Midterm (1)
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University of California, Berkeley *
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Course
158
Subject
Statistics
Date
Feb 20, 2024
Type
Pages
13
Uploaded by GeneralSteel1537
Stat 158 MIDTERM
2023-10-13
Kyle Abilar
Student ID: 3037901752
Task 1.
#Loading in the data
df
=
read.csv
(
"motivation.csv"
,
header =
TRUE
)
The units of this experiment are going to be the 96 workers in the call center.
The conditions of this experiment have two main factors: conscious goal setting and non-conscious priming.
Each has at least two levels: for the conscious goal setting: having half of the subjects assigned a monetary
goal of $1200 while the other half is told is simply to do their best. For the non conscious priming: 1/3 of
them receive packets with a color photo of a woman winning a race, 1/3 receive packets with a collage of
achievements-realted photos, and the final 1/3 receive packets with no images.
The response of this experiment is the amount of dollars raised by each employee during the 3 hour shift.
There are two potential outcomes for conscious goal setting and three potential outcomes for non conscious
priming which results in 6 potential outcomes.
Since there are 96(N) employees in the study, the total
potential outcomes is 96 x 6 = 576N.
As long as the process of recording the amount of dollars is standardized and consistent, the response should
be considered reliable.
In this experiment, the amount of dollars raised is the direct measure of the subjects performance to reflect
their efforts.
There are factors such as experience in talking to people to get them to donate and even
willingness of donors that can affect the results. However based on this experiment since we are just examining
their efforts, this can be considered valid.
1
Task 2. If I was conducting this experiment I would assign every single person an id number from 1-96 in order,
from who signed up first to the last. I assume that wouldn’t create any sort of bias due to signing up having
no specific order. From there I would a random number generator in R to give which conscious goal groups
the subjects will be put in such as using sample(1:96). I will run the random number generator three times
and on the third time is when I’ll divide the subjects, the first 48 numbers will be group “Raise_1200” and
the remaining will be assigned to “Do_Your_Best”. To get the priming groups I would use the same random
generator three times and on the third time divide the subjects, first 32 numbers = “Photo_Backdrop”, the
next 32 numbers = “Collage_Top, and finally the remaining will =”No_Image”.
2
Task 3.
interaction.plot
(
x.factor =
df
$
Conscious_Goal,
trace.factor =
df
$
Priming,
response =
df
$
Funds_Raised,
main =
"Interaction Plot"
,
xlab =
"Priming"
,
ylab =
"Amount Raised"
,
trace.label =
"Conscious Goal"
)
400
800
1200
1600
Interaction Plot
Priming
Amount Raised
Do_Your_Best
Raise_1200
Conscious Goal
Photo_Backdrop
Collage_Top
No_Image
Based on this interaction plot we can see here that lines are mainly parallel to one another, indicating that
there’s no interaction between the factors. However, there seems to be a slight indication that a photo back
drop and collage top may have some interaction because the lines aren’t exactly parallel to eachother and
slightlty touch.
ggplot
(df,
aes
(
x =
Priming,
y =
Funds_Raised,
fill =
Conscious_Goal))
+
geom_col
()
+
coord_flip
()
3
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Collage_Top
No_Image
Photo_Backdrop
0
10000
20000
30000
40000
Funds_Raised
Priming
Conscious_Goal
Do_Your_Best
Raise_1200
Based on this column graph we can see that using pictures in comparison to no pictures raised more overall
money. We can also see that majority of that money was made up from subjects being told to raise $1200 in
comparison to being told to do their best.
ggplot
(df,
aes
(
x =
Priming,
y =
Funds_Raised))
+
geom_point
(
position =
"dodge"
)
+
facet_wrap
(
~
Conscious_Goal)
## Warning: Width not defined
## i Set with
`
position_dodge(width = ...)
`
4
Do_Your_Best
Raise_1200
Collage_Top
No_Image
Photo_Backdrop
Collage_Top
No_Image
Photo_Backdrop
0
1000
2000
3000
4000
Priming
Funds_Raised
From this dotplot we can see that again subjects that were given pictures raised more money in comparison
to subjects that didn’t have any picutres.
We can also see the distribution is the symmetrical for the
conscious goal setting, however, subjects told to raise $1200(right side) earned more money.
5
Task 4.
