Low et al (2016) examined the effects of two different anesthetics on aspects of the physiology of the mouse. Twelve mice were anesthetized with isoflurane and eleven mice were anesthetized with alpha chloralose and blood CO2 levels were recorded after 120 minutes. The H0 was that there is no difference between the anesthetics in the mean blood CO2 level. This is an independent comparison because individual mice were only given one of the two anesthetics.
First, load the required packages (tidyverse, RMisc, MKinfer, car, emmeans)
Import low data file
low <- read.csv("data/lowco2.csv")
low anesth co2
1 iso 43
2 iso 35
3 iso 50
4 iso 39
5 iso 56
6 iso 54
7 iso 39
8 iso 51
9 iso 49
10 iso 54
11 iso 51
12 iso 79
13 ac 60
14 ac 53
15 ac 54
16 ac 73
17 ac 64
18 ac 95
19 ac 57
20 ac 80
21 ac 115
22 ac 79
23 ac 50low_stats <- summarySE(data=low,measurevar="co2", groupvars="anesth")
low_stats anesth N co2 sd se ci
1 ac 11 70.90909 20.20126 6.090909 13.571391
2 iso 12 50.00000 11.39378 3.289100 7.239261low %>% dplyr::count(anesth) anesth n
1 ac 11
2 iso 12low %>%
group_by(anesth) %>%
dplyr::summarise(n = n(),
mean = mean(co2),
median = median(co2),
sd = sd(co2),
variance = var(co2),
se = sd / sqrt(n),
CI_upper = mean + se * qt(p = 0.975, df = n-1),
CI_lower = mean + se * qt(p = 0.025, df = n-1),
CI = se * qt(p = 0.975, df = n-1),
upper = mean + CI,
lower = mean - CI
)# A tibble: 2 × 12
anesth n mean median sd variance se CI_upper CI_lower CI upper
<chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 ac 11 70.9 64 20.2 408. 6.09 84.5 57.3 13.6 84.5
2 iso 12 50 50.5 11.4 130. 3.29 57.2 42.8 7.24 57.2
# ℹ 1 more variable: lower <dbl>Play around with df to see how the z-multiplier changes when using the T-distribution to calculate the 95% confidence interval.
# Standard normal distribution
qnorm(p = 0.025)[1] -1.959964qnorm(p = 0.975)[1] 1.959964# Student-t distribution
qt(p = 0.025, df = 100)[1] -1.983972qt(p = 0.975, df = 100)[1] 1.983972low %>%
ggplot(aes(anesth, co2)) +
geom_point(alpha = 0.5) +
theme_qk()
low.aov <- aov(co2~anesth,data=low)
tidy(low.aov, conf.int=TRUE)# A tibble: 2 × 6
term df sumsq meansq statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 anesth 1 2509. 2509. 9.56 0.00552
2 Residuals 21 5509. 262. NA NA low.emm <- emmeans(low.aov,"anesth")
eff_size(low.emm, sigma=sigma(low.aov), edf=df.residual(low.aov)) contrast effect.size SE df lower.CL upper.CL
ac - iso 1.29 0.463 21 0.329 2.25
sigma used for effect sizes: 16.2
Confidence level used: 0.95 Note that we’ve chosen to show a standardized effect size, using the pooled variance from the analysis of variance - Residual MS = 262.44, and √262.44 = 16.2
leveneTest(co2 ~ anesth, low)Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 2.604 0.1215
21 t.test(co2~anesth,var.equal=TRUE, data=low)
Two Sample t-test
data: co2 by anesth
t = 3.0927, df = 21, p-value = 0.005515
alternative hypothesis: true difference in means between group ac and group iso is not equal to 0
95 percent confidence interval:
6.849172 34.969010
sample estimates:
mean in group ac mean in group iso
70.90909 50.00000 t.test(co2~anesth,data=low)
Welch Two Sample t-test
data: co2 by anesth
t = 3.0206, df = 15.485, p-value = 0.008362
alternative hypothesis: true difference in means between group ac and group iso is not equal to 0
95 percent confidence interval:
6.194866 35.623316
sample estimates:
mean in group ac mean in group iso
70.90909 50.00000 wilcox.test(co2~anesth,data=low)Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
compute exact p-value with ties
Wilcoxon rank sum test with continuity correction
data: co2 by anesth
W = 114, p-value = 0.003398
alternative hypothesis: true location shift is not equal to 0sum(rank(low$co2)[low$anesth=="ac"])[1] 180sum(rank(low$co2)[low$anesth=="iso"])[1] 96