Pilot Testing & Analysis of Primary Data

Outline:
• Data, Data set, Variable, Element, Observation, Population, Sample
• Scale of Measurement/Instrument
• Pilot Testing (Subjective measure & numerical Measure)
• Subjective Measure (Face and Content validity)
• Numerical Measure (Exploratory Factor Analysis, Confirmatory Factor
Analysis, and Goodness fit Indexes)
• Validity of the newly developed Instrument by (EFA)
• Validity of the Instrument by (CFA)
• Treatment of missing Values
• Reliability of the Data
• Normality of Data
• Descriptive Statistics
• Inferential Statistics: (Measure of Differences and Measure of Association)
• Measure of Differences (Mean differences between the groups, one sample
T-test, Independent sample T-test, Paired sample T-test, One way ANOVA)
• Measure of Association (Regression, Correlation)
• Structural Equation Model (SEM) by AMOS
• Mediation Analysis through AMOS & SPSS
• Moderation Analysis through AMOS & SPSS
 Data and Data Sets
• Data are the facts and figures that are
collected, summarized, analyzed, and
interpreted. E.g.,
– IBM’s sales revenue is $100 bn.; stock price $80.
• The data collected in a particular study are
referred to as the data set. E.g.,
– The sales revenue and stock price data for a
number of firms including IBM, Dell, Apple, etc.
Elements, Variables, and Observations
• The elements are the entities on which data
are collected. E.g.,
– IBM, Dell, Apple, etc. in the previous setting.
• A variable is a characteristic of interest for
the elements. E.g.,
– Sales revenue, stock price (of a company)
• The set of measurements collected for a
particular element is called an observation.
– Sales revenue, stock price for 2003
 Population versus Sample
 A population is a collection of all possible individuals,
objects, or measurements of interest.
 A sample is a portion, or part, of the population of interest
 Scales of Measurement
• Scales of measurement include:
– Nominal
– Ordinal
– Interval
– Ratio
• The scale determines the amount of
information contained in the data.
• The scale indicates the data summarization and
statistical analyses that are most appropriate.
 Scales of Measurement
• Nominal
– data that is classified into categories and cannot be
arranged in any particular order. A numeric code may
be used. The Nominal Scales Categorize Individuals or
Groups And This Scale Measure The Percentage
Response E.G. Male- Female, Pakistani-American
Example:
Students of a university are classified by the school in which
they are enrolled using a nonnumeric label such as Business,
Humanities, Education, and so on.
Alternatively, a numeric code could be used for the school
variable (e.g. 1 denotes Business, 2 denotes Humanities, 3
denotes Education, and so on).
 Scales of Measurement
• Ordinal
similar to the nominal level, with the additional property that
meaningful amounts of differences between data values
can be determined. It categorizes and ranks the variables
according to the preferences e.g. from best to worst, first
to last, a numeric code may be used.
e.g. rank job characteristics
– Example:
Students of a university are classified by their class standing
using a nonnumeric label such as Freshman, Junior, Senior.
Alternatively, a numeric code could be used for the class
standing variable (e.g. 1 denotes Freshman, 2 denotes, Junior
and so on).
 Scales of Measurement
• Interval
– The data have the properties of ordinal and
interval between observations is expressed in
terms of a fixed unit of measure. Preferences on
a 5/7 point scale. It also measures the
magnitude of the differences in the preferences
among the individuals. Interval data are always
numeric.
– Example:
strongly disagree, disagree, neither agree nor disagree
Agree, Strongly Agree.
 Scales of Measurement
• Ratio
– The data have all the properties of interval data
and the ratio of two values is meaningful. This
scale must contain a zero value at it starts that
indicates that nothing exists for the variable at
the zero point.
– Example:
Variables such as distance, height, weight, and time use
the ratio scale.
 Scales of Measurement
• Ratio scales: used when exact numbers are
given for e.g. how many orders do you
operate?
• Interval scale: used for responses to various
items on 5/7 points use of stats measures are
mean, stand. deviation.
• Ordinal scale: for preference in use, stats
measures are median, range, rank order
correlations
• Nominal scale: used for personal data
 Instrument
• Instrument is a tool which is used to collect the
primary data and it is collected through
questionnaires, interviews, observations etc..
 Pilot Testing

