Mgt 540
Research Methods
Data Analysis
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Additional “sources”
Compilation
of sources:
http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
http://web.utk.edu/~dap/Random/Order/Start.htm
Data
Analysis Brief Book (glossary)
http://rkb.home.cern.ch/rkb/titleA.html
Exploratory
Data Analysis
http://www.itl.nist.gov/div898/handbook/eda/eda.htm
http://obelia.jde.aca.mmu.ac.uk/resdesgn/arsham/opre330.htm
Statistical
Data Analysis
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Copyright © 2003 John Wiley & Sons, Inc. Sekaran/RESEARCH 4E
FIGURE 12.1
Data Analysis
Get the “feel” for the data
Get
Mean, variance' and standard deviation
on each variable
See if for all items, responses range all over
the scale, and not restricted to one end of the
scale alone.
Obtain Pearson Correlation among the
variables under study.
Get Frequency Distribution for all the
variables.
Tabulate your data.
Describe your sample's key characteristics
(Demographic details of sex composition,
education, age, length of service, etc. )
See Histograms, Frequency Polygons, etc.
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Quantitative Data
Each
type of data requires
different analysis method(s):
Nominal
Labeling
No
inherent “value” basis
purposes only
Categorization
Ordinal
Ranking,
Interval
sequence
Relationship
basis (e.g. age)
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Descriptive Statistics
Describing key features of data
Central
Mean,
Tendency
median mode
Spread
Variance,
standard deviation, range
Distribution
Skewness,
(Shape )
kurtosis
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Descriptive Statistics
Describing key features of data
Nominal
Identification
/ categorization only
Ordinal (Example on pg. 139)
Non-parametric
Do
statistics
not assume equal intervals
Frequency
Averages
Interval
counts
(median and mode)
Parametric
Mean,
Standard Deviation, variance
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Testing “Goodness of Fit”
Split Half
Reliability
Internal
Consistency
Convergent
Validity
Involves Correlations
and Factor Analysis
Discriminant
Factorial
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Testing Hypotheses
Use
appropriate statistical
analysis
T-test (single or twin-tailed)
Test
the significance of differences of
the mean of two groups
ANOVA
Test
the significance of differences
among the means of more than two
different groups, using the F test.
Regression (simple or multiple)
Establish
the variance explained in the
DV by the variance in the IVs
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Statistical Power
Claiming
Errors
Type
a significant difference
in Methodology
1 error
Reject
the null hypothesis when you should not.
an “alpha” error
Called
Type
Fail
2 error
to reject the null hypothesis when you
should.
Called a “beta” error
Statistical
power refers to the ability to
detect true differences
avoiding
type 2 errors
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Statistical Power see discussion at
http://my.execpc.com/4A/B7/helberg/pitfalls/
Depends
Sample
on 4 issues
size
The effect size you want to detect
The alpha (type 1 error rate) you
specify
The variability of the sample
Too
little power
Too
much power
Overlook
Any
effect
difference is significant
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Parametric vs.
nonparametric
Parametric (characteristics referring to
specific population parameters)
Parametric
assumptions
Independent
samples
Homogeneity of variance
Data normally distributed
Interval or better scale
Nonparametric
Sometimes
assumptions
independence of
samples
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t-tests
(Look at t tables; p. 435)
Used to compare two means or one
observed mean against a guess about
a hypothesized mean
For
large samples t and z can be
considered equivalent
Calculate
t
=
- µ
S
Where S is the standard error of the
mean,
S/√n and df = n-1
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t-tests
Statistical
programs will give you
a choice between a matched pair
and an independent t-test.
Your
sample and research design
determine which you will use.
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z-test for Proportions
(Look at t tables; p. 435)
When
data are nominal
Describe
by counting occurrences of
each value
From counts, calculate proportions
Compare proportion of occurrence
in sample to proportion of
occurrence in population
Hypotheses
testing allows only one of
two outcomes: success or failure
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z-test for Proportions
(Look at t tables; p. 435)
Comparing sample proportion to the
population proportion
H0:
π = k, where k is a value
H1:
π≠k
between 0 and 1
z=p-π =
p-π
σp
√(π(1- π)/n)
Equivalent
to χ2 for df = 1
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Chi-Square Test(sampling distribution)
One Sample
Measures sample variance
Squared
deviations from the mean –
based on normal distribution
Nonparametric
Compare expected with observed
proportion
H0: Observed proportion = expected
proportion
df = number of data points
categories,
cells (k) minus 1
χ2 = (O – E)
2
E
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Univariate z Test
Test
a guess about a proportion
against an observed sample;
eg.,
MBAs constitute 35% of the
managerial population
H0:
π = .35
H1: π .35 (two-tailed test suggested)
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Univariate Tests
Some
univariate tests are
different in that they are among
statistical procedures where you,
the researcher, set the null
hypothesis.
In many other statistical tests the
null hypothesis is implied by the
test itself.
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Contingency Tables
Relationship between nominal variables
http://www.psychstat.smsu.edu/introbook/sbk28m.htm
Relationship between subjects' scores on
two qualitative or categorical variables (Early
childhood intervention)
If the columns are not contingent on the
rows, then the rows and column frequencies
are independent. The test of whether the
columns are contingent on the rows is called
the chi square test of independence. The
null hypothesis is that there is no relationship
between row and column frequencies.
