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

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")

Athlete YOYOIRL1.Pre YOYOIRL1.Post v3015IFT.Pre v3015IFT.Post
1 Shrestha, Ezell 2000.00 2520.00 18.50 19.50
2 Cha, Gequan 1440.00 2080.00 20.50 20.00
3 Brown, Hindav 2360.00 2040.00 19.50 19.50
4 Venegas Delarosa, Destinee 1640.00 1800.00 19.50 21.50
5 Simon, Barrington 2240.00 1800.00 19.00 19.50
6 Williams, Hyeju 2200.00 2280.00 18.00 19.00
7 Gutierrez, Sabrina 1760.00 2400.00 17.50 23.00
8 Wilder, Johannah 1920.00 1640.00 19.00 22.00
9 Martin Dean, Jillian 1440.00 1960.00 21.00 22.00
10 Thomas, Neil 1840.00 2400.00 19.00 20.50
11 Nosker, Andrew 2080.00 2120.00 19.00 21.00
12 Blackford, Matthew 1760.00 2880.00 19.50 21.50
13 Mata, Rachel 1600.00 2640.00 18.50 19.50
14 Cheng, Ryan 1560.00 2440.00 17.50 21.00
15 True, Ashley 1720.00 2240.00 21.50 21.00

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")

Athlete Test Score
1 Shrestha, Ezell YOYOIRL1.Pre 2000.00
2 Cha, Gequan YOYOIRL1.Pre 1440.00
3 Brown, Hindav YOYOIRL1.Pre 2360.00
4 Venegas Delarosa, Destinee YOYOIRL1.Pre 1640.00
5 Simon, Barrington YOYOIRL1.Pre 2240.00
6 Williams, Hyeju YOYOIRL1.Pre 2200.00
7 Gutierrez, Sabrina YOYOIRL1.Pre 1760.00
8 Wilder, Johannah YOYOIRL1.Pre 1920.00
9 Martin Dean, Jillian YOYOIRL1.Pre 1440.00
10 Thomas, Neil YOYOIRL1.Pre 1840.00
11 Nosker, Andrew YOYOIRL1.Pre 2080.00
12 Blackford, Matthew YOYOIRL1.Pre 1760.00
13 Mata, Rachel YOYOIRL1.Pre 1600.00
14 Cheng, Ryan YOYOIRL1.Pre 1560.00
15 True, Ashley YOYOIRL1.Pre 1720.00
16 Inouye, Connor YOYOIRL1.Pre 2080.00
17 Tatum, Janice YOYOIRL1.Pre 1600.00
18 Latour, Pearl YOYOIRL1.Pre 1720.00
19 Tripathi, Juan YOYOIRL1.Pre 1360.00
20 Moore, Michelle YOYOIRL1.Pre 1880.00
21 O’Sullivan, Johanna YOYOIRL1.Pre 2160.00
22 Sharp, Gregory YOYOIRL1.Pre 2200.00
23 Blum, Jennifer YOYOIRL1.Pre 2000.00
24 Doering, Darius YOYOIRL1.Pre 1200.00
25 Sohn, Kendle YOYOIRL1.Pre 1880.00
26 Horton, Grant YOYOIRL1.Pre 1880.00
27 Waynewood, Nicholas YOYOIRL1.Pre 1640.00
28 Pallen, Raymundo YOYOIRL1.Pre 1800.00
29 Montoya, Simon YOYOIRL1.Pre 1480.00
30 Clark, Bryce YOYOIRL1.Pre 1960.00

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)

plot of chunk unnamed-chunk-3


# 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")

Test N Mean SD
1 YOYOIRL1.Pre 150 1749.60 309.40
2 YOYOIRL1.Post 150 2246.13 318.41
3 v3015IFT.Pre 150 18.86 1.12
4 v3015IFT.Post 150 20.98 1.09

From the table above we can calculate the percent change.

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.Change v3015IFT.Change
1 28.38 11.22

But as mentioned in the beginning of the post, percent change is not the best way to express change and sensitivity of the tests (although it is great to impress the managers or your superiors, or claim that your test is more sensitive).

What we need to do is to calculate effect size (ES). ES takes into account the difference between the means and SD (in this case of the Pre- test, but it can also use pooled SD).

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")

YOYOIRL1.ES v3015IFT.ES
1 1.60 1.88

From the data above we can conclude that they are pretty similar and that 30-15IFT might be a bit more sensitive (or the Coach B did a better job).

Anyway, to summarize this blog post – start reporting ES alongside with percent change. If someone claims high improvements in testing scores to show how great coach he is, or how great his program is, ask to see ES or the distribution of the change scores or Pre- and Post- tests. Besides we need to also ask for SWC and TE, but more on that later.

 

I am a physical preparation coach from Belgrade, Serbia, grow up in Pula, Croatia (which I consider my home town). I was involved in physical preparation of professional, amateur and recreational athletes of various ages in sports such as basketball, soccer, volleyball, martial arts and tennis. Read More »
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