To check the measurement problems and the reliability and

validity of the questions first pilot testing should be done.
There are two methods to refine (validate) the instrument
• Subjective Measure (Face or content Validity)
• Numerical Measure (Exploratory Factor Analysis &
Confirmatory Factor Analysis)
 Face Validity
The extent to which the content of the items is
consistent with the construct definition, it totally
based on the researcher’s judgment. An expert of
the specific area check the face validity.
It is a subjective measure
 Exploratory Factor Analysis (EFA)
When the new instrument is introduced to
measure any concept, it should be checked
through EFA. Followings are the criterias to
validate the instrument:
• Extraction Value/Load Factor
• Kaiser-Meyer-Olkin (KMO) Measure and
Bartelett test
• Total Variance Explained
• Scree plot
 Extraction Value/Load Factor
According to Habing (2003) an
item/statement/question having the factor
loadings above or equal to 0.40 considered as
practically significant construct. The table will
be as follows:

Items Mean Extraction values

Q1 3.81 .781

Q2 3.44 .825
Kaiser-Meyer-Olkin (KMO) Measure and
Bartelett test
• The instrument/construct will be statistically valid if
the KMO value is greater than 0.50 and According to
Kaiser (1974) if value of KMO lies between 0.8 to 0.9
shows the greatness and sample is adequate.
• Bartlett's Test p-value should be significant (<0.05),
table will be as follows:
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. 0.781
Bartlett's Test Approx. Chi-Square 3805.971
Df 1035
Sig. .000
 Total Variance Explained
• Next component to determine the number of factors
is total variance explained. This is considered by
taking the eigenvalues into account. The factors
having eigenvalue greater than one will be considered
much important. Table will be as follows:
Component Initial Eigenvalues Extraction Sums of Squared Loadings

% of Total % of Variance Cumulative %

Total Variance Cumulative
%
1 9.383 20.397 20.397 9.383 20.397 20.397

2 4.999 10.868 31.266 4.999 10.868 31.266

3 3.770 8.195 39.461 3.770 8.195 39.461

 Scree Plot
Scree plot is another technique to ascertain the number of
factors to be incorporated in final solution. This plot
shows the eigenvalues and related component numbers.
The point where this plot starts to descend, next coming
factors describe less variance.
 Commands in SPSS
Analyze Dimension Reductions Factors
Select the items from left to right window
Descriptive (Select KMO & Bartlett's)
Extraction (Select Scree plot) Continue
Ok and look at the results and make decision
 Confirmatory Factor Analysis
• Confirmatory factor analysis (CFA) is another process to validate the
instrument. It also checks the goodness fit of the model discloses the
measurement errors in the model.
• According to Steenkamp and Baumgartner (2000) CFA is the best
method to understand either the questions/items/statements have
strong interest or not to explain the variable.
• The tests required to know the fitness of model under confirmatory
test analysis are stated. Fitness of a model tells either it is close to
acceptance or not. There are different parameters to check the fitness
of model.
• Another modeling approach that is more accurate is presented by
Mulaik and Millsap (2000), Confirmatory Factor Analysis (CFA),
which not only tells about the measurement but to test the structural
model as well. It is also supported by other researchers such as
Anderson and Gerbing (1988) and Kline (2005), summarizing the
features of the variables.
• According to Scarpi (2006) Structural Equation Modeling (SEM)
technique is more appropriate to use because of its feature is to
highlight the measurement errors and the cause and effect of variables
on each other.
 Confirmatory Factor Analysis
In order to check the validity of the instrument
and model fit CFA is used.
Construct validity of measured variables actually
represent the theoretical latent construct which is
designed to measure. It is made up of three
components:
• Convergent Validity (Factor Loadings, Average
Variance Extracted (AVE) & Construct Reliabilities)
• Discriminant Validity
• Nomological Validity
 Convergent Validity
The extent to which indicators of a specific
construct ‘converge’ or share a high proportion of
variance in common.
Factor Loadings:
The factors loadings are examined first to determine
convergent validity. All factor loadings should be
statistically significant (p<0.05), and all loadings
should be above 0.5. and some scholars suggest the
it should be greater than 0.40. The value nearest to 1
the better will the construct. According to Cua et al.
(2001) if the load factor is > or equal to 0.40 that
will be included in final survey.
This is the “Estimates”
portion of the output.

