Case I - Business Sucess or Failure

7/31/2019 Case I - Business Sucess or Failure

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CASE I

Study of Small Businesses

Group 2

Ashwani Sinha (10), Atul Mehta (11), PrashantAkhawat (28) and Suresh Jangra (35)


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Definition revisited

Factor analysis is an interdependent technique

in that an entire set of interdependence

relationships is examined


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About the study

Objective of the study Determine the reasons for success or failure of small business

Research design

150 entrepreneurs asked to indicate the perceived areas of strength andweaknesses of their organisations

11 variables rated on a five point scale (1 represents very weak area and 5

represents very strong area)

Variables

V1 = Location of firm/Business

V2 = Type of plant, equipment and other

physical facilities

V3 = Product/ service qualityV4=Pricing of products/services

V5=Customer Services

V6=Innovations in product/services

offered

V7=Cost control

V8=Employee productivity

V9=Marketing (Personal selling,promotion, adv, etc)

V10=Cash and Financial mgmt

V11=Overall quality of mgmt

Number of observations should be atleast four or five times the number of variables


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Step 1 - Formulate the problem

11 variables are too many to handle, so

Should we go for factor analysis?

For the factor analysis to be meaningful, the variable

must be correlated.

Problem formulated >> The problem is to identify the

underlying factors which represents the impact of these

11 variables


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Step 2 Construct the correlation

matrix

For the factor analysis to be meaningful, the

variable must be correlated. How do we check

that?

By constructing a correlation matrix

Any double check mechanism?

Yes. Bartletts test of

sphericity can be used totest the null hypothesis that the variables are

uncorrelated in the population


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Step 3 -Determine the method of

factor analysis

Once it has been determined that factor analysis

is suitable for analysing the data, an appropriate

method must be selected

Two approaches are used

Principal components analysis (when objective is to determine

the min number of factors that will account for maximum

variance in the data for use in subsequent multivariateanalysis)

Common factor analysis (when identifying the underlying

dimensions and the common variance is of interest)


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DATA


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SPSS1. Select ANALYZE from the SPSS menu bar

2. Click DATA REDUCTION and then FACTOR

3. Move variables V1 to V11 into the VARIABLES box

4. Click on DESCRIPTIVES. In the pop-up window, in theSTATISTICS box check INITIAL SOLUTION. In the

CORRELATION MATRIX box check COEFFICIENTS, checkKMO AND BARTLETTS TEST OF SPHERICITY and alsocheck REPRODUCED. Click CONTINUE

5. Click on EXTRACTION. In the pop-up window, for METHOD

select PRINCIPAL COMPONENTS. In the ANALYZE box,check CORRELATION MATRIX. In the EXTRACT box, selectBASED ON EIGENVALUE and enter 1 for EIGENVALUESGREATER THAN box. In the DISPLAY box checkUNROTATED FACTOR SOLUTION. Click CONTINUE


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SPSS (Concluded)

6. Click on ROTATION. In the METHOD box check

VARIMAX. In the DISPLAY box check ROTATED

SOLUTION. Click CONTINUE

7. Click on SCORES. In the pop-up window, check

DISPLAY FACTOR SCORE COEFFICIENT

MATRIX. Click CONTINUE

8. Click OK.


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KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy..542

Bartlett's Test of Sphericity Approx. Chi-Square 148.271

df 55

Sig. .000

Interpretation A high Chi-square value of 148.271 with p-value less than 0.05 implies

rejection of the null hypothesis. The variables are thus correlated

Higher KMO measure of 0.542 further testifies that correlation is significant

(KMO>0.5 is desirable)

RecommendationFactor analysis may be considered an appropriate technique for analyzing

the given data


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Results of Principal Components Analysis

Communality

Communalities

Initial Extraction

VAR00001 1.000 .839

VAR00002 1.000 .604

VAR00003 1.000 .748VAR00004 1.000 .768

VAR00005 1.000 .547

VAR00006 1.000 .608

VAR00007 1.000 .769

VAR00008 1.000 .754

VAR00009 1.000 .737VAR00010 1.000 .802

VAR00011 1.000 .656

Extraction Method: Principal Component

Analysis.

Communality is the amount of variance a

variable shares with all the other variables

being considered. This is also the proportion

of variance explained by the common factors.

