DPPH Results

Data

library(readxl)

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data2 <- read_excel("D:/COLLEGE 3RD YEAR/2nd SEMESTER/STAT 50 STATISTICAL SOFTWARE/MIDTERM/data2.xlsx")

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data2

data2<-data2[, 1:2]
data2

library(tidyverse)

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library(ggpubr)

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library(rstatix)

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library(dplyr)
data2 <- data2 %>%
  reorder_levels(Treatment, order = c("T0+", "T0-", "T1", "T2", "T3"))

library(dplyr)
library(rstatix)
data2%>%
  group_by(Treatment)%>%
  get_summary_stats(DPPH, type="common")

Interpretation

  The mean for treatment T0+ is 0.054.
  The mean for treatment T0- is 0.045.
  The mean for treatment T1 is 0.153.
  The mean for treatment T2 is 0.158.
  The mean for treatment T3 is 0.150.

library(ggplot2)
ggplot(data2) +
  aes(x = Treatment, y = DPPH, color = Treatment) +
  geom_jitter() +
  theme(legend.position = "none")

Interpretation

  The graph shows plotting of the data per treatment. The factor is the treatment variable which contains 5 treatments          namely, T0+, T0-, T1, T2, and T3.
  
  
  

library(tidyverse)
library(ggpubr)
library(rstatix)
ggboxplot(data2, x = "Treatment", y = "DPPH", fill="Treatment")

Interpretation

  Based on the box plot, it is evident that there are differences exist among the five treatments (T0+, T0-, T1, T2, T3).

ANOVA

res_aov <- aov(DPPH ~ Treatment, data = data2)

Normality Test

par(mfrow = c(1, 2)) # combine plots
# histogram
hist(res_aov$residuals)
# QQ-plot
library(car)

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qqPlot(res_aov$residuals,
       id = FALSE # id = FALSE to remove point identification
)

Interpretation

  As gleaned above, we can see that the histogram roughly form a bell curve. This means that it indicates that the residuals     follow a normal distribution. Moreover, points in the QQ-plots roughly follow the straight line and most of them are within     the confidence bands. This is also indicating that residuals follow approximately a normal distribution.  

Normality Test

shapiro.test(res_aov$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  res_aov$residuals
## W = 0.93435, p-value = 0.003052

Interpretation

  The p-value of the Shapiro-Wilk on the residuals is smaller than the usual significance level of 0.05. Thus, we do reject     the hypothesis that residuals follow a normal distribution (p-value = 0.003052).

Equality of Variances Test

library(car)
leveneTest(DPPH ~ Treatment,
  data = data2)

Interpretation

  The p-value being larger than the significance level of 0.05.

res.kruskal <- data2 %>% kruskal_test(DPPH ~ Treatment)
res.kruskal

Interpretation

  Based on the p-value significant difference was observed among the five treatments.

Effect size

The effect size values normally interpreted as 0.01- < 0.06 (small effect), 0.06 – < 0.14 (moderate effect) and >= 0.14 (large effect).

data2 %>% kruskal_effsize(DPPH ~ Treatment)

Interpretation

  The effect size is large. This means that we can easily identify the significant differences based on small number of         sample size.

Pairwise Comparison

res1<- data2 %>%
  dunn_test(DPPH ~ Treatment, p.adjust.method = "bonferroni")
res1

Interpretation

  Based on the pairwise comparison, there is a significant difference observed in T0+, T0-, T1, T2, and T3.

res1 <- res1 %>% add_xy_position(x = "Treatment")
ggboxplot(data2, x = "Treatment", y = "DPPH") +
  stat_pvalue_manual(res1, hide.ns = TRUE) +
  labs(
    subtitle = get_test_label(res.kruskal, detailed = TRUE),
    caption = get_pwc_label(res1))