Homework 10: For Loops and Randomization tests

Question 1 Directions: Using a for loop, write a function to calculate the number of zeroes in a numeric vector. Before entering the loop, set up a counter variable counter <- 0. Inside the loop, add 1 to counter each time you have a zero in the matrix. Finally, use return(counter) for the output.

counter <- 0
num_vector<-c(0,0,0,0,3,4,5,3,6,7,5,3,2,4,2,1,4,6,9,0,3,4,7,8,0,2,34,56,6,9,0,2,3,56,7,8,9,0,2,2,4,4,6,7,9,9,0,0,8,7,5)
for (i in 1:length(num_vector)) {
  if(num_vector[i]==0) {
    counter <- counter+1
  }
}
print(counter)

## [1] 10

Question 2 Directions: Use subsetting instead of a loop to rewrite the function as a single line of code.

num_vector_sub <-length(num_vector[num_vector==0])
print(num_vector_sub)

## [1] 10

Question 3 Directions: Write a function that takes as input two integers representing the number of rows and columns in a matrix. The output is a matrix of these dimensions in which each element is the product of the row number x the column number.

#############################################
# FUNCTION: my_function
# input:two integers representing the number of rows and columns in a matrix
# output: a matrix of these dimensions in which each element is the product of the row number x the column number
# -------------------------------------------
my_function <- function(x=5, y=5) {
  mat <- matrix(sample(runif(10), size=x*y, replace=TRUE),
              nrow=x,
              ncol=y)
    for(i in 1:x) {
      for(j in 1:y){
        mat[i,j] <- i*j
      }
    } 
  return(mat)
}  
print(my_function())

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    2    3    4    5
## [2,]    2    4    6    8   10
## [3,]    3    6    9   12   15
## [4,]    4    8   12   16   20
## [5,]    5   10   15   20   25

Question 4a-d Directions:

Simulate a dataset with 3 groups of data, each group drawn from a distribution with a different mean. The final data frame should have 1 column for group and 1 column for the response variable.
Write a custom function that 1) reshuffles the response variable, and 2) calculates the mean of each group in the reshuffled data. Store the means in a vector of length 3.
Use a for loop to repeat the function in b 100 times. Store the results in a data frame that has 1 column indicating the replicate number and 1 column for each new group mean, for a total of 4 columns.
Use qplot() to create a histogram of the means for each reshuffled group. Or, if you want a challenge, use ggplot() to overlay all 3 histograms in the same figure. How do the distributions of reshuffled means compare to the original means?

# Part a, simulating a data set 
three_groups <- c(rep("group_1",4),rep("group_2",5), rep("group_3",3))
print(three_groups)

##  [1] "group_1" "group_1" "group_1" "group_1" "group_2" "group_2" "group_2"
##  [8] "group_2" "group_2" "group_3" "group_3" "group_3"

response_variable <- c(runif(4)+3, runif(5)+7, runif(3)-0.5)
print(response_variable)

##  [1]  3.21041973  3.77519260  3.83654354  3.62866688  7.59105523  7.57911946
##  [7]  7.46562993  7.70913067  7.43242684  0.40827959 -0.06492981  0.07491984

df<- data.frame(group=three_groups,res=response_variable)
print(df)

##      group         res
## 1  group_1  3.21041973
## 2  group_1  3.77519260
## 3  group_1  3.83654354
## 4  group_1  3.62866688
## 5  group_2  7.59105523
## 6  group_2  7.57911946
## 7  group_2  7.46562993
## 8  group_2  7.70913067
## 9  group_2  7.43242684
## 10 group_3  0.40827959
## 11 group_3 -0.06492981
## 12 group_3  0.07491984

# part b, custom function
df_sim <- df
df_sim$res <- sample(df_sim$res)
print(df_sim)

##      group         res
## 1  group_1  3.77519260
## 2  group_1  7.43242684
## 3  group_1  0.40827959
## 4  group_1  3.21041973
## 5  group_2  7.59105523
## 6  group_2  3.83654354
## 7  group_2 -0.06492981
## 8  group_2  3.62866688
## 9  group_2  0.07491984
## 10 group_3  7.70913067
## 11 group_3  7.57911946
## 12 group_3  7.46562993

sim <- tapply(df_sim$res,df$group,mean)
print(sim)

##  group_1  group_2  group_3 
## 3.706580 3.013251 7.584627

sim_vector <- as.vector(sim)
print(sim_vector)

## [1] 3.706580 3.013251 7.584627

# Part c, for loop
##################################################
# function: shuffle_data
# Purpose: use for loop to repeat function 100 times
# input: means of shuffled response variables in vector form
# output: 4-column data frame (replicate #, group mean 1, group mean2, group mean 3)
#------------------------------------------------- 
shuffle_data <-  function(data=NULL) {
  data$res <- sample(data$res)
                 
return(data)
}
shuffle_data(df)

##      group         res
## 1  group_1  7.57911946
## 2  group_1  7.43242684
## 3  group_1  3.77519260
## 4  group_1  3.62866688
## 5  group_2  7.59105523
## 6  group_2  7.46562993
## 7  group_2  0.40827959
## 8  group_2  3.83654354
## 9  group_2  7.70913067
## 10 group_3  0.07491984
## 11 group_3  3.21041973
## 12 group_3 -0.06492981

get_metric <- function(data=NULL) {
. <- summary(aov(data=data,res~group))
p_val <- .[[1]][["Pr(>F)"]][1]

return(p_val)
}
get_pval <- function(z=NULL) {
                    if(is.null(z)){
                      z <- list(x_obs=runif(1),x_sim=runif(1000))}
                      p_lower <- mean(z[[2]]<=z[[1]])
                      p_upper <- mean(z[[2]]>=z[[1]])
return(c(pl=p_lower,pu=p_upper))
                    }          
n_sim <- 100
x_sim <- rep(NA,n_sim) # vector of simulated slopes
df <- df
x_obs <- get_metric(df)
for (i in seq_len(n_sim)) {
x_sim[i] <- get_metric(shuffle_data(df))
}
head(x_sim)

## [1] 0.8454053 0.5278592 0.5680170 0.2110502 0.1069622 0.6178352

p_value <- list(x_obs,x_sim)
get_pval(p_value)

## pl pu 
##  0  1

library(ggplot2)
plot_ran_test <- function(z=NULL) {
                if(is.null(z)){
                  z <- list(rnorm(1),rnorm(1000)) }
df <- data.frame(ID=seq_along(z[[2]]),sim_x=z[[2]])

p1 <- ggplot(data=df) + 
       aes(x=sim_x)

p1 + geom_histogram(aes(fill=I("goldenrod"),
                        color=I("black"))) +
     geom_vline(aes(xintercept=z[[1]],
               col="blue")) 

                  }

plot_ran_test(p_value)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Homework_10

Grace Durant

3/30/2022

Homework 10: For Loops and Randomization tests

Question 1 Directions: Using a for loop, write a function to calculate the number of zeroes in a numeric vector. Before entering the loop, set up a counter variable counter <- 0. Inside the loop, add 1 to counter each time you have a zero in the matrix. Finally, use return(counter) for the output.

Question 2 Directions: Use subsetting instead of a loop to rewrite the function as a single line of code.

Question 3 Directions: Write a function that takes as input two integers representing the number of rows and columns in a matrix. The output is a matrix of these dimensions in which each element is the product of the row number x the column number.

Question 4a-d Directions: