Homework_09

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# FUNCTION: sim_treat_data

# purpose: Simulates treatment data between two groups of n size drawn from two separate normal distributions wiht parameters mean and sd as defined by user. both starting variable (weight for example) population of groups A and B are drawn from a normal distribution as well as the change in that variable dependant on treatment (ie. change in weight). In the end it calculates the result from the start + change in start variable = end variable. 

# input: number of samples for each treatment (nA,NB), means start_Var (mean_A, mean_B), standard deviation of each start_Var (sd_A, sd_B), change in means of each treatment(dmean_A, dmean_B) and standard deviation of each treatment (dsd_A, dsd_B).

# output:  returns 1. a boxplot of the two treatment groups measuring the end-result of each treatment being compaired 2. A t test compairing the changes between the two groups. 
# ------------------------------------------
sim_treat_data <- function(n_A=30, n_B=30, mean_A=33.5, mean_B=33.5, sd_A=10, sd_B=10, dmean_A=3, dmean_B=3, dsd_A=1, dsd_B=1) {
  
  library(tidyverse)

  #Simulate Datasets
  start_Var_A <- rnorm(n=n_A, mean=mean_A, sd=sd_A)
  start_Var_B <- rnorm(n=n_B, mean=mean_B, sd=sd_B)
  
  delta_Var_A <- rnorm(n=n_A, mean=dmean_A, sd=dsd_A) 
  delta_Var_B <- rnorm(n=n_B, mean=dmean_B, sd=dsd_B)
 
  start_Var <- c(start_Var_A, start_Var_B)
  delta_Var <- c(delta_Var_A, delta_Var_B) #must add up to start weight n
  treatment <- c(rep('A', n_A),rep('B', n_B)) # assign into groups A and B
  
  # compile into dataframe and calculate end weight
  d_frame <- data.frame(treatment, start_Var, delta_Var)
  d_frame <- mutate(.data = d_frame, end_Var = start_Var + delta_Var)
  
  #Graph data
  G <- ggplot(d_frame, aes(x=treatment, y=end_Var)) + 
    geom_boxplot()
  print(G)
  
  #t.test between final weights of each treatment group
  t_test <- t.test(data = d_frame, end_Var ~ treatment)
  print(c('p.value= ', t_test$p.value))
  
  ### ScatterPlot of the two groups
  
  G2 <- ggplot(data=d_frame, aes(x = start_Var, y = end_Var, color = treatment)) +
  geom_point(shape = 17, size = 2)
  print(G2)
}

Simulating Data with two treatment groups drawn from different normal distributions but with the same parameters. the delta_mean of the change in Variable_A has been changed for each of these groups to demonstrate the differences two treatments could cause in Varailbe_A as the resulting end_Variable (end_Var)

sim_treat_data(dmean_A=10, dmean_B=3)

## Warning: package 'tidyverse' was built under R version 4.1.2

## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --

## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.5     v dplyr   1.0.7
## v tidyr   1.1.4     v stringr 1.4.0
## v readr   2.0.2     v forcats 0.5.1

## Warning: package 'ggplot2' was built under R version 4.1.2

## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

## [1] "p.value= "         "0.194213382117346"

Making a For loop for running multiple parameters.

dmean_A = 3,6,9 ; dmean_B = 3,3,3

for(i in 1:3) {
  print(c('average change in group_A=',3*i, 'average change in group_b= 3'))
  sim_treat_data(dmean_A=3*i)
}

## [1] "average change in group_A="   "3"                           
## [3] "average change in group_b= 3"

## [1] "p.value= "         "0.926621370089444"

## [1] "average change in group_A="   "6"                           
## [3] "average change in group_b= 3"

## [1] "p.value= "         "0.729220480805366"

## [1] "average change in group_A="   "9"                           
## [3] "average change in group_b= 3"

## [1] "p.value= "           "0.00861887489604542"