Bioplastic

Determine if there is a significant difference between the average thickness of the Control Group, Experimental Group A, and Experimental Group B.

Result

Kruskal-Wallis Test

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(Thickness), Mean = mean(Thickness), SD = sd(Thickness))

## # A tibble: 3 x 4
##   Group   Count  Mean     SD
##   <chr>   <int> <dbl>  <dbl>
## 1 Control     5 0.150 0.0569
## 2 GroupA      5 0.104 0.0146
## 3 GroupB      5 0.162 0.0549

kruskal.test(Thickness~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Thickness by Group
## Kruskal-Wallis chi-squared = 6.02, df = 2, p-value = 0.04929

boxplot(Thickness~Group, data1)

Post-Hoc Analysis using Dunn Test

dunn_test(data1, Thickness~Group, p.adjust.method = "none")

## # A tibble: 3 x 9
##   .y.       group1  group2    n1    n2 statistic      p  p.adj p.adj.signif
## * <chr>     <chr>   <chr>  <int> <int>     <dbl>  <dbl>  <dbl> <chr>       
## 1 Thickness Control GroupA     5     5    -2.05  0.0403 0.0403 *           
## 2 Thickness Control GroupB     5     5     0.141 0.888  0.888  ns          
## 3 Thickness GroupA  GroupB     5     5     2.19  0.0284 0.0284 *

Initial Analysis

boxplot(Thickness~Group, data1)

normality2(data1$Thickness, data1$Group, data1)

## T statistic of Raw Data:  3.540633 
## T statistic of Rank Data:  5.61607 
## Difference:  2.075437 
## 
## Decision: Assume that the variables are not normally distirubted and use Kruskal-Wallis Test

Determine if there is a significant difference between the average water solubilities of the Control Group, Experimental Group A, and Experimental Group B.

Result

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(Solubility), Mean = mean(Solubility), SD = sd(Solubility))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  23.5  13.7
## 2 GroupA      5  33.5  12.0
## 3 GroupB      5  25.2  14.5

kruskal.test(Solubility~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Solubility by Group
## Kruskal-Wallis chi-squared = 1.5, df = 2, p-value = 0.4724

boxplot(Solubility~Group, data1)

Initial Analysis

boxplot(Solubility~Group, data1)

normality2(data1$Solubility, data1$Group, data1)

## T statistic of Raw Data:  0.8278986 
## T statistic of Rank Data:  0.7006762 
## Difference:  0.1272223 
## 
## Decision: Assume that the variables are normally distirubted and use ANOVA. Check the number of observations per group

Determine if there is a significant difference between the compatibilities of the Control Group, Experimental Group A, and Experimental Group B when it comes to food item immersion

Result

Soy Sauce

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(WeighChangeSoySauce), Mean = mean(WeighChangeSoySauce), SD = sd(WeighChangeSoySauce))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  9.82 0.328
## 2 GroupA      5  9.78 1.41 
## 3 GroupB      5  9.59 0.860

kruskal.test(WeighChangeSoySauce~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  WeighChangeSoySauce by Group
## Kruskal-Wallis chi-squared = 0.78, df = 2, p-value = 0.6771

boxplot(WeighChangeSoySauce~Group, data1, ylab="Weight Change (Soy Sauce)")

Vegetable Oil

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(WeightChangeVegOil), Mean = mean(WeightChangeVegOil), SD = sd(WeightChangeVegOil))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5 24.7  28.6 
## 2 GroupA      5  4.67  1.66
## 3 GroupB      5  8.47  3.59

kruskal.test(WeightChangeVegOil~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  WeightChangeVegOil by Group
## Kruskal-Wallis chi-squared = 8.06, df = 2, p-value = 0.01777

boxplot(WeightChangeVegOil~Group, data1, ylab="Weight Change (Vegetable Oil)")

Post-Hoc Analysis using Dunn Test

dunn_test(data1, WeightChangeVegOil~Group)

## # A tibble: 3 x 9
##   .y.                group1  group2    n1    n2 statistic       p  p.adj p.adj.signif
## * <chr>              <chr>   <chr>  <int> <int>     <dbl>   <dbl>  <dbl> <chr>       
## 1 WeightChangeVegOil Control GroupA     5     5     -2.83 0.00468 0.0140 *           
## 2 WeightChangeVegOil Control GroupB     5     5     -1.20 0.229   0.229  ns          
## 3 WeightChangeVegOil GroupA  GroupB     5     5      1.63 0.104   0.208  ns