These are “unstandardized”

regression weights.

The asterisks indicate statistical

significance <= .05. We use this
information to determine if the
standardized regression weights are
statistically significant.
 Factor Loadings – Convergent Validity . . .

These are factor loadings but in

AMOS they are called “standardized”
regression weights.

Factor loadings are the first thing to

look at in examining convergent validity.
Our guidelines are that all loadings
should be at least .5, and preferably .7 or
higher. All loadings are significant as
required for convergent validity. The
lowest is .592 (OC1) and there are only
two below .70 (EP1 & OC3).

When examining convergent validity, we look at two additional measures:

(1) Average Variance Extracted (AVE) by each construct.
(2) Construct Reliabilities (CR).
The AVE and CR are not provided by AMOS software so they have to be calculated.
 Average Variance Extracted (AVE)
• After finding the factor loadings in acceptable range,
Average Variance Extracted (AVE) is calculated next. Since
AVE cannot be computed in AMOS, it is calculated in MS
Excel by using the following formula:
•

• Where,
• λ is the standardized factor loadings.
• n is the number of items.
• AVE is therefore calculated by the sum of the square of all
factor loadings relating to one construct divided by the
number of items. A good rule of thumb is an AVE of .5 or
higher indicates adequate convergent validity.
e.g. AVE for Problem Solving= [(0.716)2 + (0.767)2 +
(0.860)2] / 3 = 0.613
Formula for Variance Extracted The sum of the squared loadings

This is the squared

n

i
loading for OC4 –
 2 .842 = .709

VE  i 1 Calculated Variance Extracted (AVE):

OC Construct = .349 + .759 + .448 + .709 = 2.264 / 4 = .5661

n
EP Construct = .477 + .658 + .596 + .679 = 2.410 / 4 = .6025

AC Construct = .676 + .674 + .699 + .666 = 2.714 / 4 = .6786

In the formula above the λ represents the standardized factor loading and i is the
number of items. So, for n items, AVE is computed as the sum of the squared standardized
factor loadings divided by the number of items, as shown above.
A good rule of thumb is an AVE of .5 or higher indicates adequate convergent validity.
An AVE of less than .5 indicates that on average, there is more error remaining in the
items than there is variance explained by the latent factor structure you have imposed on
the measure.
An AVE estimate should be computed for each latent construct in a measurement model.
 Construct Reliabilities
Construct reliabilities are another way to measure construct validity.
Construct reliabilities are not computable in AMOS; therefore, it is also
computed in MS Excel by using the following formula:
•
•

Where
• λi is the factor loadings.
• δi is the error variances (δ=1- Item Reliability).
• Item Reliability= squared each factor loading
• Construct reliabilities are calculated by using the sum of squared
factor loadings and the sum of error variances for the constructs in
the above formula.
• The rule of thumb for a construct reliability estimate is that 0.7 or
higher suggests good reliability. Reliability between 0.6 and 0.7
may be acceptable provided that other indicators of a model’s
construct validity are good.
 Construct Reliabilities
Its table will seems like:
Construct Items Factor loadings Item Reliabilities Delta

Policy (Squared of the

load factors) δ=1- Item Reliability
POL1 0.823 0.677329 0.322671
POL2 0.843 0.710649 0.289351
(∑ λ1)2=2.775556
∑ δ1=0.612022

CR = 2.775556 / 2.775556 + 0.612022

CR = 0.819
HBAT CFA Three Factor Completely Standardized This is the same as the
Factor Loadings, Variance Extracted, and eigenvalue in exploratory
factor analysis, This is the sum
Reliability Estimates of construct reliability

Item
OC EP AC Reliabilities delta
OC1 0.59 0.349 0.65
OC2 0.87 Factor Loadings 0.759 0.24
OC3 0.67 0.448 0.55
OC4 0.84 0.709 2.264 0.29
EP1 0.69 0.477 0.52
EP2 0.81 0.658 0.34
EP3 0.77 0.596 0.40
EP4 0.82 0.679 2.410 0.32
AC1 0.82 0.676 0.32
AC2 0.82 0.674 0.33
AC3 0.84 0.699 0.30
AC4 2.264/4 = 56.61 0.82 0.666 2.714 0.33

