COMMUNITY CORRECTIONSPrepared ByDatePROBATIONDescr.docx

COMMUNITY CORRECTIONS
Prepared By:
Date:
PROBATION
Description:
Purpose(s) served:
Advantages:
1.
2.
3.
Drawbacks:
1.
2.
3.
INTERMEDIATE SANCTIONS
Name of punishment: COMMUNITY SERVICE
Description:
Purpose(s) served:
Advantages:
1.

2.
3.
Drawbacks:
1.
2.
3.
Name of punishment: RESTITUTION
Description:
Purpose(s) served:
Advantages:
1.
2.
3.
Drawbacks:
1.
2.
3.
Name of punishment: HOUSE ARREST
Description:
Purpose(s) served:
Advantages:
1.
2.
3.
Drawbacks:

1.
2.
3.
REFERENCES
1
Day 08 ActivityFisher & HughesSeptember 21, 2018Study
A study was conducted to determine the effects of alcohol on
human reaction times. Fifty-seven adult individuals within two-
age groups were recruited for this study and were randomly
allocated into one of three alcohol treatment groups – a control
where the subjects remain sober during the entire study, a
moderate group were the subject is supplied alcohol but is
limited in such a way that their blood alcohol content (BAC)
remains under the legal limit to drive (BAC of 0.08) and a
group that received a high amount of alcohol to which their
BAC may exceed the legal limit for driving. Each subject was
trained on a video game system and their reaction time (in
milliseconds) to a visual stimulus was recorded at 7 time points
30 minutes apart (labeled T0=0, T1=30, T2=60 and so on). At
time point T0, all subjects were sober and those in one of the
alcohol consumption groups began drinking after the first
measured reaction time (controlled within the specifications
outlined). The researcher is interested in determining the
influence alcohol and age (namely, is reaction time different for
those in the 20s versus 30s) has on reaction times.
The task for today is to do a complete analysis for this study
and dig into the effects of alcohol, age and time have on
reaction times.Data input and wrangling
First read in the data:alcohol <- read.csv("alcoholReaction.csv")
head(alcohol)## Subject Age Alcohol T0 T1 T2 T3
T4 T5 T6
## 1 1 24 Control 255.3 254.8 256.4 255.1 257.0 256.1
257.0
## 2 2 34 Control 250.1 249.2 249.0 248.0 248.0 248.9
248.1

## 3 3 31 Control 248.2 247.1 246.9 246.7 246.0 246.0
247.0
## 4 4 24 Control 253.9 253.8 254.9 254.1 253.2 254.1
255.0
## 5 5 38 Control 250.0 251.0 250.0 249.9 248.8 249.1
249.9
## 6 6 38 Control 246.0 248.0 247.0 248.1 248.1 246.9
244.0
Note, the Age variable is recorded as an actual age in years, not
the category of 20s or 30s like we want – we need to
dichotomize this variable. Also note the data is in wide format –
the reaction times (the response variables) are spread over
multiple columns. We need a way to gather these columns into a
single column. So we need to do some data processing.
First consider the below code:head(alcohol %>%
mutate(Age = case_when(Age<31 ~ "20s",
Age %in% 31:40 ~ "30s")))## Subject Age
Alcohol T0 T1 T2 T3 T4 T5 T6
## 1 1 20s Control 255.3 254.8 256.4 255.1 257.0 256.1
257.0
## 2 2 30s Control 250.1 249.2 249.0 248.0 248.0 248.9
248.1
## 3 3 30s Control 248.2 247.1 246.9 246.7 246.0 246.0
247.0
## 4 4 20s Control 253.9 253.8 254.9 254.1 253.2 254.1
255.0
## 5 5 30s Control 250.0 251.0 250.0 249.9 248.8 249.1
249.9
## 6 6 30s Control 246.0 248.0 247.0 248.1 248.1 246.9
244.0
case_when is essentially a piece-wise comparison. When Age is
less than 31, you overwrite Age variable with “20s”. If the Age
is greater than 30, you replace it with “30s”. In this example we
used both a < comparison and the %in% statement we’ve seen
before just to show multiple functionality. Also note we include
30 in the 20s group and 40 in the 30s group so they are each of

