) recommend: "If the distribution is symmetric with low kurtosis values (i.e. symmetric short-tailed distribution), then the D'Agostino-Pearson and Shapiro-Wilkes tests have good power. For symmetric distribution with high sample kurtosis (symmetric long-tailed), the researcher can use the JB, Shapiro-Wilkes, or Anderson-Darling test." The Kolmogorov-Smirnov (K-S) test is often used, but no longer recommended, and not included here.

If a normality test rejects the assumptions that the data is normally distributed (with p < .05) non-parametric or robust statistics have to be used (robust analyses are provided below).

The normality assumption was rejected in r normality_rejections_x out of 4 normality tests for the r xlabel condition, and in r normality_rejections_y out of 4 normality tests for the r ylabel condition.

Test Name | p-value r xlabel | p-value r ylabel ------------- | -------------- | ------------- Shapiro-Wilk | p r ifelse(statcompute(21, x, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(21, x, levels = c(0.05))$pvalue>0.001, round(statcompute(21, x, levels = c(0.05))$pvalue, digits=3), "0.001") | p r ifelse(statcompute(21, y, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(21, y, levels = c(0.05))$pvalue>0.001, round(statcompute(21, y, levels = c(0.05))$pvalue, digits=3), "0.001")
D'Agostino-Pearson | p r ifelse(statcompute(6, x, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(6, x, levels = c(0.05))$pvalue>0.001, round(statcompute(6, x, levels = c(0.05))$pvalue, digits=3), "0.001") | p r ifelse(statcompute(6, y, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(6, y, levels = c(0.05))$pvalue>0.001, round(statcompute(6, y, levels = c(0.05))$pvalue, digits=3), "0.001") Anderson-Darling | p r ifelse(statcompute(2, x, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(2, x, levels = c(0.05))$pvalue>0.001, round(statcompute(2, x, levels = c(0.05))$pvalue, digits=3), "0.001") | p r ifelse(statcompute(2, y, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(2, y, levels = c(0.05))$pvalue>0.001, round(statcompute(2, y, levels = c(0.05))$pvalue, digits=3), "0.001")
Jarque-Berra | p r ifelse(statcompute(7, x, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(7, x, levels = c(0.05))$pvalue>0.001, round(statcompute(7, x, levels = c(0.05))$pvalue, digits=3), "0.001") | p r ifelse(statcompute(7, y, levels = c(0.05))$pvalue>0.001," = ", " < ") r ifelse(statcompute(7, y, levels = c(0.05))$pvalue>0.001, round(statcompute(7, y, levels = c(0.05))$pvalue, digits=3), "0.001")

In very large samples (when the test for normality has close to 100% power) tests for normality can result in significant results even when data is normally distributed, based on minor deviations from normality. In very small samples (e.g., n = 10), deviations from normality might not be detected, but this does not mean the data is normally distributed. Always look at a plot of the data in addition to the test results.

Histogram, kernel density plot (black line) and normal distribution (red line) of difference scores

The density (or proportion of the observations) is plotted on the y-axis. The grey bars are a histogram of the scores in the two groups. Judging whether data is normally distributed on the basis of a histogram depends too much on the number of bins (or bars) in the graph. A kernel density plot (a non-parametric technique for density estimation) provides an easier way to check the normality of the data by comparing the shape of the density plot (the black line) with a normal distribution (the red dotted line, based on the observed mean and standard deviation). For independent t-tests, the dependent variables in both conditions should be normally distributed.

#density plot with normal distribution (red) and kernel desity plot
ggplot(x.alldata, aes(x=eval(parse(text=paste(measurelabel)))))  + 
  geom_histogram(colour="black", fill="grey", aes(y = ..density..)) +
  stat_function(fun = dnorm, args = c(mean=mean(x), sd=sd(x)), size = 1, color = "red", lty=2) +
  geom_density(fill=NA, colour="black", size = 1) +
  xlab(measurelabel)  + ggtitle(xlabel)+ theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())

ggplot(y.alldata, aes(x=eval(parse(text=paste(measurelabel)))))  + 
  geom_histogram(colour="black", fill="grey", aes(y = ..density..)) +
  stat_function(fun = dnorm, args = c(mean=mean(y), sd=sd(y)), size = 1, color = "red", lty=2) +
  geom_density(fill=NA, colour="black", size = 1) +
  xlab(measurelabel)  + ggtitle(ylabel)+ theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank())

Q-Q-plot

In the Q-Q plots for the r xlabel and r ylabel conditions the points should fall on the line. Deviations from the line in the upper and lower quartiles indicates the tails of the distributions are thicker or thinner than in the normal distribution. An S-shaped curve with a dip in the middle indicates data is left-skewed (more values to the right of the distribution), while a bump in the middle indicates data is right-skewed (more values to the left of the distribution). For interpretation examples, see here.

#Q-Q plot
qq1<-ggplot_qqnorm(x, line = "quantile") + ggtitle(xlabel) + theme_bw(base_size=14) + 
  theme(panel.grid.major = element_blank(),panel.grid.minor = element_blank())
qq2<-ggplot_qqnorm(y, line = "quantile") + ggtitle(ylabel) + theme_bw(base_size=14) + 
  theme(panel.grid.major = element_blank(),panel.grid.minor = element_blank())
grid.arrange(qq1, qq2, ncol=2)

Equal variances assumption

In addition to the normality assumption, a second assumption of Student's t-test is that variances in both groups are equal. As Ruxton (2006) explains: "If you want to compare the central tendency of 2 populations based on samples of unrelated data, then the unequal variance (or Welch's) t-test should always be used in preference to the Student's t-test or Mann-Whitney U test." This is preferable to the more traditional two-step approach of first testing equality of variances using Levene's test, and then deciding between Student's and Welch's t-test. The degrees of freedom for Welch's t-test is typically not a round number.

Levene's test

The equality of variances assumption is typically examined with Levene's test, although as explained above, Welch's test is used below regardless of the outcome. Levene's test for equality of variances (p r ifelse(pvalue_levene>0.001," = ", " < ") r ifelse(pvalue_levene>0.001,round(pvalue_levene, digits=3), "0.001")) indicates that r equalvar

Comparing the two sets of data

Before looking at the results of the Frequentist statistics and the Robust statistics, decide which of these answer the question you are interested in. Choosing between these two options depending on the outcome of the statistical test inflates the Type 1 error rate. You can always report Bayesian statistics.

Frequentist statistics

A p-value is the probability of obtaining the observed result, or a more extreme result, assuming the null-hypothesis is true. It is not the probability that the null-hypothesis or the alternative hypothesis is true (for such inferences, see Bayesian statistics below). In repeated sampling, r 100*conf_int% of future r 100*conf_int% confidence intervals can be expected to contain the true population paramters (e.g, the mean difference or the effect size). Confidence intervals are not a statement about the probability that a single confidence interval contains the true population parameter, but a statement about the probability that future confidence intervals will contain the true population parameter. Hedges' g (also referred to as d~unbiased~, see Borenstein, Hedges, Higgins, & Rothstein, 2009) is provided as best estimate of Cohen's d, but the best estimate of the confidence interval is based on d (as recommended by Cumming, 2012). Hedges's g and the r 100*conf_int% CI around the effect size are calculated using the MBESS package by (Kelley (2007). The common language effect size expresses the probability that in any random pairing of two observations from both groups, the observation from one group is higher than the observation from the other group, see McGraw & Wong, 1992. Default interpretations of the size of an effect as provided here should only be used as a last resort, and it is preferable to interpret the size of the effect in relation to other effects in the literature, or in terms of its practical significance.