Variance
Extracted 56.61% 60.25% 67.86%
Squared Factor Loadings
Construct (communalities)
Reliability 0.84 0.86 0.89
The delta is calculated as 1 minus the item reliability, e.g.,
the AC4 delta is 1 – .666 = .33
The delta is also referred to as the standardized error
variance.
 Formula for Construct Reliability
The sum of the loadings, squared
n
( i ) 2
CR  n
i 1
n
( i )  (  i )
2

i 1 i 1 Computation of Construct Reliability (CR)

The sum of the loadings, squared The sum of the error

variance (delta)

CR (OC) = (.59 +.87 +.67 +.84)2 / [(.59 +.87 +.67 +.84)2 + (.65 +.24 +.55 +.29)] = 0.84
CR (EP) = (.69 +.81 +.77 +.82)2 / [(.69 +.82 +.84 +.82)2 + (.52 +.34 +.40 +.32)] = 0.86
CR (AC) = (.82 +.82 +.84 +.82)2 / [(.82 +.82 +.84 +.82)2 + (.32 +.33 +.30 +.33)] = 0.89

Construct reliability – is computed from the sum of factor loadings (λi), squared for each
construct and the sum of the error variance terms for a construct (δi) using the above formula. Note:
error variance is also referred to as delta.
The rule of thumb for a construct reliability estimate is that .7 or higher suggests good reliability.
Reliability between .6 and .7 may be acceptable provided that other indicators of a model’s construct
validity are good. A high construct reliability indicates that internal consistency exists. This
means the measures all are consistently representing something.
 Discriminant Validity
• Discriminant validity is used to check the
degree to which one construct is different from
others.
• In order to check out the discriminant validity
the value of AVE (Average Variance Extracted)
is compared with respective squared inter-
construct correlation estimates (SIC).
• SIC = Square of the IC
• If the value of AVE exceeds, this shows
discriminant validity is there.
 Discriminant Validity

Covariances
between the EP,
AC and OC
constructs.

Correlations between the EP,

AC and OC constructs. These are
standardized covariances.
These are used in calculating
discriminant validity.
 Discriminant Validity

In the columns below we calculate the SIC Discriminant validity – compares the average
(Squared Interconstruct Correlations) from the variance extracted (AVE) estimates for each
IC (Innerconstruct Correlations) obtained from factor with the squared inter construct
the correlations table on the AMOS printout correlations (SIC) associated with that factor,
(see previous slide): as shown below:
IC SIC AVE SIC

EP – AC .254 .0645 OC Construct .5661 .0645

EP Construct .6025 .2500
EP – OC .500 .2500
AC Construct .6786 .0918
AC – OC .303 .0918

All variance extracted (AVE) estimates in the above table are larger than the
corresponding squared interconstruct correlation estimates (SIC). This means the
indicators have more in common with the construct they are associated with than
they do with other constructs. Therefore, the HBAT three construct CFA model
demonstrates discriminant validity.
 Discriminant Validity
Its table will be constructed as:

Construct AVE IC SIC

Customer 0.508 CC <--> REL 0.112 0.012544
Convenience
CC <--> PIN 0.119 0.014161
CC <--> PS 0.094 0.008836
CC <--> POL 0.153 0.023409
 Nomological Validity
• In order to assess the nomological validity the
inter-construct correlations (IC) in the
measurement models are taken into
consideration.
• Inter-construct correlations (IC) in the
measurement models should be significant
(<0.05) and direction of relationship should be
same as per the theory; thus, indicating
nomological validity.
HBAT 3-Construct Nomological Validity

The asterisks
indicate that all
correlations are
significant.

