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Transcript of Professor Felix Famoye
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Research Methodology and Data
Analysis
Felix Famoye
Central Michigan University, USACurrently a Fulbright Scholar, Unilag
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Thanks to Workshop Organizers
Thanks for the Invitation
My research area is Statistics
Additional thanks to Dean, SPGS, Unilag
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Outline of the talk
Introduction
Research Types
Sub-sections of Research Methodology Data Analysis
Conclusion/Final Comments
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Introduction
The methodology section shows how your
research questions will be answered.
It must be appropriate for your research type.
Describe in detail what methodology and
materials, if any, that you will use to carry out
your research.
This section may have some of the following
sub-sections:
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Some sub-sections:
Conceptual and/or Theoretical Framework
Models and/or Theorems Formulation
Research/Experimental Design
Sampling Method
Measurement Instruments
Materials and Experiments
Data Collection Method
Data Analysis
Sub-sections choice depends on research type.
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Research Types
Broadly speaking, we have qualitative and
quantitative research studies.
These two broad methods have further been
divided into different types.
Boundaries between the research types may
not be that clear.
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Qualitative method:
In this approach, narrative data is collected in
order to study the topic of interest.
It is also called ethnographic (investigating
cultures) or anthropological research.
The data analysis includes coding and
production of verbal synthesis.
No statistical procedures or other means of
quantification is involved.
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Types of Qualitative Research:
Historical research, allows one to discuss past
and present events. The method investigates
the whyand howof decision making. An
example: Factors that led to the creation of
more states (or more universities) in Nigeria.
Qualitative research is involved in the study of
current events rather than past events.
Examples: A case study of how students solvealgebraic equations.
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Quantitative method:
In this approach, data (both numerical and
non-numerical) is collected in order to
describe, predict and/or control phenomena
of interest.
The data analysis is mainly statistical.
Quantitative research can be used to verify
such hypotheses formulated through
qualitative research. Consider the example onhow students solve algebraic equations.
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Quantitative research generally includes:
Development of models, theories and
hypotheses.
Development of instruments and methods to
collect data.
Experimental control and manipulation of
variables.
Collection of empirical data.
Modeling and analysis of data.
Evaluation of results.
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Statistics is widely used in quantitative
research.
Quantitative method can be divided into four
types:odescriptive research
ocorrelational research
ocausal-comparative research
oexperimental research
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Jokes:
[http://www.btinternet.com/~se16/hgb/statjoke.htm]
How many statisticians does it take to change alight bulb? 1-3, alpha = 0.05.
There is no truth to the allegation thatstatisticians are mean. They are just yourstandard normal deviates.
Did you hear about the statistician who inventeda device to measure the weight of trees? Itsreferred to as the log scale.
Did you hear about the statistician who wasthrown in jail? He now has zero degrees offreedom.
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Sub-sections of Research Methodology
Research/Experimental Design: This depends on your research type.
Is it descriptive, correlational, causal-
comparative or experimental research? For example, one may want to compare two
teaching methods. One possible design is to
have three groups of subjects (method 1,method 2, and a control; pre/post tests).
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Sampling Methods:
For surveys or any research in which you plan
to collect data, define your population.
What is the sampling design? (or How will you
select your subjects?)
How many subjects will you select?
For example, to estimate proportion:
n= Npq/[(N1)B2
/4 +pq], where N=population size, B= error bound,p= 0.5]
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Sampling Methods continued:
To generalize your result, use a probability
sampling method.
Among the probability sampling methods are
simple random sample; systematic random
sample; stratified random sample; cluster
sample.
Among the non-probability sampling methods
are voluntary response sample; convenience
sample.
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Measurement Instruments (and/or Materials):
Are you using a survey designed by you or
someone else? Give reference, if other(s).
Address the reliability of the instrument.
In the biological or medical sciences, address
the materials that will be used.
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Data Collection Methods:
If you do not have adequate training in thisarea (or in data analysis), seek help before
you begin to collect your data.
Quite often, researchers collect inadequate
data or data that are not properly recorded.
You want to be sure that the data you collect
can be used to answer your questions or test
your hypotheses.
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Data Collection Methods continued:
Data from surveys and experiments are calledprimary data.
Data obtained from a source are calledsecondary data.
