dt <- read.table("SI_quiz4.txt",header=TRUE)
dt
## Subject Baseline Week2
## 1 1 140 132
## 2 2 138 135
## 3 3 150 151
## 4 4 148 146
## 5 5 135 130
t<- t.test(x=dt$Baseline, y=dt$Week2, paired=TRUE)
t$p.value
## [1] 0.08652278
n <- 9
mean <- 1100
sd <- 30
p <- .95+(1-.95)/2
error <- qt(p,df=n-1)*sd/sqrt(n)
ci_low <- mean - error
ci_high <- mean + error
ci_low
## [1] 1076.94
ci_high
## [1] 1123.06
# Ha: Coke is preferred to Pepsi (p>0.5)
binom.test(c(3,1),p=0.5, alt="greater")$p.value
## [1] 0.3125
pbar <- 10/1787 # sample proportion
p0 <- 1/100 # hypothesized value
n <- 1787 # sample size
z <- (pbar-p0)/sqrt(p0*(1-p0)/n)
pval <- pnorm(z, lower.tail=TRUE)
pval
## [1] 0.03066625
# treatment
x1 <- -3
s1 <- 1.5
n1 <- 9
# placebo
x2 <- 1
s2 <- 1.8
n2 <- 9
# weighted sd
sp <- sqrt(((n1-1)*s1**2+(n2-1)*s2**2)/(n1+n2-2))
t <- (x1-x2)/(sp*sqrt(1/n1+1/n2))
pval <- 2*pt(t,df=n1+n2-1)
pval
## [1] 8.50523e-05
mu = 1078 falls in 1077- 1123 range, so you wouldn’t reject the H0.
n <- 100
mua <- 0.01
s <- 0.04
alpha <- 0.05
mu0 <- 0 # no brain volum loss
power.t.test(n=n, delta=mua-mu0, sd=s, type="one.sample", alt="one.sided", sig.level=alpha)$power
## [1] 0.7989855
mua <- 0.01
s <- 0.04
power <- 0.9
alpha <- 0.05
mu0 <- 0
power.t.test(power=power, delta=mua-mu0, sd=s, type="one.sample", alt="one.sided", sig.level=alpha)$n
## [1] 138.3856
Power increases as you increase alpha.