#Reporting the ANOVA table
anova
(
lm
(Funds_Raised
~
Conscious_Goal
*
Priming,
data =
df))
## Analysis of Variance Table
##
## Response: Funds_Raised
##
Df
Sum Sq
Mean Sq F value
Pr(>F)
## Conscious_Goal
1 11725026 11725026
51.631 1.878e-10 ***
## Priming
2
7204740
3602370
15.863 1.255e-06 ***
## Conscious_Goal:Priming
2
461927
230964
1.017
0.3658
## Residuals
90 20438281
227092
## ---
## Signif. codes:
0
'
***
'
0.001
'
**
'
0.01
'
*
'
0.05
'
.
'
0.1
' '
1
#Random inference
df
$
Conscious_Goal.Priming
<-
paste
(df
$
Conscious_Goal,
df
$
Priming,
sep =
'
.
'
)
my_design
<-
declare_ra
(
N =
nrow
(df),
m_each =
table
(df
$
Conscious_Goal.Priming),
conditions =
names
(
table
(df
$
Conscious_Goal.Priming)))
test_statistic
<-
function
(dat){
split.Conscious_Goal.Priming
<-
apply
(
matrix
(df
$
Conscious_Goal.Priming),
1
,
function
(x)
strsplit
(x,
split =
'
.
'
,
fixed =
TRUE
)[[
1
]])
dat
$
Conscious_Goal
<-
as.factor
(split.Conscious_Goal.Priming[
1
,])
dat
$
Priming
<-
as.factor
(split.Conscious_Goal.Priming[
2
,])
anova.tab
<-
anova
(
lm
(Funds_Raised
~
Conscious_Goal
*
Priming,
data =
dat))
return
(anova.tab[
"Conscious_Goal:Priming"
,
"F value"
])
}
ri_out
<-
conduct_ri
(
test_function =
test_statistic,
declaration =
my_design,
assignment =
'
Conscious_Goal.Priming
'
,
sharp_hypothesis =
0
,
data =
df,
sims =
1000
)
summary
(ri_out)
##
term estimate two_tailed_p_value
## 1 Custom Test Statistic 1.017048
1
Since there were two facotrs I decided to use an ANOVA table to compare the differences between conscious
goal and priming. The p-value for conscious goals and priming = 0.3658 > 0.05 indicating that there isn’t
significant differences between the two. After performing random inference, I came up with a p-value of 1
which again indicates no significant difference between the two groups.
Contrasts
Contrasts 1: The effects of Conscious goal setting
Going to be testing if employees with specific monetary goals, raise more money on average compared to
those who are encouraged to do their best.
6
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Reasoning: This contrast provides insight into the overall impact of conscious goal-setting on performance,
irrespective of non-conscious priming conditions.
# Calculating the observed difference
df_Conscious_Goal
<-
df
%>%
filter
(Conscious_Goal
==
"Raise_1200"
)
df_Do_Your_Best
<-
df
%>%
filter
(Conscious_Goal
==
"Do_Your_Best"
)
obs_diff
<-
mean
(df_Conscious_Goal
$
Funds_Raised)
-
mean
(df_Do_Your_Best
$
Funds_Raised)
# Permutations for randomization inference
n_permutations
<-
1000
permuted_diffs
<-
numeric
(n_permutations)
for
(i
in
1
:
n_permutations) {
combined
<-
c
(df_Conscious_Goal
$
Funds_Raised, df_Do_Your_Best
$
Funds_Raised)
shuffled
<-
sample
(combined)
permuted_diffs[i]
<-
mean
(shuffled[
1
:
5
])
-
mean
(shuffled[
6
:
10
])
}
#
P-value
p_value
<-
sum
(
abs
(permuted_diffs)
>=
abs
(obs_diff))
/
n_permutations
p_value
## [1] 0.092
contrast1
<-
lm
(Funds_Raised
~
Conscious_Goal,
data =
df)
summary
(contrast1)
##
## Call:
## lm(formula = Funds_Raised ~ Conscious_Goal, data = df)
##
## Residuals:
##
Min
1Q
Median
3Q
Max
## -1075.00
-338.28
-76.04
224.22
2975.00
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept)
726.04
78.92
9.199 9.27e-15 ***
## Conscious_GoalRaise_1200
698.96
111.61
6.262 1.13e-08 ***
## ---
## Signif. codes:
0
'
***
'
0.001
'
**
'
0.01
'
*
'
0.05
'
.
