Load the ToothGrowth data

library(tidyverse) # graphing and wrangling
library(knitr) # for kable tables

data("ToothGrowth")

ToothGrowth data set contains the result from an experiment studying the effect of vitamin C on tooth growth in 60 Guinea pigs. Each animal received one of three dose levels of vitamin C (0.5, 1, and 2 mg/day) by one of two delivery methods, (orange juice or ascorbic acid (a form of vitamin C and coded as VC).

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Exploratory data analyses

dim(ToothGrowth)
## [1] 60  3
# Summary of the data 

summary(ToothGrowth)
##       len        supp         dose      
##  Min.   : 4.20   OJ:30   Min.   :0.500  
##  1st Qu.:13.07   VC:30   1st Qu.:0.500  
##  Median :19.25           Median :1.000  
##  Mean   :18.81           Mean   :1.167  
##  3rd Qu.:25.27           3rd Qu.:2.000  
##  Max.   :33.90           Max.   :2.000

A dataframe with 60 observations and 3 variables len : Tooth length supp : Supplement type (VC or OJ) dose : Dose in milligrams

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Effect of Vitamin C on guinea pig tooth growth

ToothGrowth %>% 
ggplot(aes(as.factor(dose), len)) +
  geom_boxplot(aes(fill = supp))+
  scale_fill_brewer(palette = "Dark2") +
  facet_wrap(~supp) +
  labs(
      title =" Effect of Vitamin C on guinea pig tooth growth",
      subtitle ="Orange Juice (OJ) and Ascorbic Acid (VC) administered at 0.5, 1, 2 (mg)",
      x ="Dose (mg)", 
      y ="Tooth length"
  ) +
  theme_bw() +
  theme(
    legend.position = "none"
  )

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Average tooth length per treatment

ToothGrowth %>% group_by(supp, dose) %>% 
                summarise(mean = mean(len)) %>% 
                ggplot(aes(as.factor(dose), mean)) +
                geom_line(aes(group = supp)) +
                geom_point(aes(color = supp), size = 4) +
                scale_color_brewer(palette = "Dark2") +
                labs(
                  title =" Effect of Vitamin C on guinea pig tooth growth",
                  subtitle =  "Average tooth length per treatment",
                  x ="Dose (mg)", 
                  y ="Average tooth length"
                   ) +
              
                theme_bw() +
                theme(
                      legend.position = "bottom")
## `summarise()` has grouped output by 'supp'. You can override using the `.groups` argument.

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kable(
  ToothGrowth %>% group_by(supp, dose) %>% 
                summarise(mean = mean(len))
     )
## `summarise()` has grouped output by 'supp'. You can override using the `.groups` argument.
supp dose mean
OJ 0.5 13.23
OJ 1.0 22.70
OJ 2.0 26.06
VC 0.5 7.98
VC 1.0 16.77
VC 2.0 26.14

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# By dose 
kable( 
ToothGrowth %>% group_by(dose) %>% 
                summarise(mean = mean(len))
      )
dose mean
0.5 10.605
1.0 19.735
2.0 26.100

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# By supplement 
kable(
ToothGrowth %>% group_by(supp) %>% 
                summarise(mean = mean(len))
          )
supp mean
OJ 20.66333
VC 16.96333

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ToothGrowth <- ToothGrowth %>% mutate(id = 1:60)

ToothGrowth %>%  ggplot(aes(x = id, y = len)) +
                    geom_point(aes(color = as.factor(dose)), size = 2.5) +
                    facet_wrap(~supp) +
                    scale_color_brewer(palette = "Dark2") +
                    theme_bw() +
                    theme(
                      legend.title = element_blank(),
                      legend.position = "bottom"
                    )

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Statisitical tests to compare tooth growth by supp and dose

Assumptions

  1. There are variances in tooth growth when using supplements at different dosages.
  2. The measurements are not paired
  3. the variances are not equal
  4. The populations are independent
  5. The guinea pigs were randomly assigned to the different treatment groups
  6. The data follows normal distrubution

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# Normality test
library(ggpubr)
ggqqplot(ToothGrowth$len)

shapiro.test(ToothGrowth$len)
## 
##  Shapiro-Wilk normality test
## 
## data:  ToothGrowth$len
## W = 0.96743, p-value = 0.1091

p-value > 0.05 implying that the distribution of the data are not significantly different from normal distribution

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Compare effects of orange juice vs. ascorbic acid at different dosages

# Orange Juice vs. Ascorbic Acid: 0.5mg 
# Orange Juice vs. Ascorbic Acid: 1 mg 
# Orange Juice vs. Ascorbic Acid: 2mg 
# Orange Juice vs. Ascorbic Acid: All  


