exam_score <- c(85, 88, 90, 72, 95, 80, 85, 87, 78, 91)
# shapiro-wilk normality test
result1 <-shapiro.test(exam_score)
print(result1)##
## Shapiro-Wilk normality test
##
## data: exam_score
## W = 0.96562, p-value = 0.8476#The data is likely to follow a normal distribution.
#accept the null hypothesisThis is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.
When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
before <- c(80, 85, 88, 90, 93, 95, 85, 87, 89, 92)
after <- c(82, 86, 91, 93, 95, 97, 88, 90, 91, 94)
# paired t-test
result2 <- t.test(before, after , paired = TRUE)
print(result2)##
## Paired t-test
##
## data: before and after
## t = -10.776, df = 9, p-value = 1.915e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -2.782829 -1.817171
## sample estimates:
## mean difference
## -2.3#print the p-value in standard number foramt
formatted_p_value <- format(result2$p.value, scientific = FALSE)
print(formatted_p_value)## [1] "0.000001914532"Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.
data(iris)
# setosa와 versicolor의 Sepal.Length
setosa_sepal_length <- iris$Sepal.Length[iris$Species == "setosa"]
versicolor_sepal_length <- iris$Sepal.Length[iris$Species == "versicolor"]
# shapiro-wilk normality test
result3 <-shapiro.test(setosa_sepal_length)
print(result3)##
## Shapiro-Wilk normality test
##
## data: setosa_sepal_length
## W = 0.9777, p-value = 0.4595result4 <-shapiro.test(versicolor_sepal_length)
print(result4)##
## Shapiro-Wilk normality test
##
## data: versicolor_sepal_length
## W = 0.97784, p-value = 0.4647library(car)## Loading required package: carData#Leven's Test
levene_test <- leveneTest(Sepal.Length ~ Species, data = iris[iris$Species %in% c("setosa", "versicolor"), ])
levene_test## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 8.1727 0.005196 **
## 98
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(car)
#Leven's Test
levene_test <- leveneTest(Sepal.Length ~ Species, data = iris[iris$Species %in% c("setosa", "versicolor"), ])
levene_test## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 8.1727 0.005196 **
## 98
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.2.1 ✔ readr 2.2.0
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.3 ✔ tibble 3.3.1
## ✔ lubridate 1.9.5 ✔ tidyr 1.3.2
## ✔ purrr 1.2.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::recode() masks car::recode()
## ✖ purrr::some() masks car::some()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdata(mtcars)
group_4<-mtcars %>%
filter(cyl == 4) %>%
select(mpg)
group_6<-mtcars %>%
filter(cyl == 6) %>%
select(mpg)
group_8<-mtcars %>%
filter(cyl == 8) %>%
select(mpg)library(car)
levene_test <- leveneTest(mpg~factor(cyl), data=mtcars)
print(levene_test)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 5.5071 0.00939 **
## 29
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1welch_test_result1 <- t.test(group_4$mpg, group_6$mpg, var.equal = FALSE)
welch_test_result1##
## Welch Two Sample t-test
##
## data: group_4$mpg and group_6$mpg
## t = 4.7191, df = 12.956, p-value = 0.0004048
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 3.751376 10.090182
## sample estimates:
## mean of x mean of y
## 26.66364 19.74286welch_test_result2 <- t.test(group_8$mpg, group_6$mpg, var.equal = FALSE)
welch_test_result2##
## Welch Two Sample t-test
##
## data: group_8$mpg and group_6$mpg
## t = -5.2911, df = 18.502, p-value = 4.54e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -6.482789 -2.802925
## sample estimates:
## mean of x mean of y
## 15.10000 19.74286welch_test_result3 <- t.test(group_4$mpg, group_8$mpg, var.equal = FALSE)
welch_test_result3##
## Welch Two Sample t-test
##
## data: group_4$mpg and group_8$mpg
## t = 7.5967, df = 14.967, p-value = 1.641e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 8.318518 14.808755
## sample estimates:
## mean of x mean of y
## 26.66364 15.10000data("sleep")
?sleep
view(sleep)
summary(sleep)## extra group ID
## Min. :-1.600 1:10 1 :2
## 1st Qu.:-0.025 2:10 2 :2
## Median : 0.950 3 :2
## Mean : 1.540 4 :2
## 3rd Qu.: 3.400 5 :2
## Max. : 5.500 6 :2
## (Other):8# Convert group to factor with labels A and B
sleep <- sleep %>%
mutate(group = factor(group, labels = c("A", "B")))
# Extract 'extra' values for each group (A and B)
A_group <- sleep %>%
filter(group == "A") %>%
select(extra)
B_group <- sleep %>%
filter(group == "B") %>%
select(extra)
# Paired t-test using the full dataset
t_test_AandB_trt1 <- t.test(A_group$extra, B_group$extra, var.equal = TRUE)
t_test_AandB_trt1##
## Two Sample t-test
##
## data: A_group$extra and B_group$extra
## t = -1.8608, df = 18, p-value = 0.07919
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3.363874 0.203874
## sample estimates:
## mean of x mean of y
## 0.75 2.33#There are no difference between group A and B as the P-value is more than 0.05.