title: "Calculating Percentiles / cut off values /"

author: "Martin Kennedy"

date: "February 17, 2016"

Suppose a normal distribution of a test score with mean = 21 and standard deviation = 5...

What percentile is 24?

pnorm(24, mean = 21, sd = 5)

S'pose a person scores in top 10% on SAT

Given mean SAT = 1500, SD = 300

What is lowest possible score that person could have achieved? (use 'qnorm for percentile or cutoff value)

qnorm(0.9, mean = 1500, sd = 300)

... or simply...

qnorm(0.9,1500, 300)

Suppose a person scored in bottom 10% with...

mean ACT = 21, standard dev = 5

What is highest score she could have gotten? Get cutoff value...

qnorm(0.1, mean = 21, sd = 5)

STOP HERE...

Code below uses data from Kobe Bryant and investigates the 'hot-hand' phenomenon by using simulation...

# Load the data frame (data called 'kobe')... use 'head' and / or 'tail' to check data...

load(url("http://s3.amazonaws.com/assets.datacamp.com/course/dasi/kobe.RData"))

head(kobe)

tail(kobe)

# print first 9 obs in data frame 'kobe'...

kobe[1:9,]

names(kobe)

kobe$basket[1:9]

# shooting sreak... number of baskets made until a miss

# The 'kobe' data frame is already loaded into the workspace. Assign Kobe's

# streak lengths:

kobe_streak = calc_streak(kobe$basket)

# Draw a barplot of the result:

barplot(table(kobe_streak))

# if there is a 'hot-hand' phenomenon... then prob a 'make' increases (relavitive to shooting percentage

# GIVEN that he 'made' previous shot... Then events (aka shots) are NOT independent events...

# Try some simulations! Next line simulates a coin flip where function 'c' reps 'coin'...

outcomes = c("heads", "tails")

# with one flip... w / replacement... think of pulling slips of paper from hat with 'H' or 'T' ... 'replace=TRUE'

sample(outcomes, size=1,replace=TRUE)

# Try 100 'flips'

outcomes = c("heads", "tails")

sim_fair_coin = sample(outcomes, size = 100, replace = TRUE)

# Print the object:

sim_fair_coin

# Compute the counts of heads and tails:

table(sim_fair_coin)

# Run 'unfair' coin simulation:

outcomes = c("heads", "tails")

sim_unfair_coin = sample(outcomes, size = 100, replace = TRUE, prob = c(0.2,0.8)) 0.8))

# Print the object:

sim_unfair_coin

# Compute the counts of heads and tails:

table(sim_unfair_coin)

# Run the simulation, to be comparted later with the 'kobe' data... 133 shots on basket... same percentages

# assign it to variable 'sim_basket'

outcomes = c("H", "M")

sim_basket = sample(outcomes, size = 133, replace = TRUE, prob = c(0.45,0.55))

sim_basket

table(sim_basket)