2 Randomized Complete Block Design (RCBD)

Following the in-class assignment this week, perform a complete RCBD analysis.

  1. (2 p) Reshape and plot the data, describe relationships of Sales between Items and Restaurants
  2. (0 p) Fit model
  3. (3 p) Assess model assumptions
  4. (2 p) State and interpret the hypothesis test for difference in Item mean sales
  5. (2 p) If appropriate, perform pairwise comparisons with Tukey HSD correction
  6. (1 p) What is your recommendation to the Franchise?

2.1 Data

library(tidyverse)

# load ada functions
source("ada_functions.R")

# read the data
dat_food <- read.table(text="
Restaurant Item1 Item2 Item3
A          31    27    24
B          31    28    31
C          45    29    46
D          21    18    48
E          42    36    46
F          32    17    40
", header = TRUE) %>%
  as_tibble()

2.2 (2 p) Reshape and plot the data, describe relationships of Sales between Items and Restaurants

The code below will get you started with reshaping the data. The rest is up to you!

dat_food_long <-
  dat_food %>%
  pivot_longer(
    cols      = starts_with("Item")
  , names_to  = "Item"
  , values_to = "Sales"
  ) %>%
  mutate(
    Item       = factor(Item)
  , Restaurant = factor(Restaurant)
  )

str(dat_food_long)
tibble [18 x 3] (S3: tbl_df/tbl/data.frame)
 $ Restaurant: Factor w/ 6 levels "A","B","C","D",..: 1 1 1 2 2 2 3 3 3 4 ...
 $ Item      : Factor w/ 3 levels "Item1","Item2",..: 1 2 3 1 2 3 1 2 3 1 ...
 $ Sales     : int [1:18] 31 27 24 31 28 31 45 29 46 21 ...
# Group means
m_dat_b <-
  dat_food_long %>%
  group_by(Item) %>%
  summarize(
    m = mean(Sales)
  )
m_dat_b
# A tibble: 3 x 2
  Item      m
  <fct> <dbl>
1 Item1  33.7
2 Item2  25.8
3 Item3  39.2
m_dat_c <-
  dat_food_long %>%
  group_by(Restaurant) %>%
  summarize(
    m = mean(Sales)
  )
m_dat_c
# A tibble: 6 x 2
  Restaurant     m
  <fct>      <dbl>
1 A           27.3
2 B           30  
3 C           40  
4 D           29  
5 E           41.3
6 F           29.7

2.3 (0 p) Fit model

2.4 (3 p) Assess model assumptions

2.5 (2 p) State and interpret the hypothesis test for difference in Item mean sales

2.6 (2 p) If appropriate, perform pairwise comparisons with Tukey HSD correction

2.7 (1 p) What is your recommendation to the Franchise?