size 10.alcohol <- alcohol %>%
mutate(Age = case_when(Age<31 ~ "20s",
Age %in% 31:40 ~ "30s") )
So the Age variable has been categorized. Now we need to
convert the data from wide to tall format. We do this with the
gather() function included in tidyverse.alcohol.tall <- alcohol
%>%
gather(key=Time, value=Reaction, c(T0, T1, T2, T3, T4, T5,
T6))
A blurb about gather There are essentially three inputs into the
gather() functions. Firstkey - Essentially provides the name of
the new variable we are going to create that consist of the
column namesvalue - Is the name for the new variable that will
house the values originally stored in the columns of interestThe
final part is a list of all the columns we want to gather, in this
case, T0, T1, T2, T3, T4, T5 and T6.head(alcohol.tall, n=10)##
Subject Age Alcohol Time Reaction
## 1 1 20s Control T0 255.3
## 2 2 30s Control T0 250.1
## 3 3 30s Control T0 248.2
## 4 4 20s Control T0 253.9
## 5 5 30s Control T0 250.0
## 6 6 30s Control T0 246.0
## 7 7 20s Control T0 248.8
## 8 8 30s Control T0 245.9
## 9 9 20s Control T0 246.9
## 10 10 30s Control T0 249.1
You will now note the data is a in a tall format, which is good
for analysis.
Lastly, so R doesn’t try and treat it as a number, we tell it that
the Subject variable is a factor or categorical variable. I also put
the Alcohol variables in the order we think…alcohol.tall <-
alcohol.tall %>%
mutate(Subject = as.factor(Subject),
Alcohol = factor(Alcohol, levels=c("Control",
"Moderate", "High")))Exploratory Data Analysis

There are 2 categories for age, 3 categories for alcohol use and
then 7 time points to consider. Essentially (2times 3times 7 =
42) combinations to consider. Rather than look numerically we
will consider things graphically.
First we consider a plot of the Reaction times in Time based on
Alcohol treatment with Age determining the
linetype.ggplot(alcohol.tall) +
geom_line(aes(x=Time, y=Reaction, group=Subject,
color=Alcohol, linetype=Age))
Not only is this plot noisy, it is hard to determine anything.
Let’s facet based on Ageggplot(alcohol.tall) +
geom_line(aes(x=Time, y=Reaction, group=Subject,
color=Alcohol)) +
facet_wrap(~Age)
This second plot is improved but still quite noisy. Let’s plot
average profiles rather than the raw data.ggplot(alcohol.tall,
aes(x=Time, y=Reaction, group=Alcohol, color=Alcohol)) +
stat_summary(fun.y=mean, geom="line") +
facet_wrap(~Age)
These average profiles are fairly telling and maybe even a little
surprising. Overall you see the High aclohol group (blue line)
shows an increase in reaction time over the time of the study.
The Control group shows a near decrease in the 30s group but
also note the spead is only about a half a unit decrease.Model
fitting and analysis
We fit a 2 factor repeated measure model and look at the
output.fit <- aov(Reaction ~ Age*Alcohol*Time +
Error(Subject/Time), data=alcohol.tall)
summary(fit)##
## Error: Subject
## Df Sum Sq Mean Sq F value Pr(>F)
## Age 1 18 17.72 0.254 0.616
## Alcohol 2 143 71.47 1.026 0.366

