Kindly refer to description to understand the original data frame.
Let’s explore the data a bit.
data("ToothGrowth")
Supplement <- factor(ToothGrowth$supp)
library(ggplot2)
g <- ggplot(ToothGrowth, aes(ToothGrowth$dose, ToothGrowth$len))
g <- g + geom_point(aes(colour = Supplement)) + labs(
title = "Tooth Length versus Dose", x = "Dose", y = "Length")
g
s <- split(ToothGrowth, ToothGrowth$supp)
summary(s$OJ$len); summary(s$VC$len)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.20 15.52 22.70 20.66 25.72 30.90
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.20 11.20 16.50 16.96 23.10 33.90
Are the supplements equally effective?
- H0: Orange Juice was as effective in tooth growth of guinea pigs as Vitamin C.
- Ha: Orange Juice was more effective in tooth growth of guinea pigs than Vitamin C.
Let’s do an alpha = .05 one-tailed test on the samples.
t.test(s$OJ$len, s$VC$len, alternative = "greater")
##
## Welch Two Sample t-test
##
## data: s$OJ$len and s$VC$len
## t = 1.9153, df = 55.309, p-value = 0.03032
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 0.4682687 Inf
## sample estimates:
## mean of x mean of y
## 20.66333 16.96333
H0 is rejected and the true difference in means is greater than 0.
t.test(s$OJ$len[s$OJ$dose == 0.5], s$VC$len[s$OJ$dose == 0.5],
alternative = "greater")
##
## Welch Two Sample t-test
##
## data: s$OJ$len[s$OJ$dose == 0.5] and s$VC$len[s$OJ$dose == 0.5]
## t = 3.1697, df = 14.969, p-value = 0.003179
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 2.34604 Inf
## sample estimates:
## mean of x mean of y
## 13.23 7.98
H0 is rejected and the true difference in means is greater than 0 when dose is 0.5 mg/day.
t.test(s$OJ$len[s$OJ$dose == 1], s$VC$len[s$OJ$dose == 1],
alternative = "greater")
##
## Welch Two Sample t-test
##
## data: s$OJ$len[s$OJ$dose == 1] and s$VC$len[s$OJ$dose == 1]
## t = 4.0328, df = 15.358, p-value = 0.0005192
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 3.356158 Inf
## sample estimates:
## mean of x mean of y
## 22.70 16.77
H0 is rejected and the true difference in means is greater than 0 when dose is 1.0 mg/day.
t.test(s$OJ$len[s$OJ$dose == 2], s$VC$len[s$OJ$dose == 2],
alternative = "greater")
##
## Welch Two Sample t-test
##
## data: s$OJ$len[s$OJ$dose == 2] and s$VC$len[s$OJ$dose == 2]
## t = -0.046136, df = 14.04, p-value = 0.5181
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -3.1335 Inf
## sample estimates:
## mean of x mean of y
## 26.06 26.14
Failed to rejected H0 when dose is 2.0 mg/day.
Conclusion: Perhaps orange juice was more effective on tooth growth in guinea pigs than vitamin C for lower doses (i.e. =< 1.0 mg/day). As the doses increased to 2.0 mg/day, no significant difference between the two was noted.
*** Disclaimer: The suggestions and remarks in this page are based on personal research experience. Research practices and approaches vary. Exercise your own judgment regarding the suitability of the content.
*** Analysis environment
sessionInfo()
## R version 3.3.2 (2016-10-31)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 14393)
##
## locale:
## [1] LC_COLLATE=English_Singapore.1252 LC_CTYPE=English_Singapore.1252
## [3] LC_MONETARY=English_Singapore.1252 LC_NUMERIC=C
## [5] LC_TIME=English_Singapore.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggplot2_2.2.1
##
## loaded via a namespace (and not attached):
## [1] Rcpp_0.12.8 assertthat_0.1 digest_0.6.10 rprojroot_1.2
## [5] plyr_1.8.4 grid_3.3.2 gtable_0.2.0 backports_1.0.5
## [9] magrittr_1.5 evaluate_0.10 scales_0.4.1 stringi_1.1.2
## [13] lazyeval_0.2.0 rmarkdown_1.3 labeling_0.3 tools_3.3.2
## [17] stringr_1.1.0 munsell_0.4.3 yaml_2.1.14 colorspace_1.3-2
## [21] htmltools_0.3.5 knitr_1.15.1 tibble_1.2