How to (Pretend to) Be a Better Coach Using Bad Statistics

Here is a simple scenario from practice: Coach A uses YOYOIRL1 test and Coach B uses 30-15IFT (for more info see paper by Martin Buchheit, which also stimulated me to write this blog) to gauge improvements in endurance.

Coach A: We have improved distance covered in YOYOIRL1 test from 1750m to 2250m in four weeks. That is 500m improvement or ~28%
Coach B: We have improved velocity reached in 30-15IFT from 19km/h to 21km/h in four weeks . That is 2km/h improvement or ~10%

If you present those to someone who is not statisticaly educated he/she might conclude the following:

• Coach A did a better job, since the improvement is 28% compared to 10% of Coach B
• YOYOIRL1 test is more sensitive to changes than 30-15IFT

As a coaches, we needs to report to a manager(s), so which one would you prefer reporting? 28% or 10%? Be honest here!

Unfortunately, we cannot conclude who did a better job (Coach A or Coach B), nor which test is more sensitive (YOYOIRL1 or 30-15IFT) from percent change data. A lot of managers and coaches don’t get this. At least I haven’t until recently.

What we need is Effect Size statistics, or Cohen’s D. But for that we need to know variability in the groups, expressed as SD (standard deviation). Let’s simulate the data and use usual SDs for YOYOIRL1 and 30-15IFT

require(ggplot2, quietly = TRUE)
require(reshape2, quietly = TRUE)
require(plyr, quietly = TRUE)
require(randomNames, quietly = TRUE)
require(xtable, quietly = TRUE)
require(ggthemes, quietly = TRUE)
require(gridExtra, quietly = TRUE)

set.seed(1)
numberOfPlayers <- 150
playerNames <- randomNames(numberOfPlayers)

# Create YOYOIRL1 Pre- and Post- data using 300m as SD
YOYOIRL1.Pre <- rnorm(mean = 1750, sd = 300, n = numberOfPlayers)
YOYOIRL1.Post <- rnorm(mean = 2250, sd = 300, n = numberOfPlayers)

# We need to round YOYOIRL1 score to nearest 40m, since those are the
# increments of the scores
YOYOIRL1.Pre <- round_any(YOYOIRL1.Pre, 40)
YOYOIRL1.Post <- round_any(YOYOIRL1.Post, 40)

# Create 30-15IFT Pre- and Post- data using 1km/h as SD
v3015IFT.Pre <- rnorm(mean = 19, sd = 1, n = numberOfPlayers)
v3015IFT.Post <- rnorm(mean = 21, sd = 1, n = numberOfPlayers)

# We need to round 30-15IFT to nearest 0.5km/h, since those are the
# increments of the scores
v3015IFT.Pre <- round_any(v3015IFT.Pre, 0.5)
v3015IFT.Post <- round_any(v3015IFT.Post, 0.5)

# Put those test into data.frame
testDataWide <- data.frame(Athlete = playerNames, YOYOIRL1.Pre, YOYOIRL1.Post, 
    v3015IFT.Pre, v3015IFT.Post)

# And print first 15 athletes
print(xtable(head(testDataWide, 15), border = T), type = "html")

 
To plot the data and to do simple descriptive stats we need to reshape the data from wide format to long format using reshape2 package by Hadley Wickham

# Reshape the data
testData <- melt(testDataWide, id.vars = "Athlete", variable.name = "Test", 
    value.name = "Score")

# And print first 30 rows
print(xtable(head(testData, 30), border = T), type = "html")

 
From the tables above it is easy to see the difference between wide and long data formats.

Let’s calculate simple stats using plyr package from Hadley Wickham (yes, he is a sort of celebrity in R community) and plot them using violin plots, which is great since they show the distribution of the scores

# Subset YOYOIRL1 tets
ggYOYO <- ggplot(subset(testData, Test == "YOYOIRL1.Pre" | Test == "YOYOIRL1.Post"), 
    aes(x = Test, y = Score))

ggYOYO <- ggYOYO + geom_violin(fill = "red", alpha = 0.5) + theme_few() + stat_summary(fun.y = mean, 
    geom = "point", fill = "white", shape = 23, size = 5)

# Subset 30-15IFT tets
ggIFT <- ggplot(subset(testData, Test == "v3015IFT.Pre" | Test == "v3015IFT.Post"), 
    aes(x = Test, y = Score))

ggIFT <- ggIFT + geom_violin(fill = "steelblue", alpha = 0.5) + theme_few() + 
    stat_summary(fun.y = mean, geom = "point", fill = "white", shape = 23, size = 5)

# Plot the graphs
grid.arrange(ggYOYO, ggIFT, ncol = 2)

# Calculate the summary table
testDataSummary <- ddply(testData, "Test", summarize, N = length(Score), Mean = mean(Score), 
    SD = sd(Score))
# Print the summary table
print(xtable(testDataSummary, border = T), type = "html")

YOYOIRL1.Change <- (testDataSummary$Mean[2] - testDataSummary$Mean[1])/testDataSummary$Mean[1] * 
    100
v3015IFT.Change <- (testDataSummary$Mean[4] - testDataSummary$Mean[3])/testDataSummary$Mean[3] * 
    100

print(xtable(data.frame(YOYOIRL1.Change, v3015IFT.Change), border = T), type = "html")

YOYOIRL1.ES <- (testDataSummary$Mean[2] - testDataSummary$Mean[1])/testDataSummary$SD[1]
v3015IFT.ES <- (testDataSummary$Mean[4] - testDataSummary$Mean[3])/testDataSummary$SD[3]

print(xtable(data.frame(YOYOIRL1.ES, v3015IFT.ES), border = T), type = "html")