## Age:Alcohol 2 93 46.31 0.665 0.519
## Residuals 51 3553 69.66
##
## Error: Subject:Time
## Df Sum Sq Mean Sq F value Pr(>F)
## Time 6 50.3 8.386 6.929 6.45e-07 ***
## Age:Time 6 10.3 1.714 1.416 0.20786
## Alcohol:Time 12 40.0 3.330 2.752 0.00145 **
## Age:Alcohol:Time 12 13.8 1.150 0.950 0.49702
## Residuals 306 370.4 1.210
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
First we look at the most complicated interaction term, in this
case Age:Alcohol:Time and it is NOT significant. So we follow
up by considering the two-way interaction terms. We see
Age:Alcohol and Age:Time are not significant but
Alcohol:Time is. There is an interaction between Alcohol group
and Time. Given the interactions involving Age are not
significnat, we can also consider the Age main effect, but see it
is also insignificant (F-stat 0.252 on 1 and 51 degrees of
freedom, (p)-value=0.616). Age appears to have no influence
on the reaction times. We follow up with conditional multiple
comparisons.Multiple Comparison Follow ups
Note: We have two levels of control in this study, there is an
explicit Control group and at time point T0 no subjects had been
given a treatment, so it also operates as a control. Dunnett’s
method for multiple comparison is most appropriate (see chapter
2.7 of the text).
We see that Alcohol and Time both matter, but perhaps in
different ways. We consider both conditional comparisons. First
we run the emmeans() codemc.alc <- emmeans(fit, ~ Alcohol |
Time)## Warning in emm_basis.aovlist(object, ...): Some
predictors are correlated with the intercept - results are biased.
## May help to re-fit with different contrasts, e.g. 'contr.sum'##
NOTE: Results may be misleading due to involvement in
interactionsmc.time <- emmeans(fit, ~ Time | Alcohol)##

Warning in emm_basis.aovlist(object, ...): Some predictors are
correlated with the intercept - results are biased.
## May help to re-fit with different contrasts, e.g. 'contr.sum'##
NOTE: Results may be misleading due to involvement in
interactions
First we consider the effects of alcohol conditioning at different
time points.contrast(mc.alc, "trt.vs.ctrl", ref=1)## Time = T0:
## contrast estimate SE df t.ratio p.value
## Moderate - Control 1.077143 1.0774800 51.00 1.000
0.5097
## High - Control 1.400260 0.9861516 51.00 1.420 0.2799
##
## Time = T1:
0.2590
## High - Control 1.816169 1.0995693 78.06 1.652 0.1841
##
## Time = T2:
0.1950
## High - Control 2.023896 1.0995693 78.06 1.841 0.1274
##
## Time = T3:
0.1450
## High - Control 2.613442 1.0995693 78.06 2.377 0.0380
##
## Time = T4:
0.0907
## High - Control 2.814351 1.0995693 78.06 2.560 0.0239
##

## Time = T5:
0.0975
## High - Control 3.206623 1.0995693 78.06 2.916 0.0090
##
## Time = T6:
0.0781
## High - Control 3.517532 1.0995693 78.06 3.199 0.0039
##
## Results are averaged over the levels of: Age
## P value adjustment: dunnettx method for 2
testsplot(contrast(mc.alc, "trt.vs.ctrl", ref=1))
First note, that in all seven comparisons, the Moderate group is
never different than the Control group (this is true for all time,
smallest adjusted (p)-value is 0.0781). Thus, the profiles of
the Moderate group and the Control group are statistically the
same.
We can see that in the early time points, there was no difference
between the treatment groups receiving alcohol and those not
but as time progressed the “High” alcohol group had higher
reaction times than the control (starting at T3, it always
significant with adjusted (p)-value of 0.0380).
Next we compare the effects of time conditioning on the alcohol
group.contrast(mc.time, "trt.vs.ctrl", ref=1)## Alcohol =
Control:
## T1 - T0 0.1700000 0.3478929 306 0.489 0.9675
## T2 - T0 0.1750000 0.3478929 306 0.503 0.9647
## T3 - T0 0.2600000 0.3478929 306 0.747 0.8938
## T4 - T0 0.0700000 0.3478929 306 0.201 0.9976
## T5 - T0 -0.1750000 0.3478929 306 -0.503 0.9647
## T6 - T0 -0.1600000 0.3478929 306 -0.460 0.9727