The interconstruct
correlations are all positive
and significant (see above
Covariances table).
 Structural Model Analysis
The structural model is the second part of SEM that
demonstrates the direct and indirect relationship
between the variables.
• Relative chi-square (CMIN/DF)
• Root Mean Square Error of Approximation
(RMSEA)
• Goodness-of-Fit Index (GFI)
• Adjusted Goodness-of-Fit Index (AGFI)
• Comparative Fit Index (CFI)
These are the multiple indices to assess structural
model.
 Relative chi-square CMIN/DF
• The chi-square fit index is divided by the
degree of freedom.
• The chi-square test is more affected by the
sample size specifically when it is more than
200.
• Marsh and Hocevar (1985) suggested in terms
of at maximum 5 and at minimum 2 for the
acceptable fit.
 Root Mean Square Error of Approximation
(RMSEA)
• Byrne (2001) suggested that model fit statistics due to
its contemplation of both degree of freedom and sample
size and if it lies from 0.08 to 0.10, then it’s a good fit .
• Furthermore, Lomax and Schumacker (2004) suggested
that if RMSEA value is less or equal than 0.05 then it
indicates the good fit. If value is less or equal to 0.08,
then it is significant enough.
• Hu and Bentler (1999) proposed a cut-off point for it if
the value is less or equal to 0.06. To conclude, Browne,
Sugawara and MacCallum (1996) stated a standard
value of RMSEA i.e. greater than or equal to 0.10 for a
poor fit.
 Goodness-of-Fit Index (GFI)
• Boudreau, Gefen and Straub (2000), GFI test
is used for the absolute fit of the model.
• Raykov and Marcoulides (2000) suggested that
GFI is a degree of co-variance proportion as
per model and the variance.
• GFI value lie from 0 to 1 and 1 shows the
perfect fit. For well-fitted model, GFI should
be close to 1 because the value below 0.90
gives the poor fit.
 Adjusted Goodness-of-Fit Index (AGFI)
• In order to adjust the degree of freedom
number for the model, Byrne (2001) suggested
a method and called it as the AGFI. AGFI is
quite different from GFI.
• AGFI is similar to the theorized model; with
no model whose range of fit lies between 0 and
1 whereas AGFI should be above 0.80 for the
well-fitted model.
 Comparative Fit Index (CFI)
• The primary function of comparative fit index is to make
a comparison of the observed covariance matrix and
predicted covariance matrix of the model.
• Thompson, Fan and Wand (1999) suggested that the
heteroscedastic relationship among the dependent and
independent variables is tested by the CFI that varies
with the class of the modifier as it is less affected by
sample size. Its range is from 0 to 1 where significant of
perfect fit is 1. By rule the recognition of model, CFI co-
efficient needs to be above 0.90 depicting that the given
model comes out with 90% of co-variation in data.
• The best fitness of model if it represents the value of CFI
0.95 or 1. and it is also called normed fit index (NFI)
 Standardized Values of Adopted Goodness of Fit
Statistics
Sr.# Fit indices Ranges and acceptance criteria

(1.00< CMIN/DF <5.00)

Relative / Normal chi-square (CMIN/
Best/excellent fit: 1-3
1 DF)
Reasonably acceptable: 3-5
Poor fit: above 5
(0.90< GFI <1.00)
2 Goodness Fit Index (GFI) Best/excellent fit: ≥ 0.95
Reasonably acceptable: ≥ 0.90
(0.80< AGFI <1.00)
3 Adjusted Goodness Fit Index (AGFI) Best/excellent fit: ≥ 0.90
Reasonably acceptable: ≥ 0.80
(0.90< CFI <1.00)
4 Comparative Fit Index (CFI) Best/excellent fit: ≥ 0.95
Reasonably acceptable: ≥ 0.90
(0.01< RMSEA <1.00)
Root Mean Square Error of Best/excellent fit: < 0.05
5
Approximation (RMSEA) Reasonably acceptable: 0.06 – 0.08
Poor fit: above 0.10
 Three Construct Results – Model Fit Diagnostics
CMIN/DF – a value below 2 is preferred but
between 2 and 5 is considered acceptable.

The AGFI is .946 – above the

.90 minimum.

The GFI is .965 – above the .90

recommended minimum.

The CFI is 0.984 – it exceeds the

minimum (>0.90) for a model of this
complexity and sample size.
 CMIN/DF – a value below 2 is preferred but
between 2 and 5 is considered acceptable.

