Coursera Statistics One Week 5 Assignment 5

Suppose an experiment was conducted to test whether Working Memory (WM) training works as well as Study Program (SP) training
to boost performance on a university admission test (UAT). Assume that high school students were recruited and randomly assigned
to ONE (1) of TWO (2) conditions: WM training or SP training. Further assume that EACH student was tested on the UAT BEFORE and
AFTER training (so we have pre- and post-training scores on the UAT). Use the data in DAA.04.txt.

Round to TWO (2) significant digits (for example, if the correlation is .456 then write .46).

library(psych)

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Init <- function(fileStr, workDirStr = "C:/Users/denbrige/100 FxOption/103 FxOptionVerBack/080 Fx Git/R-nonsource") {
    setwd(workDirStr)
    retDfr <- read.table(fileStr, header = T)
    return(retDfr)
}

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# --- Init loading raw data
rawDfr <- Init("DAA.04.txt")

# --- Count of raw data
nrow(rawDfr)

## [1] 40

# --- Names of header
names(rawDfr)

## [1] "training" "pre.uat"  "post.uat" "gain"

# --- Create subsets of data for EACH group
wmDfr <- subset(rawDfr, rawDfr$training == "WM")
spDfr <- subset(rawDfr, rawDfr$training == "SP")

# --- Dependent t-test for SP group
t.test(spDfr$pre.uat, spDfr$post.uat, paired = T)

## 
##  Paired t-test
## 
## data:  spDfr$pre.uat and spDfr$post.uat 
## t = -5.685, df = 19, p-value = 1.763e-05
## alternative hypothesis: true difference in means is not equal to 0 
## 95 percent confidence interval:
##  -31.47 -14.53 
## sample estimates:
## mean of the differences 
##                     -23

# --- Calculate effect size for dependent t-test (Cohen's d value) d =
# (Mean(X) - 0) / SD(X), pop mean = 0
spDescDfr <- describe(spDfr)
spDescDfr[4, 3]/spDescDfr[4, 4]

## [1] 1.271

# --- Dependent t-test for WM group
t.test(wmDfr$pre.uat, wmDfr$post.uat, paired = T)

## 
##  Paired t-test
## 
## data:  wmDfr$pre.uat and wmDfr$post.uat 
## t = -4.199, df = 19, p-value = 0.0004863
## alternative hypothesis: true difference in means is not equal to 0 
## 95 percent confidence interval:
##  -28.47  -9.53 
## sample estimates:
## mean of the differences 
##                     -19

# --- Calculate effect size for dependent t-test (Cohen's d value) d =
# (Mean(X) - 0) / SD(X), pop mean = 0
wmDescDfr <- describe(wmDfr)
wmDescDfr[4, 3]/wmDescDfr[4, 4]

## [1] 0.9389

# --- Independent t-test
t.test(rawDfr$gain ~ rawDfr$training, var.equal = T)

## 
##  Two Sample t-test
## 
## data:  rawDfr$gain by rawDfr$training 
## t = 0.659, df = 38, p-value = 0.5139
## alternative hypothesis: true difference in means is not equal to 0 
## 95 percent confidence interval:
##  -8.288 16.288 
## sample estimates:
## mean in group SP mean in group WM 
##               23               19

# --- Calculate effect size for independent t-test SD_Pooled ^ 2 =
# (DF_1/DF_Total) * SD_1 ^ 2 + (DF_2/DF_Total) * SD_2 ^ 2 d = (Mean(X_1) -
# Mean(X_2)) / SD_Pooled
sdPooledNum <- sqrt(19/38 * spDescDfr[4, 4]^2 + 19/38 * wmDescDfr[4, 4]^2)
(spDescDfr[4, 3] - wmDescDfr[4, 3])/sdPooledNum

## [1] 0.2084

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