##
## Alcohol = Moderate:
## T1 - T0 0.8466667 0.4017122 306 2.108 0.1603
## T2 - T0 1.0450000 0.4017122 306 2.601 0.0492
## T3 - T0 1.3166667 0.4017122 306 3.278 0.0065
## T4 - T0 1.3983333 0.4017122 306 3.481 0.0032
## T5 - T0 1.1133333 0.4017122 306 2.771 0.0309
## T6 - T0 1.2500000 0.4017122 306 3.112 0.0111
##
## Alcohol = High:
## T1 - T0 0.5859091 0.3398943 306 1.724 0.3302
## T2 - T0 0.7986364 0.3398943 306 2.350 0.0929
## T3 - T0 1.4731818 0.3398943 306 4.334 0.0001
## T4 - T0 1.4840909 0.3398943 306 4.366 0.0001
## T5 - T0 1.6313636 0.3398943 306 4.800 <.0001
## T6 - T0 1.9572727 0.3398943 306 5.758 <.0001
##
## Results are averaged over the levels of: Age
## P value adjustment: dunnettx method for 6
testsplot(contrast(mc.time, "trt.vs.ctrl", ref=1))
We see that the Control group never deviates from the control
time point (T0). This should not be surprising given they
remained sober for the entire study. In both of the other
treatments we see the influence of Time (and thus alcohol
consumption) on reaction times.
Even though the profile of the Moderate group was not
significantly different than the Control group, they did
experience an increase in reaction times with the consumption
of alcohol (just not enough to deviate overall from the Control
group). We see that the High consumption did deviate from the
Control group sometime around time point T3 (90
minutes).Conclusions
We established above that the key finding is that those with a

high dosage of alcohol had a longer reaction time compared to
the the control group as time progressed. We also find that
those receiving a moderate amount of alcohol performed
similarly to the control group. We close by building a profile
plot to summarize the findings (remember, Age was not
important).
First we plot the profiles of the three alcohol treatments
summarizing over all ages.alcohol.summary <- alcohol.tall
%>%
group_by(Alcohol, Time) %>%
summarize(Mean=mean(Reaction),
SE= sd(Reaction)/sqrt(n()))
ggplot(alcohol.summary, aes(x=Time, y=Mean, color=Alcohol))
+
geom_errorbar(aes(ymin=Mean-SE, ymax=Mean+SE),
width=0.1, position=position_dodge(0.3)) +
geom_line(aes(group=Alcohol), position=position_dodge(0.3))
+
geom_point(position=position_dodge(0.3))
Note this plot is a bit misleading since we have plotted the
moderate group even though it is statistically similar to the
control group (note the SE bars overlap for all time points for
the moderate and contrl groups). To link the control and
moderate groups, we have to do a bit more data processing. In
the below code we recast the Alcohol variable to only two
groups.alcohol.summary2 <- alcohol.tall %>%
mutate(Alcohol = case_when(Alcohol=="High" ~ "Legally
Drunk",
TRUE ~ "Legally Sober")) %>% # `TRUE
~` is everything else
group_by(Alcohol, Time) %>%
summarize(Mean=mean(Reaction),
SE= sd(Reaction)/sqrt(n()))
The TRUE ~ "Legally Sober" line essentially tells R that in any
other case (TRUE is always True) to mark it as Legally Sober.

In the first line of the case_when statement we use the ==
notation to compare for equality.
Now we make an overall plot summarizing the findings of our
study. To demonstrate the level of sophistication we can include
in a plot, I do quite a bit with axes, labeling and color choices.
Note this is sort of thing covered in detail in STA404. Here we
demonstrate the functionality.ggplot(alcohol.summary2,
aes(x=Time, y=Mean, color=Alcohol)) +
geom_errorbar(aes(ymin=Mean-SE, ymax=Mean+SE),
width=0.1, position=position_dodge(0.3)) +
geom_line(aes(group=Alcohol), position=position_dodge(0.3))
+
geom_point(position=position_dodge(0.3)) +
scale_x_discrete(name="Minutes since start of study",
labels=c("0","30","60","90", "120", "150", "180")) +
scale_color_manual(name="Alcohol level",
values=c("darkgreen", "cyan")) +
labs(y="Mean Reaction Time (ms)") +
theme_bw() +
ggtitle("Alcohol effects on Reaction time to Visual Stimulus")
+
theme(legend.position=c(0.125,0.85)) # 0.125 (ie 12.5%) from
the left edge and 0.85 from the bottom edge

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