GFI = Goodness of
Chi-square (X2) =
Fit Index
likelihood ratio chi-square

AGFI = Adjusted
Goodness of Fit Index

This is the
PGFI = Parsimonious
“Model Fit”
Goodness of Fit Index
portion of the
output.
TLI = Tucker- Lewis

NFI = Normed
Fit Index CFI = Comparative
Fit Index

PNFI = Parsimonious
Normed Fit Index

Note: If you click on any of the “Fit Indices” it will give guidelines for
interpretation and references supporting the guidelines.
 RMSEA = Root Mean Squared Note that when we
Error of Approximation – a value evaluate the measures we
of 0.10 or less is considered use the numbers for the
acceptable (7e, p. 649). default model.

Three Types of Models:

1. Default = your model, the
relationships you propose and
are testing.
2. Saturated model = a model
that hypothesizes that
everything is related to
RMSEA – represents the everything (just-identified).
degree to which lack of fit is
due to misspecification of 3. Independence model =
the model tested versus hypothesizes that nothing is
being due to sampling error. related to anything.
HBAT Three Construct Results
The GFI, an absolute fit index, is .965. This
value is above the .90 guideline for this
model . Higher values indicate better fit
(7e, p. 649).

The AGFI, a parsimony fit index, is .946.

This value is above the .90 guideline for
this model . Attempts to adjust for model
complexity, but penalizes more complex
models.

The CFI, an incremental fit index, is 0.984,

which exceeds the guidelines (>0.90) for a
model of this complexity and sample size (7e,
p. 650).

CFI – represents the improvement of fit of the

specified model over a baseline model in which all
variables are constrained to be uncorrelated.
 Other Indices

The NFI, RFI and IFI are other

incremental fit indices. Our
guidelines indicate the NFI
should be >0.90 for a model of
this complexity and sample
size. For the RFI and IFI we
indicate that larger values (0 –
1.0) are better.
 The RMSEA, an absolute fit
index, is 0.043. This value is quite
low and well below the .08
guideline for a model with 12
measured variables and a sample
size of 400. This also is called a
Badness-Of-Fit index.

The 90 percent confidence

interval for the RMSEA is between
a LO of .028 and a HI of 0.058.
Thus, even the upper bound is not
close to .08.

Using the RMSEA and the CFI satisfies our rule of thumb
that both a badness-of-fit index and a goodness-of-fit index
be evaluated. In addition, other index values also are
supportive. For example, the GFI is 0.95, and the AGFI is
0.93.
We therefore now move on to examine the construct
validity of the model.
 Diagnosing Measurement Model Problems
In addition to evaluating goodness-of-fit (GOF) statistics, the
following diagnostic measures for CFA should be checked:
Path Estimates:
The completely standardized loadings (standardized regression
weights) that link the individual indicators to a particular
construct. The recommended minimum = 0.7; but 0.5 is
acceptable. Variables with insignificant or low loadings should
be considered for deletion.
Connector Among Error Terms:
If model is not good fit, we will put the connector between the
largely error term of the same variable. If the large values of
error are existing in the model in different variables then we
can not put the connector and will go for the standardized
residual covariance approach for the goodness of fit of the
model.
 Standardized Residuals Covariance
Standardized residual covariance is used to check the
discrepancies (differences) between proposed and
estimated model.

For the model fit purpose, standardized residual

covariance are checked and to find that which item/s is
decreasing the model fitness and that items are excluded
from the model for the goodness of fit of the model.

