# This set of commands calculate means, standard deviations, standard errors, and confidence intervals for a data set
# Written by Dave Jenkins, Oct. 2016, based on code at http://www.cookbook-r.com/Manipulating_data/Summarizing_data

# First run the entire summarySE function - from line 5 through line 38. 
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 import data from
# http://jenkins.cos.ucf.edu/wordpress/wp-content/uploads/copter-data-F16.csv
# and then specify appropriate details inside the summarySE parentheses below. 

# Here we are interested in Time for combinations of Design and Group within the data file
summarySE(data, measurevar="Time", groupvars=c("Design", "Group"), na.rm=TRUE)

# Now use print to make a data frame containing the results of summarySE. Beyond graphing this could be handy for a table later
result <- print(summarySE(data, measurevar="Time", groupvars=c("Design", "Group"), na.rm=TRUE))

# To save the result table (e.g., as a csv file), you could use a write command (e.g., write.csv(result, "results.csv"))
# Here we graph the result file but first we 
attach(result) # for convenience

# Now we can plot those means and CIs using the package plotrix
library(plotrix) # you may have to first install this package, which is handy for a variety of graphs

# then make simple scatterplot of means +/- CIs
plotCI(Design, Time, ci, main="95% CIs", ylim=c(3.0,7.0))

# Oops. You have multiple means and CIs per Design, because we calculated them per Group. 
# Recalculate per Design only to ignore among-Group differences.

# Now repeat but using std. deviations and then std. errors for error bars in the plots
# to plot all 3 graphs side by side, use this command first: par(mfrow=c(1,3))
plotCI(Design, Time, sd, main="SDs", ylim=c(3.0,7.0))
plotCI(Design, Time, se, main="SEs", ylim=c(3.0,7.0))

# Notice how appearances change with different error bars?
# What do each of the error bars say about your data?
# Which one most honestly represents mean Times? 
# Which one most honestly represents data distributions?
# Which one most cynically manipulates readers' visual impressions of our data?

# For plotting using ggplot2, see http://www.cookbook-r.com/Graphs/Plotting_means_and_error_bars_(ggplot2)
# or Box 5.2 on pg. 74 in Hector's book