'
0.1
' '
1
##
## Residual standard error: 546.8 on 94 degrees of freedom
## Multiple R-squared:
0.2944, Adjusted R-squared:
0.2869
## F-statistic: 39.22 on 1 and 94 DF,
p-value: 1.128e-08
Contrasts 2: The effect of priming
Testing if there’s a difference between the employees seeing photos vs no photos.
Reasoning: This contrast explores the influence of a specific non-conscious priming condition on performance.
# Calculating the observed difference
photos
<-
df
%>%
filter
(Priming
==
c
(
"Collage_Top"
,
"Photo_Backdrop"
))
nothing
<-
df
%>%
filter
(Priming
==
"No_Image"
)
obs_diff
<-
mean
(photos
$
Funds_Raised)
-
mean
((nothing
$
Funds_Raised))
7
# Permutations for randomization inference
n_permutations
<-
1000
permuted_diffs
<-
numeric
(n_permutations)
for
(i
in
1
:
n_permutations) {
combined
<-
c
(photos
$
Funds_Raised, nothing
$
Funds_Raised)
shuffled
<-
sample
(combined)
permuted_diffs[i]
<-
mean
(shuffled[
1
:
5
])
-
mean
(shuffled[
6
:
10
])
}
# P-value
p_value
<-
sum
(
abs
(permuted_diffs)
>=
abs
(obs_diff))
/
n_permutations
p_value
## [1] 0.158
contrast2
<-
lm
(Funds_Raised
~
Priming,
data =
df)
summary
(contrast2)
##
## Call:
## lm(formula = Funds_Raised ~ Priming, data = df)
##
## Residuals:
##
Min
1Q
Median
3Q
Max
## -1006.3
-382.4
-73.4
271.9
3170.3
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept)
1229.69
104.70
11.744
< 2e-16 ***
## PrimingNo_Image
-539.06
148.07
-3.641 0.000447 ***
## PrimingPhoto_Backdrop
76.56
148.07
0.517 0.606342
## ---
## Signif. codes:
0
'
***
'
0.001
'
**
'
0.01
'
*
'
0.05
'
.
'
0.1
' '
1
##
## Residual standard error: 592.3 on 93 degrees of freedom
## Multiple R-squared:
0.1809, Adjusted R-squared:
0.1633
## F-statistic: 10.27 on 2 and 93 DF,
p-value: 9.343e-05
Constrast 3: (Raise 1200 + Priming) vs (Do your best + No image)
Testing if there’s a difference between people who seen the photo backdrop vs the collage
Reasoning: This contrast helps determine whether the combination of setting specific goals and using the
achievement-related collage has a unique impact on performance.
# Calculating the observed difference
rm
<-
df
%>%
filter
(Priming
==
c
(
"Photo_Backdrop"
,
"Collage_Top"
)
&
Conscious_Goal
==
"Raise_1200"
)
dn
<-
df
%>%
filter
(Priming
==
"No_Image"
&
Conscious_Goal
==
"Do_Your_Best"
)
obs_diff
<-
mean
(rm
$
Funds_Raised)
-
mean
(dn
$
Funds_Raised)
# Permutations for randomization inference
n_permutations
<-
1000
permuted_diffs
<-
numeric
(n_permutations)
for
(i
in
1
:
n_permutations) {
8
combined
<-
c
(rm
$
Funds_Raised, dn
$
Funds_Raised)
shuffled
<-
sample
(combined)
permuted_diffs[i]
<-
mean
(shuffled[
1
:
5
])
-
mean
(shuffled[
6
:
10
])
}
# P-value
p_value
<-
sum
(
abs
(permuted_diffs)
>=
abs
(obs_diff))
/
n_permutations
p_value
## [1] 0.003
contrast3
<-
lm
(Funds_Raised
~
Conscious_Goal
*
Priming,
data =
df)
summary
(contrast3)
##
## Call:
## lm(formula = Funds_Raised ~ Conscious_Goal * Priming, data = df)
##
## Residuals:
##
Min
1Q
Median
3Q
Max
## -740.62 -242.97
-35.94
153.91 2809.38
##
## Coefficients:
##
Estimate Std. Error t value
## (Intercept)
868.750
119.135
7.292
## Conscious_GoalRaise_1200
721.875
168.483
4.285
## PrimingNo_Image
-437.500
168.483
-2.597
## PrimingPhoto_Backdrop
9.375
168.483
0.056
## Conscious_GoalRaise_1200:PrimingNo_Image
-203.125
238.271
-0.852
## Conscious_GoalRaise_1200:PrimingPhoto_Backdrop
134.375
238.271
0.564
##
Pr(>|t|)
## (Intercept)
1.14e-10 ***
## Conscious_GoalRaise_1200
4.58e-05 ***
## PrimingNo_Image
0.011 *
## PrimingPhoto_Backdrop
0.956
## Conscious_GoalRaise_1200:PrimingNo_Image
0.396
## Conscious_GoalRaise_1200:PrimingPhoto_Backdrop
0.574
## ---
## Signif. codes:
0
'
***
'
0.001
'
**
'
0.01
'
*
'
0.05
'
.
'
0.1
' '
1
##
## Residual standard error: 476.5 on 90 degrees of freedom
## Multiple R-squared:
0.4869, Adjusted R-squared:
0.4584
## F-statistic: 17.08 on 5 and 90 DF,
p-value: 7.595e-12
9
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Task 5. What I found is that the betweem conscious goal setting and non conscious goal setting, there wasn’t
stastically strong enough evidence to prove that there was a difference between them. The data visualizations
showed that overall, people that did receive photos or a specific goal raised more money, however, after
performing inferences and contrasts we can see that the data suggests there they weren’t significantly different
from eachother.
This experiment design has it’s strengths and weaknesses. Some of it’s strengths were the use of randomization,
which minizes bias and helps the validaty of the experiment. Manipulating both conscious and non-conscious
goal setting allows you to observe the difference in perfromance between groups, which can strengthen the
results of the inference. Having a balanced factorial design also makes it easier to examine the potenial
interactions and relationship between the factors.
Some weakness because there was no differination of
experience, the results may be unable to generalize to all real world work environments to examine the affect
of motiavtion. 96 people is a lot but still a small sample size to generalize the findings to a bigger population.
The study was also examining the effects after a 3 hour shift, which can be completely different than the
effects of motivation long term.
Experimental designs allow you to make better causation and inferences, whereas an observation study can
only show associations. The controlled environment and random assignment in experimental designs help
minimize internal problems to validity. Observational studies often struggle to control for confounding factors,
which can introduce bias and reduce the reliability of the results.Experimental designs can be replicated more
easily, and the conditions can be more controlled. In observational studies, it can be challenging to replicate
the exact conditions, leading to inconsistencies in results.
Task 6. 1 potential blocking factor I thought would be beneficial would be blocking based on experience level.
Employees with more experience in call centers can significantly affect their performance, therefore blocking
by their experience level could’ve helped the results of this experiment. I would first divide the subjects into
three groups: Block 1(beginner): less than 6 months of experience, Block 2(Intermediate): 6 months to a
year of experience, Block 3(Experienced): Over a year of experience. Then I would assign everyone randomly
into the groups as mentioned in question 2 using a random number generator.
By including a block in this experiments allows you to better assess the impact of conscious goal-setting and
non-conscious priming on employee performance. By examining treatment effects within different experience
groups, the study’s findings may be more generalization to call centers with diverse levels of employee
experience. Blocking will improve the precision of this study by reducing variability, which in turn increases
the reliability of the results.
10
R code
# #Loading in the data
# df = read.csv("motivation.csv", header = TRUE )
#
# Question 3:
#
# interaction.plot(x.factor = df$Conscious_Goal,
#
trace.factor = df$Priming,
#
response = df$Funds_Raised,
#
main = "Interaction Plot",
#
xlab = "Priming",
#
ylab = "Amount Raised",
#
trace.label = "Conscious Goal")
#
#
# ggplot(df, aes(x = Priming, y = Funds_Raised, fill = Conscious_Goal)) +
#
geom_col() +
#
coord_flip()
#
#
# ggplot(df, aes(x = Priming, y = Funds_Raised)) +
#
geom_point(position = "dodge") +
#
facet_wrap(~Conscious_Goal)
#
#
# Question 4:
#
# #Report the ANOVA table
# anova(lm(Funds_Raised ~ Conscious_Goal * Priming, data = df))
#
# #Random inference
# df$Conscious_Goal.Priming <- paste(df$Conscious_Goal,
#
df$Priming, sep =
'
.
'
)
#
# my_design <- declare_ra(N = nrow(df),
#
m_each = table(df$Conscious_Goal.Priming),
#
conditions = names(table(df$Conscious_Goal.Priming)))
#
# test_statistic <- function(dat){
#
split.Conscious_Goal.Priming <- apply(matrix(df$Conscious_Goal.Priming), 1,
#
function(x) strsplit(x, split =
'
.
'
, fixed = TRUE)[[1]])
#
dat$Conscious_Goal <- as.factor(split.Conscious_Goal.Priming[1,])
#
dat$Priming <- as.factor(split.Conscious_Goal.Priming[2,])
#
anova.tab <- anova(lm(Funds_Raised ~ Conscious_Goal * Priming, data = dat))
#
return(anova.tab["Conscious_Goal:Priming", "F value"])
# }
#
#
# ri_out <- conduct_ri(test_function = test_statistic,
#
declaration = my_design,
#
assignment =
'
Conscious_Goal.Priming
'
,
#
sharp_hypothesis = 0,
#
data = df,
11
#
sims = 1000)
#
# summary(ri_out)
#
#
# # Calculating the observed difference
# df_Conscious_Goal <- df %>% filter(Conscious_Goal == "Raise_1200")
# df_Do_Your_Best <- df %>% filter(Conscious_Goal == "Do_Your_Best")
#
# obs_diff <- mean(df_Conscious_Goal$Funds_Raised) - mean(df_Do_Your_Best$Funds_Raised)
#
# # Permutations for randomization inference
# n_permutations <- 1000
# permuted_diffs <- numeric(n_permutations)
# for (i in 1:n_permutations) {
#
combined <- c(df_Conscious_Goal$Funds_Raised, df_Do_Your_Best$Funds_Raised)
#
shuffled <- sample(combined)
#
permuted_diffs[i] <- mean(shuffled[1:5]) - mean(shuffled[6:10])
# }
#
# #
P-value
# p_value <- sum(abs(permuted_diffs) >= abs(obs_diff)) / n_permutations
# p_value
#
# contrast1 <- lm(Funds_Raised ~ Conscious_Goal, data = df)
# summary(contrast1)
#
#
# # Calculating the observed difference
# photos <- df %>% filter(Priming == c("Collage_Top", "Photo_Backdrop"))
# nothing <- df %>% filter(Priming == "No_Image")
#
# obs_diff <- mean(photos$Funds_Raised) - mean((nothing$Funds_Raised))
#
# # Permutations for randomization inference
# n_permutations <- 1000
# permuted_diffs <- numeric(n_permutations)
# for (i in 1:n_permutations) {
#
combined <- c(photos$Funds_Raised, nothing$Funds_Raised)
#
shuffled <- sample(combined)
#
permuted_diffs[i] <- mean(shuffled[1:5]) - mean(shuffled[6:10])
# }
#
# # P-value
# p_value <- sum(abs(permuted_diffs) >= abs(obs_diff)) / n_permutations
# p_value
#
# contrast2 <- lm(Funds_Raised ~ Priming, data = df)
# summary(contrast2)
#
#
#
# # Calculating the observed difference
12
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# rm <- df %>% filter(Priming == c("Photo_Backdrop", "Collage_Top") & Conscious_Goal == "Raise_1200")
#
# dn <- df %>% filter(Priming == "No_Image" & Conscious_Goal == "Do_Your_Best")
#
# obs_diff <- mean(rm$Funds_Raised) - mean(dn$Funds_Raised)
#
# # Permutations for randomization inference
# n_permutations <- 1000
# permuted_diffs <- numeric(n_permutations)
# for (i in 1:n_permutations) {
#
combined <- c(rm$Funds_Raised, dn$Funds_Raised)
#
shuffled <- sample(combined)
#
permuted_diffs[i] <- mean(shuffled[1:5]) - mean(shuffled[6:10])
# }
#
# # P-value
# p_value <- sum(abs(permuted_diffs) >= abs(obs_diff)) / n_permutations
# p_value
#
# contrast3 <- lm(Funds_Raised ~ Conscious_Goal * Priming, data = df)
# summary(contrast3)
13
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