The data file Weeklylab8data.xlsx contains participant attractiveness ratings of three versions of a commercial product. Each participant was assigned to a focus group (4-6 participants were in each focus group) and everyone in the focus group rated the same version of the product on a scale from 0 to 100 (larger numbers more support for the product). Focus groups were constructed in several different cities across the NE. Standard demographic questions were included so that they could be used to vary out their potential effects. Analyze the data, being sure to take into account the nesting structure, and summarize the results.

library(readxl)
WeeklyLab8=read_excel("C:/Users/jcolu/OneDrive/Documents/Harrisburg/Summer 2018/ANLY 510/WeeklyLab8.xlsx")
WeeklyLab8
## # A tibble: 154 x 8
##    Participant FocusGroup City    Age Gender Income Version Rating
##          <dbl>      <dbl> <chr> <dbl>  <dbl>  <dbl>   <dbl>  <dbl>
##  1        1.00       1.00 PITT   20.0   0     56594    1.00   20.7
##  2        2.00       1.00 PITT   57.0   0    114612    1.00   31.8
##  3        3.00       1.00 PITT   63.0   0     63011    1.00   34.1
##  4        4.00       1.00 PITT   42.0   0     23596    1.00   31.6
##  5        5.00       1.00 PITT   51.0   1.00  85726    1.00   14.7
##  6        6.00       2.00 PITT   48.0   1.00 103276    2.00   43.7
##  7        7.00       2.00 PITT   58.0   0     77469    2.00   59.8
##  8        8.00       2.00 PITT   63.0   0     24615    2.00   54.7
##  9        9.00       2.00 PITT   19.0   1.00  86913    2.00   38.4
## 10       10.0        3.00 PITT   29.0   0     63328    3.00   60.9
## # ... with 144 more rows

Initial Data Analysis - using str function

str(WeeklyLab8)
## Classes 'tbl_df', 'tbl' and 'data.frame':    154 obs. of  8 variables:
##  $ Participant: num  1 2 3 4 5 6 7 8 9 10 ...
##  $ FocusGroup : num  1 1 1 1 1 2 2 2 2 3 ...
##  $ City       : chr  "PITT" "PITT" "PITT" "PITT" ...
##  $ Age        : num  20 57 63 42 51 48 58 63 19 29 ...
##  $ Gender     : num  0 0 0 0 1 1 0 0 1 0 ...
##  $ Income     : num  56594 114612 63011 23596 85726 ...
##  $ Version    : num  1 1 1 1 1 2 2 2 2 3 ...
##  $ Rating     : num  20.7 31.8 34.1 31.6 14.7 ...

Data Needs to be factorized

WeeklyLab8$FocusGroup <- factor(WeeklyLab8$FocusGroup)
WeeklyLab8$Gender <- factor(WeeklyLab8$Gender)
WeeklyLab8$Version <- factor(WeeklyLab8$Gender)
WeeklyLab8$Version <- factor(WeeklyLab8$Version)
WeeklyLab8$Participant <-factor(WeeklyLab8$Participant)

Review Factored data set

str(WeeklyLab8)
## Classes 'tbl_df', 'tbl' and 'data.frame':    154 obs. of  8 variables:
##  $ Participant: Factor w/ 154 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ FocusGroup : Factor w/ 32 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 3 ...
##  $ City       : chr  "PITT" "PITT" "PITT" "PITT" ...
##  $ Age        : num  20 57 63 42 51 48 58 63 19 29 ...
##  $ Gender     : Factor w/ 2 levels "0","1": 1 1 1 1 2 2 1 1 2 1 ...
##  $ Income     : num  56594 114612 63011 23596 85726 ...
##  $ Version    : Factor w/ 2 levels "0","1": 1 1 1 1 2 2 1 1 2 1 ...
##  $ Rating     : num  20.7 31.8 34.1 31.6 14.7 ...
plot(density(WeeklyLab8$Rating))

Graph reflects that data set is skewed

library(moments)
agostino.test(WeeklyLab8$Rating)
## 
##  D'Agostino skewness test
## 
## data:  WeeklyLab8$Rating
## skew = 0.41168, z = 2.10400, p-value = 0.03538
## alternative hypothesis: data have a skewness

Since Skewness is significatnt, it needs to be addressed.

agostino.test(log(WeeklyLab8$Rating))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating)
## skew = -1.3295, z = -5.5791, p-value = 2.417e-08
## alternative hypothesis: data have a skewness
agostino.test(log(WeeklyLab8$Rating+20))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating + 20)
## skew = -0.38009, z = -1.95170, p-value = 0.05097
## alternative hypothesis: data have a skewness
agostino.test(log(WeeklyLab8$Rating+40))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating + 40)
## skew = -0.15701, z = -0.82595, p-value = 0.4088
## alternative hypothesis: data have a skewness
agostino.test(log(WeeklyLab8$Rating+60))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating + 60)
## skew = -0.038325, z = -0.202620, p-value = 0.8394
## alternative hypothesis: data have a skewness
agostino.test(log(WeeklyLab8$Rating+80))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating + 80)
## skew = 0.03755, z = 0.19852, p-value = 0.8426
## alternative hypothesis: data have a skewness

Skwenewss is too much

agostino.test(log(WeeklyLab8$Rating+70))
## 
##  D'Agostino skewness test
## 
## data:  log(WeeklyLab8$Rating + 70)
## skew = 0.0032933, z = 0.0174170, p-value = 0.9861
## alternative hypothesis: data have a skewness
plot(density(log(WeeklyLab8$Rating+70)))

The graph can show that data is better evenly distributed.