the interpretation of statistical results
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8/9/2019 The Interpretation of Statistical Results
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Reasons for dissatisfaction
80 40.0 40.0
20 40.0 -20.0
64 40.0 24.0
12 40.0 -28.0
24 40.0 -16.0
200
Poor quality
Poor voice quality
Higher cost
Billing errors
Poor customer care
Total
Observed N Expected N Residual
Test Statistics
90.400
4
.000
Chi-Squarea
df
Asymp. Sig.
Reasons for
dissatisfacti
on
0 cells (.0%) have expected frequencies less than
5. The minimum expected cell frequency is 40.0.
a.
technique: the 2 test for goodness-of-fit(null) hypothesis: that the different reasons are equally important (i.e. the theoretical distribution
is a uniform distribution)interpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
It follows that the different reasons for dissatisfaction with mobile telephone service are
not equally important, i.e. some of the reasons are more important than others. In fact, comparing the observed frequencies with the expected frequencies, one can
conclude that poor quality and higher cost represent the two most important reasons
for dissatisfaction with mobile telephone service.
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S e r v ic e p r o v i d e r * R e a s o n s f o r d i s s a t is f a c t io n C r o s s t a b u l a t io
1 6 1 2 8 8 8 5 2
3 0 .8 % 2 3 .1 % 1 5 .4 % 1 5 .4 % 1 5 .4 % 1 0 0 .0 %
2 8 4 8 0 4 4 4
6 3 .6 % 9 . 1 % 1 8 . 2 % . 0 % 9 . 1 % 1 0 0 . 0 %
1 2 0 2 8 0 0 4 0
3 0 . 0 % . 0 % 7 0 . 0 % . 0 % . 0 % 1 0 0 . 0 %
0 0 1 2 0 8 2 0
. 0 % . 0 % 6 0 . 0 % . 0 % 4 0 . 0 % 1 0 0 .0 %
2 4 4 8 4 0 4 0
6 0 .0 % 1 0 .0 % 2 0 .0 % 1 0 . 0 % . 0 % 1 0 0 . 0 %
0 0 0 0 4 4
. 0 % . 0 % . 0 % . 0 % 1 0 0 . 0 % 1 0 0 .0 %
8 0 2 0 6 4 1 2 2 4 2 0 0
4 0 .0 % 1 0 .0 % 3 2 .0 % 6 . 0 % 1 2 . 0 % 1 0 0 .0 %
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
C o u n t
% w it h in S e r v ic e p r o v id e r
A ir te l
H u tc h
S p ic e
B S N L
R e li a n c e
T a ta
S e r v ic e
p r o v id e r
T o ta l
P o o r q u a lit y
P o o r v o ic e
q u a lit y H ig h e r c o s tB ill in g e r r o r s
P o o r
c u s to m e r
c a r e
R e a s o n s f o r d is s a ti s fa c t io n
T o ta l
Chi-Square Tests
134.790a 20 .000
137.241 20 .000
.238 1 .626
200
Pearson Chi-Square
Likelihood Ratio
Linear-by-Linear
Association
N of Valid Cases
Value df
Asymp. Sig.
(2-sided)
17 cells (56.7%) have expected count less than 5. The
minimum expected count is .24.
a.
technique: the 2 test for independence(null) hypothesis: that the reasons for dissatisfaction are independent of the service providerinterpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
It follows that the reasons for dissatisfaction are not independent of the service provider,
i.e. different reasons are associated with each of the service providers.
For Hutch and Reliance, there is higher concentration in poor quality as a reason for
dissatisfaction, while for Spice and BSNL, there is higher concentration in higher cost asa reason for dissatisfaction. For Airtel, there does not seem to be significantly higherconcentration in any specific reason for dissatisfaction. (There are too few sample units
from Tata Indicom to draw a meaningful inference.)
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8/9/2019 The Interpretation of Statistical Results
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O n e - S a m p l e K o l m o g o r o v - S m irn o v T e s t
2 0 0
2 . 5 2
1 . 2 0 7
. 3 0 7
. 3 0 7
- . 1 5 3
4 . 3 3 7
. 0 0 0
N
M e a n
S t d . De v ia t io n
N o r m a l P a r a m e t e r sa ,b
A b s o l u t e
Pos i t i ve
N e g a t i v e
M o s t E x tr e m e
D i f f e r e n c e s
K o lm o g o r o v - S m ir n o v Z
A s y m p . S ig . ( 2 - t a i l e d )
S a t i s f a c t i o n
l e v e l
T e s t d i s tr ib u t io n is N o r m a l .a .
C a lc u l a te d f r o m d a t a .b .
technique: the Kolmogorov-Smirnov test for goodness-of-fit(null) hypothesis: that the satisfaction level for mobile telephone services is normally distributedinterpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
It follows that the satisfaction level for mobile telephone services is not normallydistributed.
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O n e - S a m p l e S t a t i s t ic s
2 0 0 2 . 5 2 1 . 2 0 7 . 0 8 5S a t is fa c t io n le v e l
N M e a n S t d . D e v i a t io n
S td . E r r o
M e a n
O n e - Sa m p l e T e s t
- 5 .6 2 4 1 9 9 .0 0 0 - .4 8 0 - .6 5 - .3 1S a t i s fa c t i o n l e v e l
t d f S ig . (2 - ta ile d )
M e a n
D i f f e re n c e L o w e r U p p e r
9 5 % C o n f id e n c e
In te r v a l o f t h e
D i f f e re n c e
T e s t V a lu e = 3
technique: the t-test for a single population mean(null) hypothesis: that the mean satisfaction level for mobile telephone services is equal to 3
(representing average/neutral)interpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the nullhypothesis is rejected.
It follows that the satisfaction level for mobile telephone services is significantly less
than 3.
(Note: in the above, the scaling for the satisfaction level was in reverse: 1 representedhighly satisfied, and at the other extreme, 5 represented not at all satisfied.)
Thus, it follows that the mean satisfaction level for mobile telephone services is relatively
high.
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G r o u p S t a t i s t ic s
5 2 2 .15 .8 7 2 .1 2 1
4 4 2 .82 1 .2 0 6 .1 8 2
Se rv ice p rov ide r A i r te l
H u t c h
Sat is fac t ion leve lN M e a n S td . D e v ia tio n
Std . E r ro r
M e a n
Independent Samples Test
13.331 .000 -3.124 94 .002 -.664 .213 -1.087 -.242
-3.043 76.780 .003 -.664 .218 -1.099 -.230
Equal variances
assumed
Equal variances
not assumed
Satisfaction levelF Sig.
Levene's Test for
Equality of Variances
t df Sig. (2-tailed)
Mean
Difference
Std. Error
Difference Lower Upper
95% Confidence
Interval of the
Difference
t-test for Equality of Means
technique: the independent-samples t-test for equality of two population means(null) hypothesis: that there is no difference in the mean satisfaction level for Airtel and Hutchusers.interpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
Firstly, Levenes test for equality of variance is significant. It follows that there is
significant difference in variance (in satisfaction level) between the groups; i.e.significantly higher variation in satisfaction level among Hutch users than among Airtel
users.
Secondly, the t-test with equal variances not assumed is significant, and the calculated
value of t is negative. (Note: in the above, the scaling for the satisfaction level was in reverse: 1 represented
highly satisfied, and at the other extreme, 5 represented not at all satisfied.)
Thus, it follows that the mean satisfaction level for Airtel is significantly higher than thatof Hutch.
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Ranks
52 42.04 2186.00
44 56.14 2470.00
96
Service provider
Airtel
Hutch
Total
Satisfaction level
N Mean Rank Sum of Ranks
Test Statisticsa
808.000
2186.000
-2.619
.009
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Satisfaction
level
Grouping Variable: Service providera.
technique: the Mann-Whitney U-test
(null) hypothesis: that there is no difference in the distribution of satisfaction level for Airtel
and Hutch users.interpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
The mean rank of the Airtel group is lower than that of the Hutch group.
(Note: in the above, the scaling for the satisfaction level was in reverse: 1 representedhighly satisfied, and at the other extreme, 5 represented not at all satisfied.)
Thus, it follows that the satisfaction levels for Airtel are significantly higher than that of
Hutch.
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Frequencies
52
44
96
Service provider
Airtel
Hutch
Total
Satisfaction level
N
Test Statisticsa
.287
.287
.000
1.400
.040
Absolute
Positive
Negative
Most Extreme
Differences
Kolmogorov-Smirnov Z
Asymp. Sig. (2-tailed)
Satisfaction
level
Grouping Variable: Service providera.
technique: the two-sample Kolmogorov-Smirnov test(null) hypothesis: that there is no difference in the distribution of satisfaction level for Airtel
and Hutch users.interpretation: the results of the test are statistically significant (i.e. p-value < 0.05); i.e. the null
hypothesis is rejected.
The difference in distribution functions is always non-negative. This means that the
distribution function for satisfaction level for Airtel is always greater than or equal to that
for Hutch. It follows that the values in the distribution of satisfaction level for Airtel arelowe than the values in the distribution of satisfaction level for Hutch.
(Note: in the above, the scaling for the satisfaction level was in reverse: 1 representedhighly satisfied, and at the other extreme, 5 represented not at all satisfied.)
Thus, it follows that the satisfaction levels for Airtel are significantly higher than that ofHutch.
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R e p o r t
S a ti s fa c t io n le v e l
2 . 1 5 . 8 7 2 . 4 2 8 - . 3 6 4
2 .8 2 1 . 2 0 6 . 3 6 6 - 1 . 1 1 4
2 .6 0 1 . 2 9 7 1 .1 0 5 - .1 2 9
2 .4 0 1 . 3 9 2 . 2 2 9 - 1 . 9 3 6
2 .7 0 1 . 3 6 3 . 3 2 3 - 1 . 3 6 3
2 .0 0 . 0 0 0 . .
2 . 5 2 1 . 2 0 7 . 6 4 5 - . 6 6 0
S e r v ic e p r o v id e r
A ir te l
H u t c h
S p ic e
B S N L
R e li a n c e
T a ta
T o ta l
M e a n S td . D e v ia tio nS k e w n e s sK u rt o s is
A N O V A T a b l e
1 3 .8 0 5 5 2 .7 6 1 1 .9 4 0 .0 8 9
2 7 6 .1 1 5 1 9 4 1 .4 2 3
2 8 9 .9 2 0 1 9 9
( C o m b i n e d )B e tw e e n G r o u p s
W i t h in G r o u p s
T o t a l
Sa t i s fac t ion leve l
* Serv ice p rov ide r
S u m o f
S q u a re s d f M e a n S q u a r e F S ig .
technique: one-way ANOVA(null) hypothesis: that there is no difference in the mean satisfaction level for different serviceproviders.
interpretation: the results of the test are not statistically significant (i.e. p-value > 0.05); i.e. the
null hypothesis cannot be rejected.
Thus, it follows that there is no significant difference in the mean satisfaction level for
different service providers.
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Ranks
52 87.12
44 114.68
40 103.70
20 90.50
40 105.90
4 82.50
200
Service provider
Airtel
Hutch
Spice
BSNL
Reliance
Tata
Total
Satisfaction level
N Mean Rank
Test Statisticsa,b
7.731
5
.172
Chi-Square
df
Asymp. Sig.
Satisfaction
level
Kruskal Wallis Testa.
Grouping Variable: Service providerb.
technique: the Kruskal-Wallis test(null) hypothesis: that there is no difference in the distribution of satisfaction levels for different
service providers.interpretation: the results of the test are not statistically significant (i.e. p-value >0.05); i.e. the
null hypothesis cannot rejected.
Thus, it follows that there is no significant difference in the distribution of satisfaction
levels for different service providers.
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F r e q u e n c i e s
1 6 2 0 1 2 8 1 6 03 6 2 4 2 8 1 2 2 4 4
> M e d ia n< = M e d ia n
S a t is fa c ti o n le v e l
A i r te l H u t c h S p i c e B S N L R e l ia n c e T a ta
S e r v ic e p ro v id e r
Test Statisticsb
200
2.00
5.616a
5.345
N
Median
Chi-Square
dfAsymp. Sig.
Satisfaction
level
2 cells (16.7%) have expected frequencies less than
5. The minimum expected cell frequency is 1.4.
a.
Grouping Variable: Service providerb.
technique: the median test(null) hypothesis: that there is no difference in the median satisfaction level for different service
providers.interpretation: the results of the test are not statistically significant (i.e. p-value >0.05); i.e. the
null hypothesis cannot rejected. Thus, it follows that there is no significant difference in the median satisfaction level for
different service providers.
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Paired Samples Statistics
1.36 200 .626 .044
2.68 200 1.050 .074
Calls
SMS/MMS
Pair
1
Mean N Std. Deviation
Std. Error
Mean
Paired Samples Correlations
200 .115 .105Calls & SMS/MMSPair 1
N Correlation Sig.
P a i re d S a m p le s T e s t
- 1 . 3 2 0 1 . 1 5 9 . 0 8 2 - 1 . 4 8 2 - 1 . 1 5 8 - 1 6 . 1 0 0 1 9 9 . 0 0 0C a lls - S M S /M M SP a ir 1M e a n S td . D e v ia tio n
S td . E rro r
M e a n L o w e r U p p e r
9 5 % C o n fid e n ce
In te r v a l o f t h e
D iffe re n c e
P a ir e d D iff e re n c e s
t d f S ig . ( 2 - t a i le d
technique: the paired-samples t-test(null) hypothesis: that there is no difference in the mean satisfaction level for calls and forSMS/MMS.
interpretation: the results of the test are statistically significant (i.e. p-value
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Ranks
8a 116.50 932.00
168b 87.17 14644.00
24c
200
Negative Ranks
Positive Ranks
TiesTotal
SMS/MMS - Calls
N Mean Rank Sum of Ranks
SMS/MMS < Callsa.
SMS/MMS > Callsb.
SMS/MMS = Callsc.
Test Statisticsb
-10.370a
.000
Z
Asymp. Sig. (2-tailed)
SMS/MMS -
Calls
Based on negative ranks.a.
Wilcoxon Signed Ranks Testb.
technique: the Wilcoxon signed-rank test
(null) hypothesis: that there is no difference in the distribution of satisfaction levels for calls and
for SMS/MMS.interpretation: the results of the test are statistically significant (i.e. p-value
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Frequencies
8
168
24200
Negative Differencesa
Positive Differencesb
TiescTotal
SMS/MMS - Calls
N
SMS/MMS < Callsa.
SMS/MMS > Callsb.
SMS/MMS = Callsc.
Test Statisticsa
-11.985
.000
Z
Asymp. Sig. (2-tailed)
SMS/MMS -
Calls
Sign Testa.
technique: the paired-samples sign test
(null) hypothesis: that there is no difference in the distribution of satisfaction levels for calls and
for SMS/MMS.interpretation: the results of the test are statistically significant (i.e. p-value
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Model Summary
.602d .363 .352 45.709
Model R R Square
Adjusted
R Square
Std. Error of
the Estimate
Predictors: SalesStaff, Average O E, Average Inventoryd.
ANOVAe,f
215337.7 3 71779.227 34.356 .000d
378161.3 181 2089.289
593499.0 184
Regression
Residual
Total
Model
Sum of
Squares df Mean Square F Sig.
Predictors: SalesStaff, Average O E, Average Inventoryd.
Dependent Variable: conversions/weekdayse.
Linear Regression through the Originf.
Coefficientsa,b
5.375 .681 .625 7.889 .000
-1.2E-005 .000 -.325 -3.572 .000
5.12E-006 .000 .227 2.512 .013
SalesStaff
Average O E
Average Inventory
Model B Std. Error
Unstandardized
Coefficients
Beta
Standardized
Coefficients
t Sig.
Dependent Variable: conversions/weekdaysa.
Linear Regression through the Originb.
Excluded Variablesd,e
.004c .069 .945 .005 .833
.028c .313 .754 .023 .449
-.020c -.262 .794 -.019 .608
-.023c -.316 .752 -.024 .683
.041c .169 .866 .013 .061
-.068c -.427 .670 -.032 .138
rentals
manpower
Electricity
total
Peak season
Off season
Model Beta In t Sig.
Partial
Correlation Tolerance
Collinearity
Statistics
Predictors in the Model: SalesStaff, Average O E, Average Inventoryc.
Dependent Variable: conversions/weekdaysd.
Linear Regression through the Origine.
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technique: stepwise multiple linear regression through the origin(null) hypothesis: that none of the independent variables affect the dependent variable:
dependent variable: conversions/weekdays
independent variables: sales staff, average operating expenses, average inventory, rentals,
manpower, electricity, total, peak season, and off-seasoninterpretation: the results of the regression are statistically significant (i.e. p-value
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