sample-proportions.r

setClass(
	Class = "Distribution",
	representation = representation(
		name = "character",
		participants = "numeric",
		conversions = "numeric",
		sample_proportion = "numeric",
		se = "numeric",
		color = "character",
		x = "vector",
		y = "vector"
	)
)

# We rewrite the initialize method for Distribution objects so that we can
# set the x and y values which are used throughout the plotting process
setMethod(
	f = "initialize",
	signature = "Distribution",
	definition = function( .Object, name, participants, conversions, color ) {
		.Object@name = name
		.Object@sample_proportion = conversions / participants
		.Object@se = sqrt( ( .Object@sample_proportion * ( 1 - .Object@sample_proportion ) ) / participants )
		.Object@color = color
		.Object@x = seq( -4, 4, length = 100 ) * .Object@se + .Object@sample_proportion
		.Object@y = dnorm( .Object@x, .Object@sample_proportion, .Object@se )

		return ( .Object )
	}
)

# Given a list of distributions, this returns a list of the x and y axis range
get_axis_ranges = function( distributions ) {
	x_all = vector()
	y_all = vector()

	for ( distribution in distributions ) {
		x_all = c( x_all, distribution@x )
		y_all = c( y_all, distribution@y )
	}

	xlim = c( min( x_all ), max( x_all ) )
	ylim = c( min( y_all ), max( y_all ) )

	# Note that by forming a list of the vectors, the vectors get converted to lists
	# which we then have to convert back to vectors in order to use them for plotting
	return ( list( xlim, ylim ) )
}

get_x_axis_values = function( x_range ) {
	by = 0.01

	min_x = floor( min( x_range ) / by ) * by
	max_x = ceiling( max( x_range ) / by ) * by

	return ( seq( min_x, max_x, by = by ) )
}

# Define the distributions that we want to plot
distributions = list(
	new( Class = "Distribution", name = "original", participants = 250, conversions = 40, color = "#00cc00" ),
	new( Class = "Distribution", name = "variation", participants = 270, conversions = 60, color = "blue" )
)

# Determine the range to use for each axis
axis_range = get_axis_ranges( distributions )
xlim = axis_range[[ 1 ]]
ylim = axis_range[[ 2 ]]

# Create the plot
plot( NULL, NULL, type = "n", xlim = xlim, ylim = ylim, xlab = "Conversion Rate", ylab = "", main = "", axes = FALSE )

# Render each of the curves
line_width = 3
for ( distribution in distributions ) {
	polygon( distribution@x, distribution@y, col = adjustcolor( distribution@color, alpha.f = 0.3 ), border = NA )
	lines( distribution@x, distribution@y, col = adjustcolor( distribution@color, alpha.f = 1 ), lwd = line_width )

	# Draw a line down the center of the curve
	ci_center_y = dnorm( distribution@sample_proportion, distribution@sample_proportion, distribution@se )
	coords = xy.coords( c( distribution@sample_proportion, distribution@sample_proportion ), c( 0, ci_center_y ) )
	lines( coords, col = adjustcolor( distribution@color, alpha.f = 0.4 ), lwd = 1 )
}

# Render the x axis
axis( side = 1, at = get_x_axis_values( xlim ), pos = 0, col = "#777777", col.axis = "#777777", lwd = line_width )

# Finally, render a legend
legend_text = vector()
legend_colors = vector()
for ( distribution in distributions ) {
	legend_text = c( legend_text, distribution@name )
	legend_colors = c( legend_colors, distribution@color )
}
legend('right', legend_text, lty = 1, lwd = line_width, col = legend_colors, bty = 'n' )