CoCalc -- ANOVA Practice Script-Arin.ipynb

Project: Sanctuary

Path: ANOVA Practice Problem/ANOVA Practice Script-Arin.ipynb

Views: ¹¹²
License: GPL3

Kernel: R (R-Project)

In [1]:

library(xlsx) # library to import excel spreadsheets as data to analyze

Warning message:
“package ‘xlsx’ was built under R version 3.6.3”

In [0]:

In [7]:

# Importing the dataset
df.data <- read.xlsx("ANOVA Practice Data File.xlsx", sheetName = 1)

In [0]:

In [10]:

# Checking whether the data frame imported correctly
df.data

   ID Experience.Level     Blurriness.Level    Throughput
 1 No Experience        Not Blurred         1.314     
 2 No Experience        Not Blurred         1.219     
 3 Moderate Experience  Not Blurred         4.413     
 4 Moderate Experience  Not Blurred         4.612     
 5 Extensive Experience Not Blurred         4.752     
 6 Extensive Experience Not Blurred         4.432     
 7 No Experience        Moderately Blurred  1.114     
 8 No Experience        Moderately Blurred  1.119     
 9 Moderate Experience  Moderately Blurred  2.113     
10 Moderate Experience  Moderately Blurred  2.235     
11 Extensive Experience Moderately Blurred  4.443     
12 Extensive Experience Moderately Blurred  4.512     
13 No Experience        Extensively Blurred 0.295     
14 No Experience        Extensively Blurred 0.113     
15 Moderate Experience  Extensively Blurred 0.443     
16 Moderate Experience  Extensively Blurred 0.452     
17 Extensive Experience Extensively Blurred 2.113     
18 Extensive Experience Extensively Blurred 2.211     

In [6]:

# Checking the import results.'data.frame':	18 obs. of  4 variables:
str(df.data)

'data.frame':	18 obs. of  4 variables:
 $ ID              : num  1 2 3 4 5 6 7 8 9 10 ...
 $ Experience.Level: Factor w/ 3 levels "Extensive Experience",..: 3 3 2 2 1 1 3 3 2 2 ...
 $ Blurriness.Level: Factor w/ 3 levels "Extensively Blurred",..: 3 3 3 3 3 3 2 2 2 2 ...
 $ Throughput      : Factor w/ 17 levels "0.113","0.295",..: 8 7 12 16 17 13 5 6 9 11 ...

In [9]:

# Throughput was recorded as a factor variable; In reality, it should be a numeric variable.
# Hence, its data type needs to be changed to reflect this fact.
df.data$Throughput <- as.numeric(as.character (df.data$Throughput))

In [0]:

In [11]:

# Import the ggplot2 library to create graphs
library(ggplot2)

Warning message:
“package ‘ggplot2’ was built under R version 3.6.3”

In [12]:

# Plot the difference of means between experience levels
ggplot(df.data, aes(x = Experience.Level, y = Throughput)) + geom_point()

In [13]:

# Plot the difference of means between experience levels
ggplot(df.data, aes(x = Blurriness.Level, y = Throughput)) + geom_point()

In [0]:

In [16]:

# First ANOVA, testing all factors and all interaction effects
# There are three hypotheses we wish to test.
# 1. Does experience affect one's annotation throughput?
# 2. Does blurriness of the image being annotated affect one's annotation throughput?
# 3. Does one's experience mitigate the effect of blurriness (i.e. are skilled annotators less slowed down by blurriness?)
result <- aov(Throughput ~ Experience.Level + Blurriness.Level + Experience.Level*Blurriness.Level, data = df.data)

In [18]:

result2 <- aov(Throughput ~ Experience.Level + Blurriness.Level + Experience.Level*Blurriness.Level, data = df.data)

In [0]:

In [15]:

# Check the results. What do you see?
summary(result)

                                  Df Sum Sq Mean Sq F value   Pr(>F)    
Experience.Level                   2 24.932  12.466  1051.0 2.16e-11 ***
Blurriness.Level                   2 19.653   9.826   828.4 6.26e-11 ***
Experience.Level:Blurriness.Level  4  5.838   1.460   123.1 7.55e-08 ***
Residuals                          9  0.107   0.012                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In [19]:

# Check the results for the new ANOVA. What do you see?
summary(result2)

                                  Df Sum Sq Mean Sq F value   Pr(>F)    
Experience.Level                   2 24.932  12.466  1051.0 2.16e-11 ***
Blurriness.Level                   2 19.653   9.826   828.4 6.26e-11 ***
Experience.Level:Blurriness.Level  4  5.838   1.460   123.1 7.55e-08 ***
Residuals                          9  0.107   0.012                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In [20]:

# Remember that ANOVA by itself doesn't give information about which classes have higher or lower means
# To gain that information, an additional test (Tukey's )
TukeyHSD(result2)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = Throughput ~ Experience.Level + Blurriness.Level + Experience.Level * Blurriness.Level, data = df.data)

$Experience.Level
                                              diff       lwr       upr p adj
Moderate Experience-Extensive Experience -1.365833 -1.541392 -1.190274     0
No Experience-Extensive Experience       -2.881500 -3.057059 -2.705941     0
No Experience-Moderate Experience        -1.515667 -1.691226 -1.340108     0

$Blurriness.Level
                                            diff       lwr      upr p adj
Moderately Blurred-Extensively Blurred 1.6515000 1.4759409 1.827059 0e+00
Not Blurred-Extensively Blurred        2.5191667 2.3436075 2.694726 0e+00
Not Blurred-Moderately Blurred         0.8676667 0.6921075 1.043226 6e-07