The communalities for the variables under

extraction are different from initial because all

of the variances associated with the variables

are not explained unless all the factors are

retained


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Results of Principal Components Analysis

Eigenvalue

Observations and InterpretationEigen values for the factors are in decreasing

order as we go from factor 1 to 11

Factors 1-5 have the highest influence on

whether a business will be successful or

unsuccessful

Sum of variances on account of all 11 factorsis 11.00, which is also equal to the number of

variables

% of Variance is calculated as Eigen value

number of factors

Several considerations are involved in

determining the number of factors that

should be used in the analysis >>>

Factors

Initial Eigenvalues

Eigenvalue

% of

Variance

Cumulative

%

1 2.373 21.574 21.574

2 1.684 15.305 36.880

3 1.455 13.224 50.104

4 1.224 11.124 61.228

5 1.098 9.980 71.208

6 .861 7.832 79.039

7 .656 5.962 85.001

8 .579 5.263 90.264

9 .445 4.041 94.306

10 .325 2.957 97.263

11 .301 2.737 100.000

Total 11.00 100.00


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Step 4 -Determine the number of factorsMethod

EIGENVALUES approach - only factors

with greater than 1.0 eigenvalues are

considered.

Extraction sums of squared loadings

Gives the variances associated with the

factors that are retained. In this case 5

factors whose eigenvalues is above 1

has been retained.

Extraction Sums of Squared Loadings

Factor Total % of Variance Cumulative %

1 2.373 21.574 21.574

2 1.684 15.305 36.880

3 1.455 13.224 50.104

4 1.224 11.124 61.228

5 1.098 9.980 71.208

Rotation Sums of Squared Loadings

Factors Total % of Variance Cumulative %

1 2.039 18.541 18.541

2 1.607 14.614 33.154

3 1.578 14.342 47.497

4 1.387 12.608 60.104

5 1.221 11.103 71.208


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Step 5 Rotate the factors (before rotation)

Factor Matrix

1 2 3 4 5

V1 .047 .503 .223 .731 -.004

V2 .436 -.250 .305 -.349 .370

V3 .215 .533 .628 .038 .151

V4 .506 .192 .521 -.386 -.236

V5 .268 .660 -.100 -.170 -.026

V6 .287 -.518 .447 .235 .043

V7 .792 -.221 -.265 -.121 -.090V8 .335 -.083 -.084 .167 .774

V9 .375 -.467 .188 .495 -.312

V10 .755 .144 -.292 .034 -.354

V11 .524 .220 -.489 .212 .222

Factor Matrix contain the coefficient used to express the standardized variables in terms of

the factors. These coefficients represent the correlation between the factors and the

variables. Coefficients highlighted in yellow represents close relation between the factors and

the variables.

InterpretationFactor matrix shouldNOTbe used to indicate the relation between the factors and the

variables. As in table above, we see factor 1 is correlated with as many as five variables. Same

is the case with factor 2. It can bet better interpreted through rotation.


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Orthogonal rotation

Orthogonal rotation if the axes are

maintained at right angle

Varimax is the most commonly used rotation

procedure

Rotation minimizes the number of variables

with high loading on a factor

Orthogonal rotation results in factors that are

uncorrelated


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Step 7a- Calculate the factor scores

A factor is simply a linear combination of the original variables. The factor

scores formulae Fi=Wi1V1+Wi2V2+Wi3V3+WikVk

The weights (factor coefficient) are obtained from the factor score

coefficient matrix

Factor Score Coefficients matrix

1 2 3 4 5

V1 -.001 -.023 .113 .675 .028

V2 -.076 .291 .058 -.281 .349

V3 -.148 .443 -.042 .285 .114

V4 .053 .527 .013 -.115 -.195

V5 .160 .180 -.348 .104 -.031V6 -.081 .102 .462 .029 .104

V7 .369 .008 .072 -.190 .034

V8 -.054 -.076 -.012 .055 .728

V9 .143 -.080 .524 .187 -.164

V10 .459 .013 -.002 .038 -.203V11 .309 -.189 -.140 .146 .279


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Step 7a- Calculate the factor scores

Variables F1 F2 F3 F4 F5

Respondent

Number 5

Respondent

Number 6V1 -0.001 -0.023 0.113 0.675 0.028 4 4V2 -0.076 0.291 0.058 -0.281 0.349 4 5V3