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Correlations
A
statistical summary of the
degree and direction of
association between two
variables
Correlation itself does not
distinguish between independent
and dependent variables
Most common – Pearson’s r
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Correlations
You
believe that a linear
relationship exists between two
variables
The range is from –1 to +1
R2, the coefficient of
determination, is the % of
variance explained in each
variable by the other
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Correlations
r = Sxy/SxSy or the covariance
between x and y divided by their
standard deviations
Calculations needed
The
means, x-bar and y-bar
Deviations from the means, (x – x-bar) and
(y – y-bar) for each case
The squares of the deviations from the
means for each case to insure positive
distance measures when added, (x - xbar)2 and (y – y-bar)2
The cross product for each case (x – xbar) times
(y – y-bar)
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Correlations
The
null hypothesis for
correlations is
H0: ρ = 0
and the alternative is usually
H1: ρ ≠ 0
However, if you can justify it prior
to analyzing the data you might
also use
H1: ρ > 0 or H1: ρ < 0 ,
a one-tailed test
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Correlations
Alternative
Spearman
measures
rank correlation, rranks
and r are nearly always equivalent
measures for the same data (even when
not the differences are trivial)
rranks
Phi
coefficient, rΦ, when both
variables are dichotomous; again, it
is equivalent to Pearson’s r
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Correlations
Alternative
measures
Point-biserial, rpb when
If
correlating a
dichotomous with a continuous
variable
a scatterplot shows a
curvilinear relationship there are
two options:
A
data transformation, or
Use the correlation ratio, η2 (etasquared)
SSwithin
1SStotal
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ANOVA
For
two groups only the t-test and
ANOVA yield the same results
You must do paired comparisons
when working with three or more
groups to know where the means
lie
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Multivariate Techniques
Dependent
variable
Regression
in its various forms
Discriminant analysis
MANOVA
Classificatory
Cluster
or data reduction
analysis
analysis
Multidimensional scaling
Factor
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Linear Regression
We
would like to be able to
predict y from x
Simple
scores
linear regression with raw
sy
= dependent variable
sx
x = independent variable
b = regression coefficient = rxy
c = a constant term
y
The
general model is
y = bx + c (+e)
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Linear Regression
The statistic for assessing the overall
fit of a regression model is the R2 , or
the overall % of variance explained by
the model
R2 = 1 – unpredictable variance
total variance
=
predictable variance
total variance
= 1 – (s2e / s2y), where s2e is the
variance of the error or residual
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Linear Regression
Multiple regression: more than one
predictor
y
= b1x1 + b2x2 + c
Each regression coefficient b is
assessed independently for its
statistical significance;
H0: b = 0
So, in a statistical program’s output a
statistically significant b rejects the
notion that the variable associated
with b contributes nothing to
predicting y
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Linear Regression
Multiple regression
R2
still tells us the amount of variation in y
explained by all of the predictors (x)
together
The F-statistic tells us whether the model
as a whole is statistically significant
Several other types of regression models are
available for data that do not meet the
assumptions needed for least-squares
models (such as logistic regression for
dichotomous dependent variables)
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Regression by SPSS &
other Programs
Methods for developing the model
Stepwise: let’s computer try to fit all chosen
variables, leaving out those not significant and reexamining variables in the model at each step
Enter: researcher specifies that all variables will
be used in the model
Forward, backward: begin with all (backward)
or none (forward) of the variables and automatically
adds or removes variables without reconsideration
of variables already in the model
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Multicollinearity
Best
regression model has
uncorrelated IVs
Model stability low with
excessively correlated IVs
Collinearity diagnostics identify
problems, suggesting variables to
be dropped
High tolerance, low variance
inflation factor are desirable
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Discriminant Analysis
Regression
requires DV to be
interval or ratio
If DV categorical (nominal) can
use discriminant analysis
IVs should be interval or ratio
scaled
Key result is number of cases
classified correctly
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MANOVA
Compare
means on two or more
DVs
(ANOVA
limited to one DV)
Pure
MANOVA via SPSS only
from command syntax
Can use the general linear model
though
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Factor Analysis
A data reduction technique – a large set of
variables can be reduced to a smaller set
while retaining the information from the
original data set
Data must be on an interval or ratio scale
E.g., a variable called socioeconomic status
might be constructed from variables such as
household income, educational attainment of
the head of household, and average per
capita income of the census block in which
the person resides
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Cluster Analysis
Cluster analysis seeks to group cases rather
than variables; it too is a data reduction
technique
Data must be on an interval or ratio scale
E.g., a marketing group might want to
classify people into psychographic profiles
regarding their tendencies to try or adopt
new products – pioneers or early adopters,
early majority, late majority, laggards
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Factor vs. Cluster Analysis
Factor
analysis focuses on
creating linear composites of
variables
Number
of variables with which we
must work is then reduced
Technique begins with a correlation
matrix to seed the process
Cluster
analysis focuses on
cases
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Potential Biases
Asking the inappropriate or wrong
research questions.
Insufficient literature survey and hence
inadequate theoretical model.
Measurement problems
Samples not being representative.
Problems with data collection:
researcher biases
respondent biases
instrument biases
Data analysis biases:
Biases (subjectivity) in interpretation of
results.
coding errors
data punching & input errors
inappropriate statistical analysis
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Questions to ask:
Adopted from Robert Niles
Where did the data come from?
How (Who) was the data reviewed,
verified, or substantiated?
How were the data collected?
How is the data presented?
What
is the context?
Cherry-picking?
Be
skeptical when dealing with
comparisons
Spurious
correlations
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Copyright © 2003 John Wiley & Sons, Inc. Sekaran/RESEARCH 4E
FIGURE 11.2
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