$`Experience.Level:Blurriness.Level`
                                                                                    diff
Moderate Experience:Extensively Blurred-Extensive Experience:Extensively Blurred -1.7145
No Experience:Extensively Blurred-Extensive Experience:Extensively Blurred       -1.9580
Extensive Experience:Moderately Blurred-Extensive Experience:Extensively Blurred  2.3155
Moderate Experience:Moderately Blurred-Extensive Experience:Extensively Blurred   0.0120
No Experience:Moderately Blurred-Extensive Experience:Extensively Blurred        -1.0455
Extensive Experience:Not Blurred-Extensive Experience:Extensively Blurred         2.4300
Moderate Experience:Not Blurred-Extensive Experience:Extensively Blurred          2.3505
No Experience:Not Blurred-Extensive Experience:Extensively Blurred               -0.8955
No Experience:Extensively Blurred-Moderate Experience:Extensively Blurred        -0.2435
Extensive Experience:Moderately Blurred-Moderate Experience:Extensively Blurred   4.0300
Moderate Experience:Moderately Blurred-Moderate Experience:Extensively Blurred    1.7265
No Experience:Moderately Blurred-Moderate Experience:Extensively Blurred          0.6690
Extensive Experience:Not Blurred-Moderate Experience:Extensively Blurred          4.1445
Moderate Experience:Not Blurred-Moderate Experience:Extensively Blurred           4.0650
No Experience:Not Blurred-Moderate Experience:Extensively Blurred                 0.8190
Extensive Experience:Moderately Blurred-No Experience:Extensively Blurred         4.2735
Moderate Experience:Moderately Blurred-No Experience:Extensively Blurred          1.9700
No Experience:Moderately Blurred-No Experience:Extensively Blurred                0.9125
Extensive Experience:Not Blurred-No Experience:Extensively Blurred                4.3880
Moderate Experience:Not Blurred-No Experience:Extensively Blurred                 4.3085
No Experience:Not Blurred-No Experience:Extensively Blurred                       1.0625
Moderate Experience:Moderately Blurred-Extensive Experience:Moderately Blurred   -2.3035
No Experience:Moderately Blurred-Extensive Experience:Moderately Blurred         -3.3610
Extensive Experience:Not Blurred-Extensive Experience:Moderately Blurred          0.1145
Moderate Experience:Not Blurred-Extensive Experience:Moderately Blurred           0.0350
No Experience:Not Blurred-Extensive Experience:Moderately Blurred                -3.2110
No Experience:Moderately Blurred-Moderate Experience:Moderately Blurred          -1.0575
Extensive Experience:Not Blurred-Moderate Experience:Moderately Blurred           2.4180
Moderate Experience:Not Blurred-Moderate Experience:Moderately Blurred            2.3385
No Experience:Not Blurred-Moderate Experience:Moderately Blurred                 -0.9075
Extensive Experience:Not Blurred-No Experience:Moderately Blurred                 3.4755
Moderate Experience:Not Blurred-No Experience:Moderately Blurred                  3.3960
No Experience:Not Blurred-No Experience:Moderately Blurred                        0.1500
Moderate Experience:Not Blurred-Extensive Experience:Not Blurred                 -0.0795
No Experience:Not Blurred-Extensive Experience:Not Blurred                       -3.3255
No Experience:Not Blurred-Moderate Experience:Not Blurred                        -3.2460
                                                                                        lwr
Moderate Experience:Extensively Blurred-Extensive Experience:Extensively Blurred -2.1453544
No Experience:Extensively Blurred-Extensive Experience:Extensively Blurred       -2.3888544
Extensive Experience:Moderately Blurred-Extensive Experience:Extensively Blurred  1.8846456
Moderate Experience:Moderately Blurred-Extensive Experience:Extensively Blurred  -0.4188544
No Experience:Moderately Blurred-Extensive Experience:Extensively Blurred        -1.4763544
Extensive Experience:Not Blurred-Extensive Experience:Extensively Blurred         1.9991456
Moderate Experience:Not Blurred-Extensive Experience:Extensively Blurred          1.9196456
No Experience:Not Blurred-Extensive Experience:Extensively Blurred               -1.3263544
No Experience:Extensively Blurred-Moderate Experience:Extensively Blurred        -0.6743544
Extensive Experience:Moderately Blurred-Moderate Experience:Extensively Blurred   3.5991456
Moderate Experience:Moderately Blurred-Moderate Experience:Extensively Blurred    1.2956456
No Experience:Moderately Blurred-Moderate Experience:Extensively Blurred          0.2381456
Extensive Experience:Not Blurred-Moderate Experience:Extensively Blurred          3.7136456
Moderate Experience:Not Blurred-Moderate Experience:Extensively Blurred           3.6341456
No Experience:Not Blurred-Moderate Experience:Extensively Blurred                 0.3881456
