Practice 3¶

1. Make a plot of the standard normal curve on the interval [-4, 4]. Give the plot a title “Standard normal curve”, an x label of “Normal deviate” and a y label of “Density”.

x <- pretty(-4:4, n=100)
y <- dnorm(x)
plot(x, y, type="l", main="Standard normal curve", xlab="Normal deviate", ylab="Density")

2. What is the area under the curve to the right of x=3? In other words, what is the probability of drawing a random number from the normal distribution that is 3 standard deviations or more larger than the mean?

1 - pnorm(3)

3. If the expression valuse for a gene are normally distributed with mean 10 and standard deviation 2, what is the value of a gene at the 95th percentile?

qnorm(0.95, mean=10, sd=2)

Generate 50 numbers from a normal distribtuion with mean=10 and sd=2. Now trnaform this vector so that the numbers have a stnadard normal distribtuion with mean=0 and sd=1.

x <- rnorm(50, 10, 2)
z <- (x - mean(x))/sd(x)

4. A t-test with 6 degrees of freedom has a score of 3.5. Using only the dt, pt, qt or rt probability functions, what is the p-value if this was a two-sided test? Recall that a p-value is the probailty of seeing a value as extreme or more extreme than the observed score, assuming the score was drawn from the specified distirbution.

2*(1 - pt(3.5, df = 6))

5. Draw 1 million random numbers from the t-distirbution with 6 degrees of freedom. How many times is the numbr less than -3.5 or greater than 3.5?

x <- rt(100000, df=6)
sum(abs(x) > 3.5)

6. Find the mean value of all numeric variables for the mtcars data, grouping by number of gears and automtatic or manual transmission. (Hint: Use the aggregate function)

with(mtcars, aggregate(mtcars, by=list(gear=gear, transmission=am), FUN=mean))

library(plyr)
library(reshape2)
data(airquality)

Warning message:
: package ‘plyr’ was built under R version 3.1.3

head(airquality)

7. Use melt to convert the airquality dataframe into a “tall” format using Month and Day as teh id variables, saving it as a new datafrmae. Print the first 6 rows.

md <- melt(airquality, id=c("Month", "Day"))
head(md)

8. Find the avarage values of Ozone, Solar.R, Wind and Temp for each month using dcast. Hint: Give an extra argument na.rm = TRUE to ignore missing data.

dcast(md, Month ~ variable, mean, na.rm = TRUE)

9. Find the avarage values of Ozone, Solar.R, Wind and Temp for each month using dcast, but only for the first 2 weeks of each month. Hint: Give an extra argument na.rm = TRUE to ignore missing data. Hint: Use the subset argument.

dcast(md, Month ~ variable, mean, subset = .(Day < 15), na.rm = TRUE)

Questions below use the day.1 and day.2 dataframes

set.seed(123)
pid.1 <- c(1,1,2,2)
gid.1 <- c(1,2,1,2)
val.1 <- rnorm(4)
day.1 <- data.frame(pid=pid.1, gid=gid.1, val=val.1)

pid.2 <- c(1,1,2,2)
gid.2 <- c(1,2,1,2)
val.2 <- 1 + rnorm(4)
day.2 <- data.frame(pid=pid.2, gid=gid.2, val=val.2)

day.1

day.2

10. Suppose day.1 and day.2 are results from experiments performed on differnet days. Merge the data from day.1 and day.2 into a single dataframe caleld days to combine the data sets.

days <- merge(day.1, day.2, by=c("pid", "gid"), suffixes = 1:2)

days

11. Sort the days dataframe by val1 in decreasing order.

days[order(-days$val1),]

(12) Remove duplicate rows from the following dataframe.

df <- read.csv("df.csv")
df

unique(df)