FINAL PROJECT: BOOKSTORES Sarah Hadyniak and Kathy Fein I cannot live without books. ~Thomas
Feb 25, 2016
FINAL PROJECT: BOOKSTORES
Sarah Hadyniak and Kathy Fein
I cannot live without books. ~Thomas Jefferson
Description of Topic
We wanted to research the top two bookstores (Borders and Barnes & Noble) to see the differences in people who frequented these stores as well as the differences of sections visited in both stores.
Additionally we wanted to see the differences in the companies based upon their stocks to see the national attitude towards each store.
Background
There are over 29,000 bookstores in the US Borders owns/operates 511 Borders
superstores plus 175 Waldenbooks stores Barnes and Noble owns/operates 717
bookstores plus 637 college bookstores February 16, 2011: Borders announced
that it had filed for Chapter 11 bankruptcy protection Also announced the liquidation/closing of 226
stores
Our Project We decided to go to two different bookstores
to observe customers Kathy went to Borders Sarah went to Barnes and Noble
We recorded the following about each subject: Section they were looking in Gender Age Group (young, adult, senior) If they bought a book If they were alone
Section Preference
Biogra
phy
History
Literat
ure
Mystery
Relig
ion
Romanc
eSci
-Fi
Self-H
elp02468
101214161820
Frequencies of Females in Each Section
Biogra
phy
History
Literat
ure
Mystery
Relig
ion
Roman
ceSci
-Fi
Self-H
elp0
5
10
15
20
25
Frequencies of Males in Each Section
Our data indicates that members of each gender do not visit each section in equal proportions. We will test this later with a chi² test.
Is there a relationship between gender and preference of section?
Biog-raphy
History Literature Mystery Religion Romance Sci-Fi Self-Help0
5
10
15
20
25Male Female
Freq
uenc
y
Section of Bookstore in which Subject was
Observed
The most males (20) were found in Sci-Fi, while the least males (0) were found in Romance. The most females (18) were found in Literature, while the least females (2) were found in Biography. This distribution contributes to our prediction that we will find evidence of an association between gender and section.
• Based on our data, the population of females visiting bookstores as a whole prefer literature the most, while males prefer sci-fi.
• Females least prefer biography while males least prefer romance when shopping or browsing for books.
Is there a relationship between gender and preference of section?
Library of Congress (not technically a bookstore, but still REALLY cool)
χ²-Test for Independence: Gender and Preference of Section
Ho: Gender and preference of section are independentHa: Gender and preference of section are not independentConditions:1. Categorical Data2. SRS3. Each count is greater than
or equal to 5
Gender and Section are categorical data
Subjects were randomly recorded at different days and times, so it is assumed to be representative
Eliminating Biography, Mystery, and Romance, all expected counts are greater or equal to 5.
Observed
History Literature
Religion
Sci-Fi Self-Help
Females 9 18 6 11 8Males 14 14 6 20 8
Expected
History Literature
Religion Sci-Fi Self-Help
Females 10.491 14.596 5.4737 14.14 7.2982Males 12.509 17.404 6.5263 16.86 8.7018
χ²-Test for Independence: Gender and Preference of Section
Conditions met, use χ²-distribution, do χ²-test for independence
χ²-Test for Independence: Gender and Preference of Section
3484.3...4.16)4.1618(
8.11)8.119(
expexp)( 222
2
obs
P(χ² >3.3484) = .5013We fail to reject our Ho because the p-value of .5013 is greater than α=.05. We have sufficient evidence that gender and preference of section (excluding romance, biography, and mystery) are independent.
Degrees Freedom = 4
Distribution of Age Groups at Different Bookstores
Young (child to 20)Adult (20 to 70ish)Senior (70ish and up)
25%
60.9%
14.1%
Barnes and Noble
Borders
Young (child to 20)Adult (20 to 70ish)Senior (70ish and up)
26.7%
73.3%
•Adults make up the largest portion of people who visit bookstores, but compared to the other two categories, “adult” encompasses the most ages and therefore the most people•Based on our data, more seniors visit Barnes and Noble than Borders
χ²-Test for Independence: Age Group and Store Choice
OBSERVED
Young Adult
Borders 12 33Barnes and Noble
23 56
EXPECTED
Young Adult
Borders 12.702 32.298Barnes and Noble
22.298 56.702
Conditions:1. Categorical Data2. SRS3. Each count is greater than
or equal to 5
Age group and store are categorical data
Subjects were randomly recorded at different days and times, so it is assumed to be representative
Eliminating the seniors, all expected counts are greater or equal to 5.
Ho: Age group and store choice are independentHa: Age group and store choice are not independent
Conditions met, use χ²-distribution, do χ²-test for independence
χ²-Test for Independence: Age Group and Store Choice
0848....234.29
)234.2933(496.11
)496.1112(expexp)( 222
2
obs
P(χ² >.0848) = .7710We fail to reject our Ho because the p-value of .7710 is greater than α=.05. We have sufficient evidence that age group and store choice are independent.
Degrees Freedom = 1
Comparing Stock Prices of Borders and Barnes and Noble We decided to compare prices from
2005 because we wanted to eliminate the lurking variable of Borders’ recent financial troubles
We assigned the days of the year from 1-365 and randomly generated 30 numbers using a calculator
We recorded the stock prices of each company for each day and ran a paired t-testAll stock prices recorded in
US Dollars
Stock Prices from 30 Days (Borders)
21.02, 20.53, 23.71, 23.16, 21.28, 25.27, 22.62, 25.39, 26.92, 21.17, 25.42, 25.24, 21.02, 21.14, 19.63, 23.07, 24.95, 20.14, 26.62, 20.59, 24.19, 20.39, 22.71, 25.80, 23.01, 24.39, 25.00, 24.88, 27.14, 26.20
Stock Prices from 30 Days (Barnes and Noble)
41.41, 40.47, 40.97, 38.39, 36.99, 36.05, 37.22, 40.76, 33.92, 36.68, 33.29, 35.73, 41.64, 41.97, 38.35, 37.70, 37.57, 34.49, 38.33, 35.60, 40.34, 36.81, 34.56, 39.46, 41.88, 37.16, 38.05, 34.64, 38.19, 36.16
Comparing Stock Prices of Borders and Barnes and Noble
1
2
3
4
5
6
Difference0 5 10 15 20 25
Collection 1 Histogram
The histogram of the differences of the Borders and Barnes and Noble stock prices is unimodal, somewhat symmetric, and has a median of $14.615. It ranges from $7 to $20.83. There are two gaps and no points that look like outliers.
Looking at this histogram, there appears to be a significant average difference between the stock prices of the two stores. If there was no difference, the histogram would be only one bar at zero.
μd = mean of the difference of Barnes & Noble - Borders
Conditions:1. Paired data2. SRS3. Normal population
of differences or nd≥30
4. Population of differences ≥ 10*nd
1. Data points paired by date 2. Dates picked through random
number generator (1,365) in 20053. nd≥304. More than 300 days of stocks
Ho: μd = 0 Ha: μd > 0
Conditions met, use Student’s t-distribution, do 1-sample paired t-test
Comparing Stock Prices of Borders and Barnes and Noble
We reject our Ho because our p-value of 1.931 x 10-19 is less than the alpha of 0.05.We have sufficient evidence that the mean of the differences between Barnes & Noble and Borders is not equal to zero. This indicates that the stock prices of the two companies were not equal over the span of 2005.
P(t > 21.0932) = 1.931 x 10-19
xtsn
Degrees Freedom
= 29= 21.0932
Comparing Stock Prices of Borders and Barnes and Noble
Bias and Error Observation of all sections is difficult for one person
and therefore some subjects may have been overlooked
Approximations of ages is difficult Borders rearranged the store and caused
difficulties for us and for costumers Double counting subjects who browse many
sections We recorded if subjects browsed or bought, but the
error in recording and determining that became too difficult to use
Because no men were observed in Romance, we could not include it in the tests. However, including it would have made finding an association between gender and section more likely.
Conclusions about the Population Excluding certain sections and age groups,
we can conclude that the population of individuals that frequent both stores are independent of age and of store choice. We also can conclude that gender and preference of section are independent as well.
We can conclude based on our paired test on the stock prices that the mean of the differences for both companies’ stock is not equal to zero, showing that Barnes and Noble’s prices are higher on average.
Personal Opinions The layout change in Borders caused
problems with data collection and led to many of our expected counts being lower than five Although we did not statistically prove it, we
believe that Borders was much better before they reorganized
Barnes & Noble’s organization system is more fluid than Borders, so people tended to drift from section to section more so than in Borders.
We Continue being Highly Opinionated Although we could not use the senior age
group category, a larger proportion of older individuals went to Barnes & Noble over Borders, perhaps because of either the accessibility or preference because Barnes & Noble is an older store.
The location of Valley Square appeals to younger individuals, and therefore the subjects at Borders were generally younger
On Friday, Valley Square was having a festival, and many young people were outside, and less people were in Borders.
Conclusion Borders had less people on average than Barnes
and Noble, causing issues with expected counts According to our experiment, gender and age do
not affect bookstore or section choice, however, these conclusions could have been skewed by error
If we re-did this experiment… We would record data from Borders on a day without a
festival at Valley Square and when the store is familiar to the subjects
We would have tried to get more data from seniors We would probably ask the people questions instead of
simply spying on them