Extensive Experience:Moderately Blurred-No Experience:Extensively Blurred         3.8426456
Moderate Experience:Moderately Blurred-No Experience:Extensively Blurred          1.5391456
No Experience:Moderately Blurred-No Experience:Extensively Blurred                0.4816456
Extensive Experience:Not Blurred-No Experience:Extensively Blurred                3.9571456
Moderate Experience:Not Blurred-No Experience:Extensively Blurred                 3.8776456
No Experience:Not Blurred-No Experience:Extensively Blurred                       0.6316456
Moderate Experience:Moderately Blurred-Extensive Experience:Moderately Blurred   -2.7343544
No Experience:Moderately Blurred-Extensive Experience:Moderately Blurred         -3.7918544
Extensive Experience:Not Blurred-Extensive Experience:Moderately Blurred         -0.3163544
Moderate Experience:Not Blurred-Extensive Experience:Moderately Blurred          -0.3958544
No Experience:Not Blurred-Extensive Experience:Moderately Blurred                -3.6418544
No Experience:Moderately Blurred-Moderate Experience:Moderately Blurred          -1.4883544
Extensive Experience:Not Blurred-Moderate Experience:Moderately Blurred           1.9871456
Moderate Experience:Not Blurred-Moderate Experience:Moderately Blurred            1.9076456
No Experience:Not Blurred-Moderate Experience:Moderately Blurred                 -1.3383544
Extensive Experience:Not Blurred-No Experience:Moderately Blurred                 3.0446456
Moderate Experience:Not Blurred-No Experience:Moderately Blurred                  2.9651456
No Experience:Not Blurred-No Experience:Moderately Blurred                       -0.2808544
Moderate Experience:Not Blurred-Extensive Experience:Not Blurred                 -0.5103544
No Experience:Not Blurred-Extensive Experience:Not Blurred                       -3.7563544
No Experience:Not Blurred-Moderate Experience:Not Blurred                        -3.6768544
                                                                                        upr
Moderate Experience:Extensively Blurred-Extensive Experience:Extensively Blurred -1.2836456
No Experience:Extensively Blurred-Extensive Experience:Extensively Blurred       -1.5271456
Extensive Experience:Moderately Blurred-Extensive Experience:Extensively Blurred  2.7463544
Moderate Experience:Moderately Blurred-Extensive Experience:Extensively Blurred   0.4428544
No Experience:Moderately Blurred-Extensive Experience:Extensively Blurred        -0.6146456
Extensive Experience:Not Blurred-Extensive Experience:Extensively Blurred         2.8608544
Moderate Experience:Not Blurred-Extensive Experience:Extensively Blurred          2.7813544
No Experience:Not Blurred-Extensive Experience:Extensively Blurred               -0.4646456
No Experience:Extensively Blurred-Moderate Experience:Extensively Blurred         0.1873544
Extensive Experience:Moderately Blurred-Moderate Experience:Extensively Blurred   4.4608544
Moderate Experience:Moderately Blurred-Moderate Experience:Extensively Blurred    2.1573544
No Experience:Moderately Blurred-Moderate Experience:Extensively Blurred          1.0998544
Extensive Experience:Not Blurred-Moderate Experience:Extensively Blurred          4.5753544
Moderate Experience:Not Blurred-Moderate Experience:Extensively Blurred           4.4958544
No Experience:Not Blurred-Moderate Experience:Extensively Blurred                 1.2498544
Extensive Experience:Moderately Blurred-No Experience:Extensively Blurred         4.7043544
Moderate Experience:Moderately Blurred-No Experience:Extensively Blurred          2.4008544
No Experience:Moderately Blurred-No Experience:Extensively Blurred                1.3433544
Extensive Experience:Not Blurred-No Experience:Extensively Blurred                4.8188544
Moderate Experience:Not Blurred-No Experience:Extensively Blurred                 4.7393544
No Experience:Not Blurred-No Experience:Extensively Blurred                       1.4933544
Moderate Experience:Moderately Blurred-Extensive Experience:Moderately Blurred   -1.8726456
No Experience:Moderately Blurred-Extensive Experience:Moderately Blurred         -2.9301456
Extensive Experience:Not Blurred-Extensive Experience:Moderately Blurred          0.5453544
Moderate Experience:Not Blurred-Extensive Experience:Moderately Blurred           0.4658544
No Experience:Not Blurred-Extensive Experience:Moderately Blurred                -2.7801456
No Experience:Moderately Blurred-Moderate Experience:Moderately Blurred          -0.6266456
Extensive Experience:Not Blurred-Moderate Experience:Moderately Blurred           2.8488544
Moderate Experience:Not Blurred-Moderate Experience:Moderately Blurred            2.7693544
No Experience:Not Blurred-Moderate Experience:Moderately Blurred                 -0.4766456