• The better the fit the smaller the residual, these should
not exceed |4.0|.
Path Estimates
Connector Among Error Terms
Variances: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
CBCI 1.175 .316 3.719 ***
CBIP 1.180 .349 3.387 ***
CBCC 1.761 .473 3.723 ***
e1 .584 .117 4.998 ***
e2 .161 .050 3.221 .001
e4 .466 .094 4.972 ***
e5 .820 .163 5.030 ***
e6 .287 .071 4.072 ***
e7 .190 .054 3.503 ***
e8 .887 .172 5.166 ***
e9 .898 .172 5.205 ***
e10 .863 .176 4.898 ***
e11 .460 .096 4.801 ***
e12 .116 .064 1.826 .068
Standardized Residuals Covariance
 Treatment of Missing Values
Missing values may exists in the final collected data
through refined instrument
• If 5% of the respondents did not give the
response of the total sample size then replace the
missing values by the mean of series or replace
with mean of the five above & below of the
missing values.
• If the response is missing between 5% to 25%
then revisit the respondents.
• If its more than 25% then revisit yourself and
your questionnaire.
 Reliability Analysis
• The Confirmatory Factor Analysis (CFA)
finalized/refined the instrument and that was used for
final survey.
• The extent of consistency between the numerous
measurements of a variable is called as reliability (Hair
et al., 1998). Internal consistency of the scale is
measured by reliability analysis and is most widely
used. Cronbach’s alpha is obtained by the Coefficient of
Alpha.
• Its limit is 0 to 1 and data will be reliable if its value is
more than or equal to 0.60
• Reliability analysis is conducted to measure the internal
consistency among the items.
 Normality of Data
• Normality of the study variables (scaled variables) should be
checked. We can name it test of homogeneity
• There might be normal or abnormal data but most of the time
data will be abnormal.
• H0: There is no significant difference in the variance of data. (Normal data)
• H1: There is significant difference in the variance of data. (Abnormal data)
 Cont.…….
• Skewnesses and Kurtosis are used to check the normality of
data. Skewness (std. deviation) represents the spread and
kurtosis (mean) represents the height of the curve.
• If skewnesses are laying between +&- 1 then data will be
normal and if the kurtosis are +ve and approaching to 3 then
data is highly normal. Descriptive are (Mean, std. deviation,
skewnesses and kurtosis) the lenient criterias to detect the
normality of data.
•
 Cont.…….
• Some are very strict (conservative) criterias to
detect the normality. Like Kolmogorov-
Smirnov and Shapiro-Wilk, decision is made
on the bases of significant values.
• If the sample size is < 50 then consider the
Shapiro-Wilk and if sample size is > 50 then
Kolmogorov-Smirnov significant value is
considered for decision of the normality
 Cont.…….
Commands in SPSS
Analyze Descriptive Explore
send the variable to dependent list plots
normality check & histogram continue
ok
and make the decision as per standardized values
For fitting the line on normal curve
Double click on histogram elements then
normal curve and close
 Descriptive Statistics
• Descriptive statistics is used to check the
application level and direction of response of
the respondents about the questions.
• Descriptive statistics employ three kinds of
indicators: dispersion measures (std. deviation,
range, skewnes), central tendency measures
(mean, median, mode, kurtosis) and frequency
distribution.
 Research Design
Exploratory Descriptive Hypothesis Testing

To Explore To Describe Measure of Difference (Parametric Tests) Measure of Association (Non-parametric Tests)

Independent
Qualitative Quantitative One Sample Multiple Sample Dependency Interdependency
Sample

When Body of When body of

One Sample t Independent One DV & one One DV &
Knowledge is Knowledge is ANOVA Multiple DVs Simple Relationship
test Sample Test IV Multiple IVs
unknown known

Open end Closed end MANOVA Pearson Spearmen

Causal Correlational
questionnairre Quistionnairre MANCOVA Corellation Corellation

