the interpretation of statistical results

8/9/2019 The Interpretation of Statistical Results

1/15

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.


2/15

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


C o u n t


C o u n t


C o u n t


C o u n t


C o u n t


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


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.)


3/15

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


It follows that the satisfaction level for mobile telephone services is not normallydistributed.


4/15

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.


5/15

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


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.


6/15

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


The mean rank of the Airtel group is lower than that of the Hutch group.


Thus, it follows that the satisfaction levels for Airtel are significantly higher than that of

Hutch.


7/15

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


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


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.


Thus, it follows that the satisfaction levels for Airtel are significantly higher than that ofHutch.


8/15

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.


9/15

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.


10/15

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.


11/15

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


12/15

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


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


13/15

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


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


14/15

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.


15/15

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

the interpretation of statistical results

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