Extensive Experience:Not Blurred-No Experience:Moderately Blurred                 3.9063544
Moderate Experience:Not Blurred-No Experience:Moderately Blurred                  3.8268544
No Experience:Not Blurred-No Experience:Moderately Blurred                        0.5808544
Moderate Experience:Not Blurred-Extensive Experience:Not Blurred                  0.3513544
No Experience:Not Blurred-Extensive Experience:Not Blurred                       -2.8946456
No Experience:Not Blurred-Moderate Experience:Not Blurred                        -2.8151456
                                                                                     p adj
Moderate Experience:Extensively Blurred-Extensive Experience:Extensively Blurred 0.0000016
No Experience:Extensively Blurred-Extensive Experience:Extensively Blurred       0.0000005
Extensive Experience:Moderately Blurred-Extensive Experience:Extensively Blurred 0.0000001
Moderate Experience:Moderately Blurred-Extensive Experience:Extensively Blurred  1.0000000
No Experience:Moderately Blurred-Extensive Experience:Extensively Blurred        0.0001005
Extensive Experience:Not Blurred-Extensive Experience:Extensively Blurred        0.0000001
Moderate Experience:Not Blurred-Extensive Experience:Extensively Blurred         0.0000001
No Experience:Not Blurred-Extensive Experience:Extensively Blurred               0.0003473
No Experience:Extensively Blurred-Moderate Experience:Extensively Blurred        0.4557486
Extensive Experience:Moderately Blurred-Moderate Experience:Extensively Blurred  0.0000000
Moderate Experience:Moderately Blurred-Moderate Experience:Extensively Blurred   0.0000015
No Experience:Moderately Blurred-Moderate Experience:Extensively Blurred         0.0031144
Extensive Experience:Not Blurred-Moderate Experience:Extensively Blurred         0.0000000
Moderate Experience:Not Blurred-Moderate Experience:Extensively Blurred          0.0000000
No Experience:Not Blurred-Moderate Experience:Extensively Blurred                0.0006952
Extensive Experience:Moderately Blurred-No Experience:Extensively Blurred        0.0000000
Moderate Experience:Moderately Blurred-No Experience:Extensively Blurred         0.0000005
No Experience:Moderately Blurred-No Experience:Extensively Blurred               0.0002994
Extensive Experience:Not Blurred-No Experience:Extensively Blurred               0.0000000
Moderate Experience:Not Blurred-No Experience:Extensively Blurred                0.0000000
No Experience:Not Blurred-No Experience:Extensively Blurred                      0.0000881
Moderate Experience:Moderately Blurred-Extensive Experience:Moderately Blurred   0.0000001
No Experience:Moderately Blurred-Extensive Experience:Moderately Blurred         0.0000000
Extensive Experience:Not Blurred-Extensive Experience:Moderately Blurred         0.9686083
Moderate Experience:Not Blurred-Extensive Experience:Moderately Blurred          0.9999912
No Experience:Not Blurred-Extensive Experience:Moderately Blurred                0.0000000
No Experience:Moderately Blurred-Moderate Experience:Moderately Blurred          0.0000915
Extensive Experience:Not Blurred-Moderate Experience:Moderately Blurred          0.0000001
Moderate Experience:Not Blurred-Moderate Experience:Moderately Blurred           0.0000001
No Experience:Not Blurred-Moderate Experience:Moderately Blurred                 0.0003127
Extensive Experience:Not Blurred-No Experience:Moderately Blurred                0.0000000
Moderate Experience:Not Blurred-No Experience:Moderately Blurred                 0.0000000
No Experience:Not Blurred-No Experience:Moderately Blurred                       0.8815911
Moderate Experience:Not Blurred-Extensive Experience:Not Blurred                 0.9965769
No Experience:Not Blurred-Extensive Experience:Not Blurred                       0.0000000
No Experience:Not Blurred-Moderate Experience:Not Blurred                        0.0000000

In [21]:

# Extracting residuals from the ANOVA results
df.data$residuals2 <- result2$residuals

In [22]:

# Performing a normality test on the residuals
shapiro.test(df.data$residuals2)

	Shapiro-Wilk normality test

data:  df.data$residuals2
W = 0.99231, p-value = 0.9998

In [24]:

# Performing a homoscedasticity test on the residuals for blurriness level
library(car)
leveneTest(residuals2 ~ Experience.Level, data = df.data)

Warning message:
“package ‘car’ was built under R version 3.6.3”Loading required package: carData

      Df F value   Pr(>F)   
group  2 0.8023609 0.4666029
      15        NA        NA

In [25]:

#Performing a homoscedasticity test on the residuals for blurriness level
leveneTest(residuals2 ~ Blurriness.Level, data = df.data)

      Df F value  Pr(>F)    
group  2 5.103015 0.02038925
      15       NA         NA

In [0]: