Assignment3

March 26, 2014
1
Memorandum
To: Professor. Kirk McClure
From: Hao Li
Date: March 26, 2014
RE: ANALYSIS OF VARIANCE
City wants to understand how Blow Market Interest Rate (BMIR) program affects development, so this
case will involve test variable (Participation) and control variable (location in four districts) to know
whether it can significant bring “spillover” effect and attract more investments in.
ONEWAY:When it only considers influence between participated and non-participated with investment
values, it is not an obvious spillover effect on properties. Further, the influence between districts and
investment values does not have obvious spillover effect on properties as well.
TWOWAY:When it adds one more variable—different locations in four districts with the interaction, the
census tracts that participated in the Blow Market Interest Rate (BMIR) program experience
approximately $5,500 to $5,700 of greater private investment.
Howard Li
Department of Urban Planning
University of Kansas
Voice: (785)551-8199
E-mail: chocolee0123@gmail.com

March 26, 2014
2
DESCRIPTIVE STATISTICS ANALYSIS
The mean of non-subsidized investment of 60 tracts is $41,517, while the standard deviation is
$17,958 (Table 1). According to table 2, 29 tracts participated in grogram have a mean $45,288;
while 30 tracts did not participate in program have a mean $37,989. It tells us that tracts
participated in program will enjoy more non-subsidized investment than those did not participate.
Also, in different districts will have different investment values, table 3 tells that means of North,
East, South, West four districts are 60,483, 48,680, 39,259, 13,913. It’s found that north has the
highest investment values, and west has the lowest investment values.
According to the investment histogram (Chart 1), it is found a non- normal distribution shape,
which $50,000-$70,000 frequency is higher than normal while 20,000-40,000 frequency is lower
than normal. Further, $10,000 and $50,000 frequencies are extremely higher than normal.
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
INVEST 60 10763 67495 41516.82 17957.651
Valid N (listwise) 60
Table1
Average Investment * Part
INVEST
PART Mean N Std. Deviation
PARTICIPATED 45287.90 29 17428.346
NOT PARTICIPATED 37989.03 31 18002.797
Total 41516.82 60 17957.651
Table 2
Average Investment * District
INVEST
DISTRICT Mean N Std. Deviation
NORTH 60482.75 16 4444.769
EAST 48679.50 16 2725.877
SOUTH 39259.29 14 9690.060
WEST 13913.07 14 2521.324
Total 41516.82 60 17957.651
Table 3

March 26, 2014
3
Chart 1
ONE-WAY ANALYSIS
 Investment VS Participation
As the table 4 shows, participated properties have investment about $45,288 compared to
$37,989 for not participated properties. It is about a $12,700 difference that is within one
Standard Deviation ($17,958). Although tracts that participated have higher than non-
participated, it is not significantly higher. The test statistics F is 2.54 with a significance 0.116
(Table 5) which is lower than 0.05 levels. Therefore, the results indicate that tracts participated in
program have higher non-subsidized investment than those did not participate, but it is not that
significantly higher. The “spillover” effect was not significantly observed between the
participated and not participated on properties’ non- subsidized investment values, which means
properties attract investment in comparable amounts on both.

March 26, 2014
4
Descriptive
INVEST
N Mean Std. Dev iation Std. Error 95% Conf idence Interv al f or Mean Minimum Maximum
Lower Bound Upper Bound
PARTICIPATED 29 45287.90 17428.346 3236.363 38658.51 51917.28 10763 67495
NOT PARTICIPATED 31 37989.03 18002.797 3233.398 31385.55 44592.51 11869 62466
Total 60 41516.82 17957.651 2318.323 36877.86 46155.77 10763 67495
Table 4
ANOVA
INVEST
Sum of Squares df Mean Square F Sig.
Between Groups 798213409.326 1 798213409.326 2.540 .116
Within Groups
18227943891.6
57
58 314274894.684
Total
19026157300.9
83
59
Table 5
 Investment VS Districts
As district is the control variable, it should be analyzed that whether tracts located in different
district will significantly have more non-subsidized investment in their properties than others.
The means of N, E, S, W are 60,483, 48,680, 39,259 and 13,913 which have 18,966, 7,163, -
2,258 and -27,604 basis points compared to total mean (Table 6). It shows that N and E are
higher than total mean, and N has the highest values. While S and W are lower than total mean,
and W has the lowest values. According to table7, the test statistics F is 188.9 with significance
lower than 0.05 levels. This one-way test indicates that the investment values of districts do
differ from each other, and location does matter in all cases.
As the Post Hoc Test which compares each possible pair among districts shows that every pair
contrast of districts is significant better than 0.01 levels (Table 8). Therefore, the test suggests
that it exists a significant difference in districts, and N, E, S, W are significantly different from
each other. In addition, the plot shows that west district has lowest non-subsidized investment
compared to north district that enjoy highest investment.

March 26, 2014
5
Descriptive
INVEST
N Mean Std. Dev iation Std. Error 95% Conf idence Interv al f or Mean Minimum Maximum
NORTH 16 60482.75 4444.769 1111.192 58114.30 62851.20 51022 67495
EAST 16 48679.50 2725.877 681.469 47226.98 50132.02 43455 53513
SOUTH 14 39259.29 9690.060 2589.777 33664.41 44854.16 24846 54503
WEST 14 13913.07 2521.324 673.852 12457.30 15368.84 10763 20219
Total 60 41516.82 17957.651 2318.323 36877.86 46155.77 10763 67495
Table 6
ANOVA
INVEST
Sum of Squares df Mean Square F Sig.
Between Groups 17315055316.198 3 5771685105.399 188.893 .000
Within Groups 1711101984.786 56 30555392.585
Total 19026157300.983 59
Table 7
Post Hoc Test—Multiple Comparisons
Dependent Variable: INVEST
LSD
(I) DISTRICT (J) DISTRICT Mean Dif f erence (I-
J)
Std. Error Sig. 95% Conf idence Interv al
NORTH
EAST 11803.250*
1954.335 .000 7888.25 15718.25
SOUTH 21223.464*
2022.929 .000 17171.05 25275.88
WEST 46569.679*
2022.929 .000 42517.27 50622.09
EAST
NORTH -11803.250*
1954.335 .000 -15718.25 -7888.25
SOUTH 9420.214*
2022.929 .000 5367.80 13472.63
WEST 34766.429*
2022.929 .000 30714.02 38818.84
SOUTH
NORTH -21223.464*
2022.929 .000 -25275.88 -17171.05
EAST -9420.214*
2022.929 .000 -13472.63 -5367.80
WEST 25346.214*
2089.272 .000 21160.90 29531.53
WEST
NORTH -46569.679*
2022.929 .000 -50622.09 -42517.27
EAST -34766.429*
2022.929 .000 -38818.84 -30714.02
SOUTH -25346.214*
2089.272 .000 -29531.53 -21160.90
*. The mean dif f erence is signif icant at the 0.05 lev el.
Table 8

March 26, 2014
7
TWO-WAY ANALYSIS
 With Interaction
As non-subsidized investment values may affect by both test variable (Participation) and control
variable (District). It’s a two way test that can involve two variables in analysis. This test also
involves an interaction effect between two variables.
Referring to “Tests of Between-Subjects Effects”, it shows that the whole model is statistically
significant (F score is 219.8) (Table 10) at better than the 0.01 level. It indicates that the
participation variable is significant after controlling for the effect of district and the interaction
between participation and district. The F score for participation controlling for the other
independent variables is 40.2 at better than the 0.01 level. The R score is 0.963 which means the
model explains 96 percent of the variation of participation and district and is a good fit model.
The result tells that although participation variable is not a significant influence (ONE-WAY
ANOVA), it is significant after controlling for the district and the interaction of participation and
district. The spillover effect is significant after controlling for other variables.
According to “K Matrix- Participation” (Table 11), it indicates the difference due to participation
controlling for district. It is significant at better than 0.01 level after controlling and interaction
effect. While the “K Matrix- District” (Table 12) show that the districts values after controlling
for participation, each pair contrast is still significant, which means each district is still
significantly different from others. Further, the participated district enjoys $5,693 of great
investment than non-participated.
The means plot (Chart 3) shows the mean investment values by district and participation. It
shows that the participated properties in East district are lower than not participated. The West
district has the lowest investment values in both participated and not participated, which the
North district is on the contrary. The “spillover” effect is significant in East district, because of
not participated properties developed better than the participated. The “spillover” effect on South
district is not significant because those participated properties’ investment values are much
higher than the not participated. Therefore, the government should invest more loans in South
district to improve the effect.

