Chapter 6 talks about experimental and statistical control. The following examples help illustrate a few items that were discussed. Follow all instructions to complete Chapter 6.
tidyverse
package (you can ignore the notes that you see below that it gives you once you load it) and the furniture
package.library(tidyverse)
library(furniture)
posttest
is the posttest scores regarding words recognized accurately from a person with a motor speech disorder; pretest
is the initial accurately recognized words; therapy
is the experimental group where 1
is the intervention group and 0
is the control group.## Don't change this code :)
set.seed(843)
df <- data_frame(
posttest = c(2,4,6,6,9,10,12, 6,7,9,9,12,12,15),
pretest = c(1,3,7,10,13,17,19, 1,5,7,9,13,16,19),
therapy = c(1,1,1,1,1,1,1, 0,0,0,0,0,0,0)
) %>%
mutate(gain = posttest - pretest)
df %>%
mutate(therapy = factor(therapy, labels = c("No Therapy", "Therapy"))) %>%
ggplot(aes(pretest, posttest, group = therapy, color = therapy)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
scale_color_manual(values = c("darkorchid", "firebrick1"))
df %>%
t.test(gain ~ therapy,
data = .,
var.equal = TRUE)
##
## Two Sample t-test
##
## data: gain by therapy
## t = 1.6672, df = 12, p-value = 0.1213
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9207101 6.9207101
## sample estimates:
## mean in group 0 mean in group 1
## 0 -3
gain
and therapy
.df %>%
lm(gain ~ therapy,
data = .) %>%
summary()
##
## Call:
## lm(formula = gain ~ therapy, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.00 -3.25 -0.50 2.00 5.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.121e-16 1.272e+00 0.000 1.000
## therapy -3.000e+00 1.799e+00 -1.667 0.121
##
## Residual standard error: 3.367 on 12 degrees of freedom
## Multiple R-squared: 0.1881, Adjusted R-squared: 0.1204
## F-statistic: 2.779 on 1 and 12 DF, p-value: 0.1213
pretest
as a covariate. What did it do to the estimate? Why?df %>%
lm(gain ~ therapy + pretest,
data = .) %>%
summary()
##
## Call:
## lm(formula = gain ~ therapy + pretest, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0000 -0.5077 0.4846 0.5029 0.5173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.01923 0.39024 12.862 5.68e-08 ***
## therapy -3.00000 0.36031 -8.326 4.46e-06 ***
## pretest -0.50192 0.02956 -16.980 3.07e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6741 on 11 degrees of freedom
## Multiple R-squared: 0.9702, Adjusted R-squared: 0.9647
## F-statistic: 178.8 on 2 and 11 DF, p-value: 4.086e-09
therapy
?Regression is well adapted for both experimental and observational research designs. Using both experimental and statistical controls within the same design can increase validity and statistical power of the analyses.