Day 08 ActivityFisher & HughesSeptember 21, 2018StudyA study was c.docx

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
UVA-M-0677H
Rev. Dec. 9, 2015
This user guide was prepared by Paul W. Farris, Landmark
Communications Professor of Business Administration; Gerry
Yemen, Senior Researcher;
University of Virginia Darden School Foundation,
Charlottesville, VA. All rights reserved.
To order copies, send an e-mail to [email protected] No part of
this publication may be reproduced, stored in a retrieval system,

used in a spreadsheet,
or transmitted in any form or by any means—electronic,
mechanical, photocopying, recording, or otherwise—without the
permission of the Darden School Foundation.
Positioning Game
User Guide
Overview
The Positioning Game simulation (UVA-M-0677) was designed
to offer an opportunity to actively
experiment with realistic problems in product marketing—
market definition, segmentation, and positioning.
The game has a focus on perceptual mapping; players will be
asked to make decisions, often quickly, in the
context of a new product launch and impending competition.
There are anywhere from two to six players in each market who
are competing for customers in the
segment. All players must be logged in at the same time to play.
Your instructor will set the number of rounds
to be played as well as the duration of each round. A timer has
been built into the game and coordinates the
rounds moving forward. No new round of positioning can occur
until all players in the market have completed
the round.
If a player’s computer is disconnected, the simulation will wait
for that player to reconnect and either click
“Submit,” or allow the timer to expire. The simulation advances

automatically when the first of the following
is true:
d to run out while open on the
computers of all users in the market
A password is required to access the simulation. If you don’t
have one prior to playing, please contact your
instructor. Once the game URL is available, your instructor will
invite you to start the game. But before you
do, please read the instructions with care.
Signing In and Starting the Game
To access the exercise, open the URL you receiveds either from
your instructor in class or in an e-mail
message sent through the Forio.com simulation platform. You
will be prompted with a log-in screen (Figure 1).
Please enter your e-mail address or username and the assigned
password, then click “Log In.”
mailto:[email protected]
Page 2 UVA-M-0677H
Figure 1. User log-in screen.
Source: All figures created by case writer.

At the start of the first round, brief instructions will ask you to
consider where the best position for your
product would be on the grid (see Figure 2). Please note that
there are two tags in the upper right corner:
People icon:
Player Identification icon:
The People icon indicates the number of players who have
already logged in to your market. Clicking on
or moving your mouse over the People icon provides the status
of all players in the group—if green, that player
is logged in, and if red, that player is not logged in (see Figure
2). The color-coded Player Identification icon
features your log-in name.
Figure 2. Game instructions.
Page 3 UVA-M-0677H
Clicking the “Join Game” button will either display a
notification in a dialog box with a progress bar
indicating the number of other players in your market who are
ready to start playing (see Figure 3) or will begin
the round and start the timer if all other players are ready. The
round cannot start until all players are logged in
and have joined the game. If you are the last player to click Join

Game, the progress bar will not appear. If for
some reason a player has to log out, the game will resume at the
place where it was left.
Once everyone has joined the game, the market interface will
appear (see Figure 4, which is the beverage
industry default market. Your instructor may have chosen a
different industry, in which case the corner products
will look different).
Each corner of the market shows one of the four product choices
based upon the extremes of taste. In this
example, in the top right quadrant is cola, which is very sweet
and fizzy. Soda water (lower right quadrant) is
plain and fizzy. Water (lower left quadrant) is plain and flat.
And juice (top left quadrant) is very sweet and flat.
On the first round, the user sees customers’ preferences graphed
within the market space. These customers are
currently buying cola, soda water, water, or juice based on how
closely their tastes are aligned to each of these
four products. The challenge is to enter the market space with a
product that matches the taste of as many
customers as possible. The trick is that there are five other
products that will be launching the same week, and
you do not yet know where they fit within the market. Your
product icon will be round with a light gray
background and your competitors will be squares with black
backgrounds. Note that there is also a timer at the
bottom of the interface that starts running when all players are
ready. There is also a cost indicator set at $0 for
the first round.
Figure 3. Number of players ready to start.

Figure 4. The market.
Page 4 UVA-M-0677H
Positioning the Product
Players will need to click on the grid to set a position
somewhere among customer preferences as an initial
product placement. The product will then be displayed on the
map with a border that matches the color of
your username in the upper right side of the header of the
simulation interface (see Figure 5). Note that players
can click elsewhere on the map (or click and drag their product)
to change their position for the week. During
the first round, there are no costs to position a product wherever
the player wants. This can be done as many
times as desired until either the Submit button is clicked or the
round timer runs out. A check mark will appear
on products whose players have already clicked Submit (see
Figure 6). This means that player can no longer
reposition their product, and their final position for that round
has been recorded. A progress bar will appear
at the bottom of the grid. The next round will not be launched
until all players in the market have submitted
their placement or their timer has run out.
Figure 5. Product placement.
Figure 6. Checked product waiting for competitors.