Simple Multiple
Regression Regression
 Measure of Differences (Parametric tests)
These tests are applied with demographic
variables and also called comparative analysis.
• One Sample t-test
• Independent Sample t-test
• Paired Sample t-test
• One way ANOVA
 One Sample T-Test
• There will be only one series of data. A cutoff
point or value is assigned for decision making.
• There should be sound support of literature,
facts/figures figures for rationale decision making
e.g. VC asks to registrar to bring the data of
CGPA of MS students and VC assumes a cutoff
point(logical value) to give the scholarship.
Commands in SPSS
Analyze compare mean one sample t-test
send the variable to dependent bar
Give the logical value to value bar
and make the decision on the significant value
 Independent Sample T-Test
• The independent sample t-test, is an inferential statistical test that
determines whether there is a statistically significant difference between the
means of two unrelated groups (male & female; foreign & local etc.). The
demographic variable having two classes will be considered.
• The test assumes that the grouping variable is measured on nominal scale
and the test or study variable is measured on interval scale. It also assumes
that data is normal
• Statistical significance is determined by the size of the difference between
the group averages, and the standard deviations of the groups. For practical
purposes statistical significance suggests that the sample of two larger
populations are “actually” different.
• Levene’s test (F-stat and its p-value or sig.) are considered for the normality
of data, keep in mind the hypothesis and decide either data is normal or not.
• If data is normal we will be considering the upper line otherwise take into
account the lower line. Take the decision on the base of t-stat and p-value for
hypothesis testing
Analyze compare mean Independent sample t-test
send the computed variable to test variable bar
demographic variable to Grouping variable Define group
and make the decision
 Paired Sample T-Test
• When before and after the event situation is given then paired
sample t-test is applied. There should be logical and
comparable situations. Two data sets should be testable.
• Make the comparison on the bases of correlation co-efficient
and it should be significant.
• The mean value of after the event should be greater than the
mean value before the event. From the last table t-stat and its
significant values are considered for proving or disapproving
the hypothesis.
Analyze compare mean paired sample t-test 1st
scaled variable 2nd scaled variable ok
and make the decision
 One Way-ANOVA
• The one-way analysis of variance (ANOVA) is used to
determine whether there are any significant differences
between the means of three or more independent (unrelated)
groups. The demographic variable having more than 2
categories is focused.
• The one-way ANOVA compares the means between the groups
you are interested in and determines whether any of those
means are significantly different from each other.
Analyze compare mean one way ANOVA
send the computed variable to dependent list send
demographic variable to factor options Descriptive
continue ok and make the decision on F-stat
and its significant value and consider the mean values
 Correlation Coefficient
• Degree and type of relationship between any two
or more variables in which they vary together
over a period.
• Correlation can vary from +1 to -1. Values close
to +1 indicate a high-degree of positive
correlation, and values close to -1 indicate a high
degree of negative correlation.
• Values close to zero indicate poor correlation of
either kind, and 0 indicates no correlation at all.
 Regression
• In statistics, regression analysis is a statistical
process for estimating the relationships among
variables. When the focus is on the relationship
between a dependent variable and one or more
independent variables.
• The two basic types of regression are simple
linear regression and multiple linear regression.
Linear regression uses one independent variable
to explain and/or predict the outcome of Y, while
multiple regression uses two or more independent
variables to predict the outcome.
 Structural Equation Model (SEM)
• SEM was applied to identify the direct, indirect and mediation
relationship between the dependent (Endogenous variable),
independents (Exogenous variable) and mediators. The
confidence interval may be 95 % with 5 % level of
significance. The level of significance of the variable is
checked at 5 %.
There are Two steps:
 First, the direct effect of the independents to the dependent
variable is to be examined.
 Second, the indirect effect of the independent to the dependent
variable is to be examined through mediating variable.
 If the relationship of the independent variable to the dependent
variable is insignificant through the mediating variable, it is
complete (full) mediation; but if it is still significant and the
path declines, it is partial mediation (Prabhu, 2007; Hoyle and
Smith, 1994; Baron and Kenny, 1986)
Theoretical Framework & Hypotheses
Employee
Involvement

(+)
(+)

Employer (+) Organizational

Branding Performance
(+) (+)

Managerial Support
 Hypotheses Statements
• H1: Employee involvement (EI) has significance effect on
organizational performance.
• H2: Managerial support (MS) has significance impact on
organizational performance.
• H3: Employee involvement (EI) has significance effect on
employer branding.
• H4: Managerial support has significance effect on employer
branding.
• H5: Employer branding has significance impact on
organizational performance
• H6: Employer branding mediate the relationship between
Employee involvement and organizational performance
• H7: Employer branding mediate the relationship between
managerial support and organizational performance
 Direct Effects
(The direct effect of the independent to the dependent variable)

Variables Estimate P-Value Hypothesis Support

Organizational Performance
Employee Involvement 0.40 0.011 H1 is Accepted

Organizational
Managerial support 0.27 0.026 H2 is Accepted
Performance
 IVs on MV & MV on DV

Variables Estimate P-Value Hypothesis Support

Employee Branding Employee Involvement 0.46 *** H3 is accepted

Employee Branding Managerial support 0.26 0.033 H4 is accepted

Organizational
Employee Branding 0.79 *** H5 is accepted
Performance
Mediation Effects (Indirect Effects)
Direct Effects Indirect Effects
Hypothesis
Variables
Support
Estimate P-Value Estimate P-Value

Organizational Employee H6 is
0.46 *** 0.04 0.690
Performance Involvement accepted.

Organizational Managerial H7 is
0.26 0.033 0.07 0.358
Performance support accepted.