Vinegar

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(WeightChangeVinegar), Mean = median(WeightChangeVinegar), SD = sd(WeightChangeVinegar))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5 15.3   7.55
## 2 GroupA      5 16.9   3.63
## 3 GroupB      5  9.93  7.90

kruskal.test(WeightChangeVinegar~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  WeightChangeVinegar by Group
## Kruskal-Wallis chi-squared = 1.58, df = 2, p-value = 0.4538

boxplot(WeightChangeVinegar~Group, data1, ylab="Weight Change (Vinegar)")

Initial Analysis

Soy Sauce

boxplot(WeighChangeSoySauce~Group, data1)

normality2(data1$WeighChangeSoySauce, data1$Group, data1)

## T statistic of Raw Data:  0.1312943 
## T statistic of Rank Data:  0.2439794 
## Difference:  0.1126851 
## 
## Decision: Assume that the variables are normally distirubted and use ANOVA. Check the number of observations per group

Vegetable Oil

boxplot(WeightChangeVegOil~Group, data1)

normality2(data1$WeightChangeVegOil, data1$Group, data1)

## T statistic of Raw Data:  3.121098 
## T statistic of Rank Data:  10.02031 
## Difference:  6.899214 
## 
## Decision: Assume that the variables are not normally distirubted and use Kruskal-Wallis Test

Vinegar

boxplot(WeightChangeVinegar~Group, data1)

normality2(data1$WeightChangeVinegar, data1$Group, data1)

## T statistic of Raw Data:  1.681052 
## T statistic of Rank Data:  0.8388575 
## Difference:  0.8421948 
## 
## Decision: Assume that the variables are not normally distirubted and use Kruskal-Wallis Test

Determine if there is a significant difference between the average tensile strengths of the Control Group, Experimental Group A, and Experimental Group B.

Result

Tear

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(Tear), Mean = mean(Tear), SD = sd(Tear))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  626. 108. 
## 2 GroupA      5  304.  61.1
## 3 GroupB      5  686  131.

kruskal.test(Tear~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Tear by Group
## Kruskal-Wallis chi-squared = 9.5, df = 2, p-value = 0.008652

boxplot(Tear~Group, data1)

Post-Hoc Analysis using Dunn Test

dunn_test(data1, Tear~Group)

## # A tibble: 3 x 9
##   .y.   group1  group2    n1    n2 statistic       p  p.adj p.adj.signif
## * <chr> <chr>   <chr>  <int> <int>     <dbl>   <dbl>  <dbl> <chr>       
## 1 Tear  Control GroupA     5     5    -2.47  0.0133  0.0267 *           
## 2 Tear  Control GroupB     5     5     0.354 0.724   0.724  ns          
## 3 Tear  GroupA  GroupB     5     5     2.83  0.00468 0.0140 *

Tensile Strength

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(TensileStrength), Mean = mean(TensileStrength), SD = sd(TensileStrength))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  40.3  6.33
## 2 GroupA      5  28.0 10.4 
## 3 GroupB      5  23.6  4.42

kruskal.test(TensileStrength~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  TensileStrength by Group
## Kruskal-Wallis chi-squared = 6.32, df = 2, p-value = 0.04243

boxplot(TensileStrength~Group, data1)

Post-Hoc Analysis using Dunn Test

dunn_test(data1, TensileStrength~Group)

## # A tibble: 3 x 9
##   .y.             group1  group2    n1    n2 statistic      p  p.adj p.adj.signif
## * <chr>           <chr>   <chr>  <int> <int>     <dbl>  <dbl>  <dbl> <chr>       
## 1 TensileStrength Control GroupA     5     5    -1.84  0.0660 0.132  ns          
## 2 TensileStrength Control GroupB     5     5    -2.40  0.0162 0.0486 *           
## 3 TensileStrength GroupA  GroupB     5     5    -0.566 0.572  0.572  ns

Elongation

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(Elongation), Mean = mean(Elongation), SD = sd(Elongation))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  72.3  14.4
## 2 GroupA      5  14.5  12.1
## 3 GroupB      5  92.9  47.0

kruskal.test(Elongation~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Elongation by Group
## Kruskal-Wallis chi-squared = 9.517, df = 2, p-value = 0.008578

boxplot(Elongation~Group, data1)

Post-Hoc Analysis using Dunn Test

dunn_test(data1, Elongation~Group)

## # A tibble: 3 x 9
##   .y.        group1  group2    n1    n2 statistic       p  p.adj p.adj.signif
## * <chr>      <chr>   <chr>  <int> <int>     <dbl>   <dbl>  <dbl> <chr>       
## 1 Elongation Control GroupA     5     5    -2.48  0.0132  0.0265 *           
## 2 Elongation Control GroupB     5     5     0.354 0.723   0.723  ns          
## 3 Elongation GroupA  GroupB     5     5     2.83  0.00464 0.0139 *

