Weekly lab 5 (2k Factorial Design)
Enrique Cruz Avila
June 4, 2018
Weekly Lab 5 - 2k Factorial Design
The cheapskates at your firm have run a study using no replicants and a 25 design and have not told you what each effect is. The data is below. Find the meaningful effects, analyze the data, check your assumptions (particularly model fit), and provide a succinct write up of the final results.
## Warning: package 'readxl' was built under R version 3.4.4## # A tibble: 32 x 6
## `Effect A` `Effect B` `Effect C` `Effect D` `Effect E` Score
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1.00 0 0 0 0 24.0
## 2 0 1.00 0 1.00 0 89.4
## 3 0 1.00 1.00 0 1.00 80.7
## 4 1.00 0 1.00 0 0 39.5
## 5 0 1.00 1.00 0 0 85.0
## 6 1.00 1.00 1.00 0 1.00 98.9
## 7 1.00 1.00 0 0 0 69.4
## 8 0 0 0 0 1.00 85.8
## 9 0 1.00 0 1.00 1.00 96.2
## 10 0 1.00 1.00 1.00 0 29.1
## # ... with 22 more rowsLet’s take a quick look at the data
## Classes 'tbl_df', 'tbl' and 'data.frame': 32 obs. of 6 variables:
## $ Effect A: Factor w/ 2 levels "1","0": 1 2 2 1 2 1 1 2 2 2 ...
## $ Effect B: Factor w/ 2 levels "0","1": 1 2 2 1 2 2 2 1 2 2 ...
## $ Effect C: Factor w/ 2 levels "0","1": 1 1 2 2 2 2 1 1 1 2 ...
## $ Effect D: Factor w/ 2 levels "0","1": 1 2 1 1 1 1 1 1 2 2 ...
## $ Effect E: Factor w/ 2 levels "0","1": 1 1 2 1 1 2 1 2 2 1 ...
## $ Score : num 24 89.4 80.7 39.5 85 ...The data looks normally distributed
Anova model with all effects as K factors:
Model=aov(Score~`Effect A`*`Effect B`*`Effect C`*`Effect D`*`Effect E`,data=Effect_Study)
Model## Call:
## aov(formula = Score ~ `Effect A` * `Effect B` * `Effect C` *
## `Effect D` * `Effect E`, data = Effect_Study)
##
## Terms:
## `Effect A` `Effect B` `Effect C` `Effect D` `Effect E`
## Sum of Squares 151.136 597.410 605.254 81.561 2632.217
## Deg. of Freedom 1 1 1 1 1
## `Effect A`:`Effect B` `Effect A`:`Effect C`
## Sum of Squares 36.413 710.365
## Deg. of Freedom 1 1
## `Effect B`:`Effect C` `Effect A`:`Effect D`
## Sum of Squares 66.249 1869.242
## Deg. of Freedom 1 1
## `Effect B`:`Effect D` `Effect C`:`Effect D`
## Sum of Squares 242.641 61.499
## Deg. of Freedom 1 1
## `Effect A`:`Effect E` `Effect B`:`Effect E`
## Sum of Squares 52.785 568.453
## Deg. of Freedom 1 1
## `Effect C`:`Effect E` `Effect D`:`Effect E`
## Sum of Squares 483.372 2727.795
## Deg. of Freedom 1 1
## `Effect A`:`Effect B`:`Effect C`
## Sum of Squares 1737.083
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect D`
## Sum of Squares 677.161
## Deg. of Freedom 1
## `Effect A`:`Effect C`:`Effect D`
## Sum of Squares 344.857
## Deg. of Freedom 1
## `Effect B`:`Effect C`:`Effect D`
## Sum of Squares 187.909
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect E`
## Sum of Squares 206.578
## Deg. of Freedom 1
## `Effect A`:`Effect C`:`Effect E`
## Sum of Squares 47.622
## Deg. of Freedom 1
## `Effect B`:`Effect C`:`Effect E`
## Sum of Squares 143.770
## Deg. of Freedom 1
## `Effect A`:`Effect D`:`Effect E`
## Sum of Squares 1126.704
## Deg. of Freedom 1
## `Effect B`:`Effect D`:`Effect E`
## Sum of Squares 1529.165
## Deg. of Freedom 1
## `Effect C`:`Effect D`:`Effect E`
## Sum of Squares 250.561
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect C`:`Effect D`
## Sum of Squares 3257.936
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect C`:`Effect E`
## Sum of Squares 266.872
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect D`:`Effect E`
## Sum of Squares 26.557
## Deg. of Freedom 1
## `Effect A`:`Effect C`:`Effect D`:`Effect E`
## Sum of Squares 771.268
## Deg. of Freedom 1
## `Effect B`:`Effect C`:`Effect D`:`Effect E`
## Sum of Squares 607.804
## Deg. of Freedom 1
## `Effect A`:`Effect B`:`Effect C`:`Effect D`:`Effect E`
## Sum of Squares 1776.926
## Deg. of Freedom 1
##
## Estimated effects may be unbalanced