Rows: 20
Columns: 3
$ extra <dbl> 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0, 1.9, 0.8, …
$ group <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
$ ID <fct> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Source: https://stats.stackexchange.com/questions/59047/how-are-regression-the-t-test-and-the-anova-all-versions-of-the-general-linear
I Always fail in remember the code to show how this models are related, so I will put here for my future me. An important thing to do is check the p-values.
The data, according help(sleep)
:
Data which show the effect of two soporific drugs (increase in hours of sleep compared to control) on 10 patients -Scheffé, Henry (1959) The Analysis of Variance. New York, NY: Wiley.
Now, load packages and data.
Regression
Call:
lm(formula = extra ~ group, data = sleep)
Residuals:
Min 1Q Median 3Q Max
-2.430 -1.305 -0.580 1.455 3.170
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7500 0.6004 1.249 0.2276
group2 1.5800 0.8491 1.861 0.0792 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.899 on 18 degrees of freedom
Multiple R-squared: 0.1613, Adjusted R-squared: 0.1147
F-statistic: 3.463 on 1 and 18 DF, p-value: 0.07919
Code
tidy(linear_model)
# A tibble: 2 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 0.75 0.600 1.25 0.228
2 group2 1.58 0.849 1.86 0.0792
ANOVA
Df Sum Sq Mean Sq F value Pr(>F)
group 1 12.48 12.482 3.463 0.0792 .
Residuals 18 64.89 3.605
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Code
tidy(anova)
# A tibble: 2 × 6
term df sumsq meansq statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 group 1 12.5 12.5 3.46 0.0792
2 Residuals 18 64.9 3.60 NA NA
\(t\)-test
Code
t_test <- t.test(extra ~ group, var.equal = TRUE, data = sleep)
t_test
Two Sample t-test
data: extra by group
t = -1.8608, df = 18, p-value = 0.07919
alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
95 percent confidence interval:
-3.363874 0.203874
sample estimates:
mean in group 1 mean in group 2
0.75 2.33
Code
tidy(t_test)
# A tibble: 1 × 10
estimate estimate1 estimate2 statistic p.value parameter conf.low conf.high
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 -1.58 0.75 2.33 -1.86 0.0792 18 -3.36 0.204
# ℹ 2 more variables: method <chr>, alternative <chr>
Reuse
Citation
BibTeX citation:
@online{kunstfuentes2021,
author = {Joshua Kunst Fuentes},
title = {Regression, {ANOVA,} t-Test Are Related...},
date = {2021-06-08},
url = {https://jkunst.com/blog/posts/2021-06-08-regression-anova-t-test},
langid = {en}
}
For attribution, please cite this work as:
Joshua Kunst Fuentes. 2021. “Regression, ANOVA, t-Test Are
Related...” June 8, 2021. https://jkunst.com/blog/posts/2021-06-08-regression-anova-t-test.