Initial Analysis

Tear

boxplot(Tear~Group, data1)

normality2(data1$Tear, data1$Group, data1)

## T statistic of Raw Data:  26.04025 
## T statistic of Rank Data:  17.42153 
## Difference:  8.618724 
## 
## Decision: Assume that the variables are not normally distirubted and use Kruskal-Wallis Test

Elongation

boxplot(Elongation~Group, data1)

normality2(data1$Elongation, data1$Group, data1)

## T statistic of Raw Data:  24.6373 
## T statistic of Rank Data:  19.76467 
## Difference:  4.872633 
## 
## Decision: Assume that the variables are not normally distirubted and use Kruskal-Wallis Test

Determine if there is a significant difference between the average percent change in mass of the Control Group, Experimental Group A, and Experimental Group B when buried in soil.

Result

With Rain

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(SoilDegradationWithRain), Mean = mean(SoilDegradationWithRain), SD = sd(SoilDegradationWithRain))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  95.0 1.86 
## 2 GroupA      5  97.0 0.903
## 3 GroupB      5  97.8 0.928

kruskal.test(SoilDegradationWithRain~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  SoilDegradationWithRain by Group
## Kruskal-Wallis chi-squared = 6.26, df = 2, p-value = 0.04372

boxplot(SoilDegradationWithRain~Group, data1, ylab="Soil Degradation (With Rain)")

Post-Hoc Analysis using Dunn Test

dunn_test(data1, SoilDegradationWithRain~Group)

## # A tibble: 3 x 9
##   .y.             group1 group2    n1    n2 statistic      p  p.adj p.adj.signif
## * <chr>           <chr>  <chr>  <int> <int>     <dbl>  <dbl>  <dbl> <chr>       
## 1 SoilDegradatio~ Contr~ GroupA     5     5     1.56  0.120  0.240  ns          
## 2 SoilDegradatio~ Contr~ GroupB     5     5     2.47  0.0133 0.0400 *           
## 3 SoilDegradatio~ GroupA GroupB     5     5     0.919 0.358  0.358  ns

Without Rain

data1 %>%
  group_by(Group) %>%
  dplyr::summarise(Count = length(SoilDegradationWithoutRain), Mean = mean(SoilDegradationWithoutRain), SD = sd(SoilDegradationWithoutRain))

## # A tibble: 3 x 4
##   Group   Count  Mean    SD
##   <chr>   <int> <dbl> <dbl>
## 1 Control     5  45.9  9.06
## 2 GroupA      5  43.6 17.0 
## 3 GroupB      5  44.0  9.55

kruskal.test(SoilDegradationWithoutRain~Group, data1)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  SoilDegradationWithoutRain by Group
## Kruskal-Wallis chi-squared = 0.06, df = 2, p-value = 0.9704

boxplot(SoilDegradationWithoutRain~Group, data1, ylab="Soil Degradation (Without Rain)")

Initial Analysis

Tear

boxplot(SoilDegradationWithRain~Group, data1)

normality2(data1$SoilDegradationWithRain, data1$Group, data1)

## T statistic of Raw Data:  4.252441 
## T statistic of Rank Data:  4.194018 
## Difference:  0.05842228 
## 
## Decision: Assume that the variables are normally distirubted and use ANOVA. Check the number of observations per group

Elongation

boxplot(SoilDegradationWithoutRain~Group, data1)

normality2(data1$SoilDegradationWithoutRain, data1$Group, data1)

## T statistic of Raw Data:  0.06104471 
## T statistic of Rank Data:  0.01757975 
## Difference:  0.04346496 
## 
## Decision: Assume that the variables are normally distirubted and use ANOVA. Check the number of observations per group

Mixed ANOVA

Result

data2 %>%
  group_by(Group, time) %>%
  get_summary_stats(score, type="mean_sd")

## # A tibble: 39 x 6
##    Group time  variable     n  mean    sd
##    <chr> <chr> <chr>    <dbl> <dbl> <dbl>
##  1 A     t1    score        5   1   0    
##  2 A     t10   score        5   1.4 0.548
##  3 A     t12   score        5   1.4 0.548
##  4 A     t14   score        5   1.8 0.837
##  5 A     t16   score        5   1.8 0.837
##  6 A     t18   score        5   2.4 0.548
##  7 A     t2    score        5   1.4 0.548
##  8 A     t20   score        5   2.8 1.10 
##  9 A     t22   score        5   3   1    
## 10 A     t24   score        5   3.4 0.894
## # ... with 29 more rows

bxp <- ggboxplot(
  data2, x = "time", y = "score",
  color = "Group", palette = "jco"
  )
bxp

res.aov <- anova_test(
  data = data2, dv = score, wid = id,
  within = time, between = Group, type=3
  )
get_anova_table(res.aov)

