# This set of commands calculate means, standard deviations, and confidence intervals for a data set
# Written by Dave Jenkins, Oct 2018, based on code at http://www.cookbook-r.com/Manipulating_data/Summarizing_data

# First run the entire summarySE function - through the } sign at line 32
summarySE <- function(data=NULL, measurevar, groupvars=NULL, na.rm=FALSE, conf.interval=.95, .drop=TRUE) {
  require(plyr)
  # New version of length which can handle NA's: if na.rm==T, don't count them
  length2 <- function (x, na.rm=FALSE) {
    if (na.rm) sum(!is.na(x))
    else       length(x)
  }
  # This does the summary. For each group's data frame, return a vector with
  # N, mean, and sd
  datac <- ddply(data, groupvars, .drop=.drop,
                 .fun = function(xx, col) {
                   c(N    = length2(xx[[col]], na.rm=na.rm),
                     mean = mean   (xx[[col]], na.rm=na.rm),
                     sd   = sd     (xx[[col]], na.rm=na.rm)
                   )
                 },
                 measurevar
  )
  # Rename the "mean" column    
  datac <- rename(datac, c("mean" = measurevar))
  datac$se <- datac$sd / sqrt(datac$N)  # Calculate standard error of the mean
  # Confidence interval multiplier for standard error
  # Calculate t-statistic for confidence interval: 
  # e.g., if conf.interval is .95, use .975 (above/below), and use df=N-1
  ciMult <- qt(conf.interval/2 + .5, datac$N-1)
  datac$ci <- datac$se * ciMult
  return(datac)
}

# Now tell summarySE to work on some data. For example, Time ~ Group within the data file.
# NOTICE that this assumes you have already loaded a file called "data" that contains these variables.

summarySE(data, measurevar="Time", groupvars=c("Group"), na.rm=TRUE)

# Here we use a print function to make a data frame containing the results of summarySE

result <- print(summarySE(data, measurevar="Time", groupvars=c("Group"), na.rm=TRUE))

# And now graph the result file 
attach(result) # for convenience

# now we plot outcomes, as means with CIs
require(ggplot2)
require(cowplot)
require(gridExtra)

# for SEs
plot1 <- ggplot(result, aes(x = Group, y = Time)) + 
  geom_errorbar(aes(ymin = Time-se, ymax = Time+se), width = 0.05, size  = 0.5) +
  geom_point() +
  ylim(3,6) +
  ylab("Time (means & SEs)") +
  xlab("Groups")

# for 95% CIs
plot2 <- ggplot(result, aes(x = Group, y = Time)) +
  geom_errorbar(aes(ymin = Time-ci, ymax = Time+ci), width = 0.05, size  = 0.5) +
  geom_point() +
  ylim(3,6) +
  ylab("Time (means & 95% CIs)") +
  xlab("Groups")

# for SDs
plot3 <- ggplot(result, aes(x = Group, y = Time)) + 
  geom_errorbar(aes(ymin = Time-sd, ymax = Time+sd), width = 0.05, size  = 0.5) +
  geom_point() +
  ylim(3,6) +
  ylab("Time (means & SDs)") +
  xlab("Groups")

grid.arrange(plot1, plot2, plot3, nrow=1, ncol=3)

# Notice how appearances change with different error bars? Only 95% CIs will translate well to inferred differences.

# Also see http://www.cookbook-r.com/Graphs/Plotting_means_and_error_bars_(ggplot2)/
# for plotting using ggplot2