OJ_v_VC <- data.frame(
  Group_A = rep( "Orange Juice", 4),
  Group_B = rep( "Ascorbic Acid", 4),
  Group_C = c(0.5, 1, 2, "All"), 
  p.value = c(
       t.test(len ~ supp, paired = FALSE, data = ToothGrowth %>% filter(dose == 0.5))$p.value, 
       t.test(len ~ supp, paired = FALSE, data = ToothGrowth %>% filter(dose == 1))$p.value, 
       t.test(len ~ supp, paired = FALSE, data = ToothGrowth %>% filter(dose == 2))$p.value, 
       t.test(len ~ supp, paired = FALSE, data = ToothGrowth)$p.value 
       )
)
 
OJ_v_VC  <- OJ_v_VC  %>%  mutate(significance = case_when(p.value < 0.05 ~ "Significant",
                           p.value > 0.05  ~ "Not Significant"))
kable(OJ_v_VC)
Group_A Group_B Group_C p.value significance
Orange Juice Ascorbic Acid 0.5 0.0063586 Significant
Orange Juice Ascorbic Acid 1 0.0010384 Significant
Orange Juice Ascorbic Acid 2 0.9638516 Not Significant
Orange Juice Ascorbic Acid All 0.0606345 Not Significant

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Compare effects of orange juice at different dosages

# Orange Juice: 0.5mg vs 1mg, 
# Orange Juice: 0.5mg vs 2mg, 
# Orange Juice: 1mg vs 2mg


OJ <- data.frame(
  
 Group_A = rep("Orange Juice", 3), 
 Group_B = c(0.5, 0.5, 1),
 Group_C =  c(1, 2, 2), 
 conf.int.1 =  c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 1)) )$conf.int[1],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 2)) ) $conf.int[1],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(1, 2)) ) $conf.int[1]
 ), 
 conf.int.2 =  c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 1)) ) $conf.int[2],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 2)) ) $conf.int[2],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(1, 2)) ) $conf.int[2]
            ),
 p.value = c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 1)) ) $p.value,
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(0.5, 2)) ) $p.value,
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "OJ", dose == c(1, 2)) ) $p.value 
 )
)

OJ <- OJ  %>%  mutate(significance = case_when(p.value < 0.05 ~ "Significant",
                                               p.value > 0.05  ~ "Not Significant"))

kable(OJ)
Group_A Group_B Group_C conf.int.1 conf.int.2 p.value significance
Orange Juice 0.5 1 -14.94689 -5.6131139 0.0012455 Significant
Orange Juice 0.5 2 -16.94335 -7.0966531 0.0005397 Significant
Orange Juice 1.0 2 -11.23644 -0.1635575 0.0450953 Significant

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Compare effects of ascorbic acid on tooth growth at different dosages

# Ascorbic Acid: 0.5mg vs 1mg, 
# Ascorbic Acid: 0.5mg vs 2mg, 
# Ascorbic Acid: 1mg vs 2mg, 

VC <- data.frame(
  
 Group_A = rep("Ascorbic Acid", 3), 
 Group_B = c(0.5, 0.5, 1),
 Group_C =  c(1, 2, 2), 
 conf.int.1 =  c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 1)) ) $conf.int[1],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 2)) ) $conf.int[1],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(1, 2)) ) $conf.int[1]
         ), 
 conf.int.2 =  c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 1)) ) $conf.int[2],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 2)) ) $conf.int[2],
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(1, 2)) ) $conf.int[2]
            ),
 p.value = c(
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 1)) ) $p.value,
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(0.5, 2)) ) $p.value,
    t.test(len ~ dose, paired = FALSE, data = ToothGrowth %>% filter(supp == "VC", dose == c(1, 2)) ) $p.value 
        
 )
)


VC <- VC  %>%  mutate(significance = case_when(p.value < 0.05 ~ "Significant",
                                               p.value > 0.05  ~ "Not Significant"))
kable(VC)
Group_A Group_B Group_C conf.int.1 conf.int.2 p.value significance
Ascorbic Acid 0.5 1 -12.65876 -6.061241 0.0005573 Significant
Ascorbic Acid 0.5 2 -25.62861 -11.651394 0.0007094 Significant
Ascorbic Acid 1.0 2 -15.32237 -1.037628 0.0305694 Significant

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Conclusion

  1. As you increase the dose of orange juice or ascorbic acid, tooth growth increases as well
  2. At 2mg, both orange juice and ascorbic acid promote tooth growth at similar rates
  3. At 0.5mg and 1mg, vitamin C intake via orange juice promotes greater tooth growth than ascorbic acid
  4. Drinking a higher concentration of orange juice can increase tooth length by (7 -20)
  5. Orange juice would be recommended if vitamin c dosage needs to be lowered