T Tests

Author:	Mitch Richling
Updated:	2022-06-04 16:17:47

1. Metadata
2. Some Data
3. Welch Two Sample t-test
4. Two Sample t-test
5. Paired t-test
6. One Sample t-test (not equal)
7. One Sample t-test (greater than)
8. Wilcoxon signed rank test with continuity correction
9. Wilcoxon rank sum test with continuity correction
10. Wilcoxon signed rank test with continuity correction

1. Metadata

The home for this HTML file is: https://richmit.github.io/ex-R/tTests.html

Files related to this document may be found on github: https://github.com/richmit/ex-R

Directory contents:

`src`	-	The org-mode file that generated this HTML document
`docs`	-	This html document
`data`	-	Data files
`tangled`	-	Tangled R code from this document

2. Some Data

popsz  <- 1000
mean1  <- 1
mean2  <- mean1
mean3  <- -1
group1 <- rnorm(popsz, mean=mean1)
group2 <- rnorm(popsz, mean=mean2)
group3 <- rnorm(popsz, mean=mean3)
allDat <- stack(list(group1=group1, group2=group2, group3=group3))
names(allDat) <- c('v', 'group')

ggplot(data=allDat, aes(x=v, col=group)) + geom_density()

3. Welch Two Sample t-test

Use when you don't know the variance of the two populations is equal

t.test(group1, group2)

    Welch Two Sample t-test

data:  group1 and group2
t = -0.022292, df = 1996.8, p-value = 0.9822
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.08912823  0.08712479
sample estimates:
mean of x mean of y 
 1.002692  1.003694

4. Two Sample t-test

Use when you DO know the variance of the two populations is equal

t.test(group1, group2, var.equal=TRUE)

    Two Sample t-test

data:  group1 and group2
t = -0.022292, df = 1998, p-value = 0.9822
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.08912820  0.08712476
sample estimates:
mean of x mean of y 
 1.002692  1.003694

5. Paired t-test

Use when the measurements in each group are related pairwise.

For example, the data could be temperature measurements taken with two thermometers each hour.

t.test(group1, group2, paired=TRUE)

    Paired t-test

data:  group1 and group2
t = -0.02259, df = 999, p-value = 0.982
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.08801952  0.08601608
sample estimates:
mean of the differences 
           -0.001001722

6. One Sample t-test (not equal)

Use when you want to know if the sample mean is equal to a hypothesized population mean

t.test(group1, mu=mean1)
t.test(group2, mu=mean2)
t.test(group3, mu=mean1)

    One Sample t-test

data:  group1
t = 0.083692, df = 999, p-value = 0.9333
alternative hypothesis: true mean is not equal to 1
95 percent confidence interval:
 0.939569 1.065815
sample estimates:
mean of x 
 1.002692

    One Sample t-test

data:  group2
t = 0.11772, df = 999, p-value = 0.9063
alternative hypothesis: true mean is not equal to 1
95 percent confidence interval:
 0.9421213 1.0652664
sample estimates:
mean of x 
 1.003694

    One Sample t-test

data:  group3
t = -61.969, df = 999, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 1
95 percent confidence interval:
 -1.058660 -0.932281
sample estimates:
 mean of x 
-0.9954705

7. One Sample t-test (greater than)

Use when you want to know if the sample mean is less than a hypothesized population mean

t.test(group3, mu=mean1, alternative="greater")

    One Sample t-test

data:  group3
t = -61.969, df = 999, p-value = 1
alternative hypothesis: true mean is greater than 1
95 percent confidence interval:
 -1.048486       Inf
sample estimates:
 mean of x 
-0.9954705

8. Wilcoxon signed rank test with continuity correction