Results

The mean r dv_labelstring of participants in the r xlabel condition (M = r round(mean(x), digits = 2), SD = r round(sd1, digits = 2), n = r n1) was r direction the mean of participants in the r ylabel condition (M = r round(mean(y), digits = 2), SD = r round(sd2,digits=2), n = r n2). The difference between the two measurements (M = r round(m_diff, digits=2), r 100*conf_int% CI = [r round(ci_l_m_diff, digits=2);r round(ci_u_m_diff,digits=2)]) was analyzed with Welch's t-test, t(r round(df, digits=2)) = r round(t_value, digits=2), p r ifelse(p_value>0.001," = ", " < ") r ifelse(p_value>0.001,formatC(round(p_value, digits=3),digits=3, format="f"), "0.001"), Hedges' g = r round(d_unb, digits=2), r 100*conf_int% CI [r round(ci_l_d_unb, digits=2);r round(ci_u_d_unb, digits=2)]. This can be considered a r effectsize effect. The observed data is r surprising under the assumption that the null-hypothesis is true. The Common Language effect size (McGraw & Wong, 1992) indicates that the likelihood that the r dv_labelstring of a random person in the r xlabel condition is r direction the r dv_labelstring of a random person in the r ylabel condition is r round(100*CL, digits=0)%.

Figure 1. Means and r 100*conf_int% CI, and violin plot

#Example 1: means and 95% CI 
ggplot(ci.sum, aes(x=as.character(eval(parse(text=paste(factorlabel)))), y=eval(parse(text=paste(measurelabel))), group=1)) +
  #  geom_bar(position=position_dodge(.9), colour="black", stat="identity", fill="white") +
  geom_errorbar(width=.1, size=1, aes(ymin=lower, ymax=upper)) +
  geom_point(size=2) +
  #  geom_point(data=alldata.long) +
  geom_violin(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), alpha=0) +
#  geom_boxplot(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), width=0.1) +
  ylab(dv_labelstring)  + xlab(iv_labelstring) + theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank())

Figure 2. Bar chart displaying means, individual datapoints, and r 100*conf_int% CI

#Example 2: bar chart with individual data point and 95% CI
ggplot(ci.sum, aes(x=as.character(eval(parse(text=paste(factorlabel)))), y=eval(parse(text=paste(measurelabel))), group=1)) +
  geom_bar(position=position_dodge(.9), colour="black", stat="identity", fill="white") +
  geom_errorbar(width=.1, size=0.5, aes(ymin=lower, ymax=upper)) +
#  geom_point(size=4) +
  geom_point(data=alldata, alpha=0.2) +
#  geom_violin(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), alpha=0) +
#  geom_boxplot(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), width=0.1) +
  ylab(dv_labelstring)  + xlab(iv_labelstring) + theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank())

Figure 3. Bar chart displaying r 100*conf_int% CI

#Example 3: bar chart with 95% CI
ggplot(ci.sum, aes(x=as.character(eval(parse(text=paste(factorlabel)))), y=eval(parse(text=paste(measurelabel))), group=1)) +
#  geom_bar(position=position_dodge(.9), colour="black", stat="identity", fill="white") +
#  geom_boxplot(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), width=0.1) +
  geom_errorbar(width=.2, size=0.5, aes(ymin=lower, ymax=upper)) +
  geom_point(size=4) +
# geom_point(data=alldata) +
# geom_violin(data=alldata, aes(group=as.character(eval(parse(text=paste(factorlabel))))), alpha=0) +
  ylab(dv_labelstring)  + xlab(iv_labelstring) + theme_bw(base_size=14) + 
  theme(panel.grid.major.x = element_blank())

References

This script uses the reshape2 package to convert data from wide to long format, the PoweR package to perform the normality tests, HLMdiag to create the QQplots, ggplot2 for all plots, gtable and gridExtra to combine multiple plots into one, car to perform Levene's test, MBESS to calculate effect sizes and their confidence intervals, WRS for the robust statistics, bootES for the robust effect size, BayesFactor for the bayes factor, and BEST to calculate the Bayesian highest density interval.

Algina, J., Keselman, H. J., & Penfield, R. D. (2005). An alternative to Cohen's standardized mean difference effect size: a robust parameter and confidence interval in the two independent groups case. Psychological Methods, 10, 317-328.

Auguie, B. (2012). gridExtra: functions in Grid graphics. R package version 0.9.1, URL: http://CRAN.R-project.org/package=gridExtra.

Baguley, T. (2012). Calculating and graphing within-subject confidence intervals for ANOVA. Behavior research methods, 44, 158-175.

Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2009). Introduction to meta-analysis. Hoboken, NJ: Wiley.

Box, G. E. P. (1953). Non-normality and tests on variance. Biometrika, 40, 318-335.