## ANOVA Table (type III tests)
## 
##       Effect DFn DFd      F        p p<.05   ges
## 1      Group   2  12  6.092 1.50e-02     * 0.331
## 2       time  12 144 39.153 2.44e-39     * 0.626
## 3 Group:time  24 144  1.700 3.00e-02     * 0.127

one.way <- data2 %>%
  group_by(time) %>%
  anova_test(dv = score, wid = id, between = Group) %>%
  get_anova_table() %>%
  adjust_pvalue(method = "bonferroni")

## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()
## Coefficient covariances computed by hccm()

one.way

## # A tibble: 13 x 9
##    time  Effect   DFn   DFd     F     p `p<.05`   ges p.adj
##  * <chr> <chr>  <dbl> <dbl> <dbl> <dbl> <chr>   <dbl> <dbl>
##  1 t1    Group      2    12  1.2  0.335 ""      0.167 1    
##  2 t10   Group      2    12  6.12 0.015 "*"     0.505 0.195
##  3 t12   Group      2    12  9.69 0.003 "*"     0.618 0.039
##  4 t14   Group      2    12  3.63 0.059 ""      0.377 0.767
##  5 t16   Group      2    12  4.16 0.042 "*"     0.409 0.546
##  6 t18   Group      2    12  3.11 0.082 ""      0.341 1    
##  7 t2    Group      2    12  0.75 0.493 ""      0.111 1    
##  8 t20   Group      2    12  1.87 0.197 ""      0.237 1    
##  9 t22   Group      2    12  5.63 0.019 "*"     0.484 0.247
## 10 t24   Group      2    12  6.5  0.012 "*"     0.52  0.156
## 11 t4    Group      2    12  1.3  0.308 ""      0.178 1    
## 12 t6    Group      2    12  1.3  0.308 ""      0.178 1    
## 13 t8    Group      2    12  4.31 0.039 "*"     0.418 0.507

pwc <- data2 %>%
  group_by(time) %>%
  pairwise_t_test(score ~ Group, p.adjust.method = "bonferroni")
pwc

## # A tibble: 39 x 10
##    time  .y.   group1 group2     n1    n2       p p.signif   p.adj p.adj.signif
##  * <chr> <chr> <chr>  <chr>   <int> <int>   <dbl> <chr>      <dbl> <chr>       
##  1 t1    score A      B           5     5 0.454   ns       1       ns          
##  2 t1    score A      Control     5     5 0.147   ns       0.442   ns          
##  3 t1    score B      Control     5     5 0.454   ns       1       ns          
##  4 t10   score A      B           5     5 0.00468 **       0.014   *           
##  5 t10   score A      Control     5     5 0.0512  ns       0.154   ns          
##  6 t10   score B      Control     5     5 0.218   ns       0.655   ns          
##  7 t12   score A      B           5     5 0.00099 ***      0.00297 **          
##  8 t12   score A      Control     5     5 0.0138  *        0.0413  *           
##  9 t12   score B      Control     5     5 0.175   ns       0.525   ns          
## 10 t14   score A      B           5     5 0.0205  *        0.0616  ns          
## # ... with 29 more rows

Bioplastic

Raffy S. Centeno

10/5/2021

Determine if there is a significant difference between the average thickness of the Control Group, Experimental Group A, and Experimental Group B.

Result

Kruskal-Wallis Test

Post-Hoc Analysis using Dunn Test

Initial Analysis

Determine if there is a significant difference between the average water solubilities of the Control Group, Experimental Group A, and Experimental Group B.

Result

Initial Analysis

Determine if there is a significant difference between the compatibilities of the Control Group, Experimental Group A, and Experimental Group B when it comes to food item immersion

Result

Soy Sauce

Vegetable Oil

Post-Hoc Analysis using Dunn Test

Vinegar

Initial Analysis

Soy Sauce

Vegetable Oil

Vinegar

Determine if there is a significant difference between the average tensile strengths of the Control Group, Experimental Group A, and Experimental Group B.

Result

Tear

Post-Hoc Analysis using Dunn Test

Tensile Strength

Post-Hoc Analysis using Dunn Test

Elongation

Post-Hoc Analysis using Dunn Test

Initial Analysis

Tear

Elongation

Determine if there is a significant difference between the average percent change in mass of the Control Group, Experimental Group A, and Experimental Group B when buried in soil.

Result

With Rain

Post-Hoc Analysis using Dunn Test

Without Rain

Initial Analysis

Tear

Elongation

Mixed ANOVA

Result