-0.148 0.443 -0.042 0.285 0.114 5 5V4 0.053 0.527 0.013 -0.115 -0.195 5 5V5 0.16 0.18 -0.348 0.104 -0.031 3 5V6 -0.081 0.102 0.462 0.029 0.104 5 5V7 0.369 0.008 0.072 -0.19 0.034 4 4V8 -0.054 -0.076 -0.012 0.055 0.728 4 4V9 0.143 -0.08 0.524 0.187 -0.164 5 -

V10 0.459 0.013 -0.002 0.038 -0.203 4 -V11 0.309 -0.189 -0.14 0.146 0.279 5 5

Factor score for

respondent number

54.648 5.407 3.957 4.16 4.341

Factor score for

respondent number

6

2.341 6.406 0.707 3 6.26


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Step 7b Select surrogate variables

There can be occasions when instead of a factor, we canconsider using the variables

Selection of such a variable is made from factor matrix

Factor Matrix

1 2 3 4 5

V1 .047 .503 .223 .731 -.004

V2 .436 -.250 .305 -.349 .370

V3 .215 .533 .628 .038 .151

V4 .506 .192 .521 -.386 -.236

V5 .268 .660 -.100 -.170 -.026

V6 .287 -.518 .447 .235 .043

V7 .792 -.221 -.265 -.121 -.090

V8 .335 -.083 -.084 .167 .774

V9 .375 -.467 .188 .495 -.312

V10 .755 .144 -.292 .034 -.354

V11 .524 .220 -.489 .212 .222

So V7=Cost control could be used as a surrogate variable for Finance & Operations

Factor

( ) f


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Step 8 (Final step) Determine the fit

model fitReproduced Corre lations

.839b -.294 .445 -.044 .198 .024 -.221 .074 .188 .070 .181

-.294 .604b .195 .379 -.029 .325 .329 .370 .050 .062 .033

.445 .195 .748b .488 .336 .082 -.132 .098 -.078 .004 -.035

-.044 .379 .488 .768b .281 .178 .288 -.138 .081 .328 -.081

.198 -.029 .336 .281 .547b -.351 .116 -.006 -.303 .330 .293

.024 .325 .082 .178 -.351 .608b .190 .174 .537 .004 -.123

-.221 .329 -.132 .288 .116 .190 .769b .216 .319 .671 .450

.074 .370 .098 -.138 -.006 .174 .216 .754b -.010 -.003 .406

.188 .050 -.078 .081 -.303 .537 .319 -.010 .737b .289 .037

.070 .062 .004 .328 .330 .004 .671 -.003 .289 .802b .498

.181 .033 -.035 -.081 .293 -.123 .450 .406 .037 .498 .656b

.139 -.128 .037 -.056 -.024 .013 -.053 -.083 .011 -.013

.139 -.059 -.128 -.043 -.107 -.113 -.204 .020 .071 .071

-.128 -.059 -.116 -.121 -.074 .066 -.035 .042 .018 .037

.037 -.128 -.116 -.089 -.016 -.022 .098 -.035 -.051 .051

-.056 -.043 -.121 -.089 .153 .011 .085 .129 -.091 -.172

-.024 -.107 -.074 -.016 .153 -.037 -.070 -.205 -.001 .092

.013 -.113 .066 -.022 .011 -.037 .041 -.004 -.114 -.106

-.053 -.204 -.035 .098 .085 -.070 .041 .092 .009 -.208

-.083 .020 .042 -.035 .129 -.205 -.004 .092 -.063 -.098

.011 .071 .018 -.051 -.091 -.001 -.114 .009 -.063 -.046

-.013 .071 .037 .051 -.172 .092 -.106 -.208 -.098 -.046

V1

V2

V3V4

V5

V6

V7

V8

V9

V10

V11V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

V11

Reproduced Correlation

Residuala

V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11

Extraction Method: Principal Component Analysis.

Residuals are computed betw een observed and reproduced correlations. There are 34 (61.0%) nonredundant res iduals w ith absolute values greater than 0.05.a.

Reproduced communalitiesb.

There are 61% nonredundant residuals with absolute values greater than 0.05.

The model is therefore not fit.


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Thank you

Documents

Case I - Business Sucess or Failure