March 26, 2014
8
Descriptive Statistics
PART DISTRICT Mean Std. Dev iation N
PARTICIPATED
NORTH 63257.25 3488.795 8
EAST 48094.50 2968.430 8
SOUTH 47486.57 4508.933 7
WEST 15021.50 3455.191 6
Total 45287.90 17428.346 29
NOT PARTICIPATED
NORTH 57708.25 3545.060 8
EAST 49264.50 2515.651 8
SOUTH 31032.00 5017.407 7
WEST 13081.75 1198.201 8
Total 37989.03 18002.797 31
Total
NORTH 60482.75 4444.769 16
EAST 48679.50 2725.877 16
SOUTH 39259.29 9690.060 14
WEST 13913.07 2521.324 14
Total 41516.82 17957.651 60
Table 9
Tests of Between-Subjects Effects
Source Ty pe III Sum of
Squares
df Mean Square F Sig.
Corrected Model 18404232189.269a
7 2629176027.038 219.829 .000
Intercept 98006291624.715 1 98006291624.715 8194.439 .000
PART 481374919.190 1 481374919.190 40.248 .000
DISTRICT 16991106515.150 3 5663702171.717 473.550 .000
PART * DISTRICT 641424687.413 3 213808229.138 17.877 .000
Error 621925111.714 52 11960098.302
Total 122444921269.000 60
Corrected Total 19026157300.983 59
a. R Squared = .967 (Adjusted R Squared = .963)
Table 10

March 26, 2014
9
Contrast Results (K Matrix)-Participation
PART Simple Contrasta
Dependent Variable
INVEST
Lev el 1 v s. Lev el 2
Contrast Estimate 5693.330
Hy pothesized Value 0
Dif f erence (Estimate - Hy pothesized) 5693.330
Std. Error 897.412
Sig. .000
95% Conf idence Interv al f or
Dif f erence
Lower Bound 3892.541
Upper Bound 7494.120
a. Ref erence category = 2
Table 11
Contrast Results (K Matrix)-District
DISTRICT Simple Contrasta
Dependent Variable
INVEST
Std. Error 1272.634
Sig. .000
Dif f erence
Std. Error 1272.634
Sig. .000
Dif f erence
Std. Error 1313.919
Sig. .000
Dif f erence

March 26, 2014
10
Table 12
Chart 3
Without Interaction
Referring to “Tests of Between-Subjects Effects”, it shows that the whole model is statistically
significant (F score is 193.3) (Table 13) at better than the 0.01 level. It indicates that the
participation variable is significant after controlling for the effect of district. The F score for
participation controlling for the other independent variables is 19.5 (Former 40.2) at better than
the 0.01 level. The R score is 0.929 (Former 96.3) which means the model explains 93 percent
of the variation of participation and district and still is a good fit model. The R score decreased
indicates the model is not as fit as former because of exclude the interaction between
participation and district. And also indicates it exist an interaction between participation and
district.
The result tells that although participation variable is not a significant influence (ONE-WAY
ANOVA), it do significant after controlling for the district. The spillover effect is significant
after considering in controlling variables—location.

March 26, 2014
11
According to “K Matrix- Participation” (Table 14), it indicates the difference due to participation
controlling for district. It is significant at better than 0.01 level after controlling and interaction
effect. While the “K Matrix- District” (Table 15) show that the districts values after controlling
for participation, each pair contrast is still significant, which means each district is still
significantly different from others. Further, the participated district enjoys $5,476 of great
investment than non-participated.
The means plot (Chart 4) shows the mean investment values by district and participation. It
shows that all participated properties have higher non-subsidized investment values in all four
districts. The “spillover” effect is not significant in all four districts, because participated
properties developed better than the not participated and have higher investment values.
Therefore, the government should invest more loan in four districts to improve the effect.
Tests of Between-Subjects Effects
Source Ty pe III Sum of
Squares
df Mean Square F Sig.
Corrected Model 17762807501.856a
4 4440701875.464 193.326 .000
Intercept 98731511036.010 1 98731511036.010 4298.282 .000
PART 447752185.658 1 447752185.658 19.493 .000
DISTRICT 16964594092.530 3 5654864697.510 246.185 .000
Error 1263349799.127 55 22969996.348
Total 122444921269.000 60
Corrected Total 19026157300.983 59
a. R Squared = .934 (Adjusted R Squared = .929)
Table 13
Contrast Results (K Matrix)
PART Simple Contrasta
Dependent Variable
INVEST
Std. Error 1240.427
Sig. .000
Dif f erence
Table 14

March 26, 2014
12
Contrast Results (K Matrix)
DISTRICT Simple Contrasta
Dependent Variable
INVEST
Std. Error 1756.186
Sig. .000
Dif f erence
Std. Error 1756.186
Sig. .000
Dif f erence
Std. Error 1813.637
Sig. .000
Dif f erence
Table 15

Assignment3

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (9)

Assignment3