Cumming, G. (2012). Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. New York: Routledge.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

Fox, J. & Weisberg, S. (2011). An R Companion to Applied Regression, Second edition. Sage, Thousand Oaks CA. URL: http://socserv.socsci.mcmaster.ca/jfox/Books/Companion.

Kelley, K. (2005). The effects of nonnormal distributions on confidence intervals around the standardized mean difference: Bootstrap and parametric confidence intervals. Educational and Psychological Measurement, 65, 51-69.

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20, 1-24.

Kelley, K. & Lai, K. (2012). MBESS. R package version 3.3.3, URL: http://CRAN.R-project.org/package=MBESS.

Kirby, K. N., & Gerlanc, D. (2013). BootES: An R package for bootstrap confidence intervals on effect sizes. Behavior Research Methods, 45, 905-927.

Kruschke, J. (2010). Doing Bayesian data analysis: A tutorial introduction with R. Academic Press.

Kruschke, J. K. (2013). Bayesian estimation supersedes the t-test. Journal of Experimental Psychology: General, 142, 573-603.

Kruschke, J. K., & Meredith, M. (2014). BEST: Bayesian Estimation Supersedes the t-test. R package version 0.2.2, URL: http://CRAN.R-project.org/package=BEST.

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in psychology, 4.

Loy, A., & Hofmann, H. (2014). HLMdiag: A Suite of Diagnostics for Hierarchical Linear Models. R. Journal of Statistical Software, 56, pp. 1-28. URL: http://www.jstatsoft.org/v56/i05/.

McGraw, K. O., & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111, 361-365.

Micheaux, PLd. & Tran, V. (2012). PoweR. URL: http://www.biostatisticien.eu/PoweR/.

Morey, R. D. (2008). Confidence intervals from normalized data: A correction to Cousineau (2005). Tutorial in Quantitative Methods for Psychology, 4, 61-64.

Morey, R. D. & Rouder, J. N. (2011). Bayes Factor Approaches for Testing Interval Null Hypotheses. Psychological Methods, 16, 406-419

Morey R and Rouder J (2015). BayesFactor: Computation of Bayes Factors for Common Designs. R package version 0.9.11-1, URL: http://CRAN.R-project.org/package=BayesFactor.

Rochon, J., Gondan, M., & Kieser, M. (2012). To test or not to test: Preliminary assessment of normality when comparing two independent samples. BMC Medical Research Methodology, 12:81.

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16, 752-760

Ruxton, G. D. (2006). The unequal variance t-test is an underused alternative to Student's t-test and the Mann-Whitney U test. Behavioral Ecology, 17, 688-690.

Wickham, H. (2007). Reshaping Data with the reshape Package. Journal of Statistical Software, 21, pp. 1-20. URL: http://www.jstatsoft.org/v21/i12/.

Wickham, H. (2009). ggplot2: elegant graphics for data analysis. Springer New York. ISBN 978-0-387-98140-6, URL: http://had.co.nz/ggplot2/book.

Wickham, H. (2012). gtable: Arrange grobs in tables. R package version 0.1.2, URL: http://CRAN.R-project.org/package=gtable.

Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing. Academic Press.

Wilcox, R. R., & Schönbrodt, F. D. (2015). The WRS package for robust statistics in R (version 0.27.5). URL: https://github.com/nicebread/WRS.

Yap, B. W., & Sim, C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 81, 2141-2155.

Apendix A: Data & Session Information

alldata

sessionInfo()

codebook_data <- alldata

codebook_data <- detect_missing(codebook_data,
    only_labelled = TRUE, # only labelled values are autodetected as
                                   # missing
    negative_values_are_missing = FALSE, # negative values are NOT missing values
    ninety_nine_problems = TRUE,   # 99/999 are missing values, if they
                                   # are more than 5 MAD from the median
    )

codebook(codebook_data)

Copyright © 2019 Daniel Lakens

Lakens, D. (2019). The perfect t-test. Retrieved from https://github.com/Lakens/perfect-t-test. doi:10.5281/zenodo.17603

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

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debruine/pipeline documentation built on May 8, 2019, 8:59 a.m.