UVA-M-0677H
As each round is played, the “Results of Week [#]” box toward
the upper right side of the interface will
display the development costs for the previous week as well as
income from orders, marketing and development
cost, and operating profit for the previous round (see Figure 7).
After the first round, the more a player changes
the taste of his or her product (the farther his or her product is
moved on the grid), the more the development
costs will increase. The simulation will automatically advance
as soon as all of the players in the same group
have pressed their Submit buttons, or their round timers have
run out. The next round starts once all players
have submitted choices from the previous round. Players will be
able to see where their competitors have
positioned their products, as well as how much of the market
their product has captured. The “Cumulative
Profits” box in the lower right side of the interface shows the
total cumulative profits each product captured
in the previous rounds.
Figure 7. End of first week in a six-player, low-cost, 15-week
game.
Each player will then have the chance to modify the taste of his
or her product by repositioning it within
the market space in the next round. Just as in the previous
round, the farther a product moves from the place
it started at the beginning of the round, the more costly the
modification to the product will be (see Figure 8).

UVA-M-0677H
Figure 8. Week two of six-player, low-cost, 15-week game.
The game will end after a predetermined number of rounds have
been played (see Figure 9), and your
instructor will then be able to review each week’s results with
the class.
Figure 9. Simulation ended.
MARKETING EXERCISE:
The Positioning
Game
In this multi-player exercise, students compete
within a single market to maximize profit and
market share for their specific product. Students
make key decisions regarding product features
and gain insights into market definition, market
segmentation, and the critical role of product
positioning in marketing strategy.
A perceptual map captures the features and benefits that
consumers seek most and displays them in 2 dimensions for
easy analysis. In The Positioning Game, groups of students
compete by using the perceptual map to position their

product at an ideal point in the market. Through a series of
rounds, students decide whether—and where—to move their
product’s position based on market conditions, competitors’
choices, and their own results. As in the real world, students
face time pressure, costs associated with product changes,
and the unseen decisions of competitors.
This online exercise can be played simultaneously by groups
of 2–6 students. Instructors can customize elements including
group size, customer preferences, timing and number of
rounds, cost to move, and variability of customer choices.
The default market is the beverage industry, with product
characteristics of “sweet,” “plain,” “fizzy,” or “flat,” but
instructors can designate alternate industries or product
characteristics. Student performance can be assessed based
on cumulative profits, average profits, development cost,
product position, and/or market share.
Developed by the University of Virginia Darden School of
Business, The Positioning Game shows students the importance
of planning and the potential positioning complexities of
launching a new or updated product. Students learn key
lessons regarding market structure and segments, brand
perception, competitive analysis, and consumer-driven
product development.
LEARN MORE ON OUR WEB SITE:
hbsp.harvard.edu
IDEAL FOR COURSES IN:
MARKETING, NEW PRODUCT DEVELOPMENT
ENGAGING AND FAST-PACED PLAY
SIMPLE, CUSTOMIZABLE SETUP AND
ADMINISTRATION

Æ CONTINUED ON REVERSE
PREVIEW AND FREE TRIAL ACCESS
FOR PREMIUM EDUCATORS
A Free Trial allows full access to the entire exercise
and is available to Premium Educators on our web site.
Premium Educator access is a free service for faculty
at degree-granting institutions and allows access to
Educator Copies, Teaching Notes, Free Trials, course
planning tools, and special student pricing. See reverse
for additional information.
Æ educatoraccess.hbsp.harvard.edu
Product #UV6715 | Multi-player | Seat Time: 30 minutes
¾ Authored by Paul W. Farris, Darden School of Business
¾ Developed by Darden School of Business
E X E R C I S E S
LEARN MORE ON OUR WEB SITE: hbsp.harvard.edu
Product #M00035 MC189431114
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Publishing is an affiliate of Harvard Business School.
Printed on recycled paper
EXERCISES
ADMINISTRATION TOOLS AND OPTIONS

Powerful administrative tools allow for
easy management of teams and real-time
reporting of student decisions. Summary
and analysis screens provide valuable
information for post-play class discussion.
Instructors can accommodate different
class sizes and learning objectives by
customizing variables such as:
¾ Group size
¾ Timing and number of rounds
¾ Cost to move
¾ Distribution of customers on map
¾ Product properties
¾ Product names
¾ Welcome and end-game messages
CUSTOMER SERVICE AND TECH SUPPORT
6 am - 8 pm ET
Monday through Friday
9 am - 5 pm ET
Saturday and Sunday
Customer Service:
1-800-545-7685
(1-617-783-7600 outside the U.S. and Canada)

[email protected]
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1-800-810-8858
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EDUCATORS Get updates from us at [email protected]
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Results can be displayed by Cumulative Profits, Average
Profits,
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