For examples, humanities, social sciences,public health, law and education are mostlikely to use surveys.
Also for examples, agriculture, physical andbiological sciences, medical sciences are mostlikely to conduct experiments.
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Some data collection methods are:
Personal interviews
Telephone interviews
Direct observation
Self-administered questionnaires (Mailed orhanded out, especially in convenience sample)
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Example of Model Developments sub-section:
R-squared measures will be developed.
The R-squared measures will be adjusted for
both the sample size and the number of
independent variables.
Power-divergent statistics will be developed.
A detailed simulation study will be conducted
to compare the log-likelihood ratio, R-squared,
and the power-divergent statistics.
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Data Analysis
Will data be analyzed qualitatively or
quantitatively?
The choice will depend on data collectionmethods and the sample size.
Describe the types of data analysis ormodeling that will be done.
Address each research question by describing
the type of statistical tests that will beperformed.
Include the name of the software used.
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Data Cleaning:
This is the process where you detect and
correct the errors.
Some could be from typing errors during data
entry or coding error.
For detection of errors-
Obtain descriptive statistics like frequency
counts, minimum, maximum, means, range,
and standard deviation. Obtain graphs like
histogram or scatter plot.
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More Jokes: The only time a pie chart is appropriate is at a
baker's convention.
Old statisticians never die, they just undergo atransformation.
How do you tell one bathroom full ofstatisticians from another? Check the p-value.
Did you hear about the statistician who made
a career change and became a surgeonspecializing in ob/gyn? His specialty washisterectograms.
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Data Types
Generally speaking, statistical techniques areoften determined based on the type of data.
The two major types of variables are
qualitative and quantitative variables. Qualitative variables:The data values are non-
numeric categories. Measurement scales are
Nominal- data are non-numeric group labelsOrdinal- values are ranked categories
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Quantitative variables: The data values are counts or numerical
measurements. It can be discrete/continuous.
The measurement scales are-
Interval- data values ranged in a real interval.
The difference, but not the ratio, of two values
is meaningful. Interval data has no absolute
zero.
Ratio- Both the difference and ratio of two
values are meaningful.
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Statistics (descriptive and inferential)
Descriptive statistics (Numeric and Graphic):
These includes summary statistics (mean,median, standard deviation, frequency) andgraphic tools (pie charts, bar charts, histograms,box plots, scatter plots)
For nominal data: Use frequency, crosstabs, barcharts and pie charts.
For ordinal data: Use frequency, crosstabs,
summary statistics, bar charts and pie charts.For continuous data: Use summary statistics,
histograms, box plots, and scatter plots.
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Estimation and Tests (Inferential statistics):
This is used to make comparisons betweentwo or more groups or study relationships.
These include point estimation, confidence
interval or interval estimation, and hypothesistesting.
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If you are interested in comparing group effects
For nominal or ordinal data: Use crosstabs (chi-square)
For continuous data (First, check for normality): For two group comparison, use independent t-test.
For three or more group comparison, use one-wayanalysis of variance (ANOVA).
For two or more factors, use multi-way ANOVA. If there are factors and covariates, use analysis of
covariance (ANCOVA).
If the same subject is measured more than one time, it
is a paired t-test for two time periods and it is arepeated measure ANOVA for more than two periods.
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If you are interested in the relationship between
two variables
For nominal data, use crosstabs, and choose
proper tests for nominal data.
For ordinal data, use crosstabs (chi-square
test), bivariate correlation such as Spearman
correlation coefficient.
For continuous data, use bivariate correlation
such as Pearson correlation.
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If you are interested in modeling a response
variable using predictor variables
For nominal data, use Logistic regression model ifthe response is a binary variable (that is only twopossible values such as yes or no). If the responsehas more than two categories, use multinomiallogistic regression.
For count data, use Poisson regression model ifthe response follows a Poisson distribution. In
general, one can use log-linear models for ordinaldata.
For continuous data, use regression analysis.
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Assumptions:
Most of statistical techniques require certain
assumptions.
Typically, for continuous response, the
assumptions may include:
Normality of the response variable.
Homogeneity of variance.
The relationship between Y and Xs is linear.
When assumptions do not hold, use
transformation or a non-parametric method.
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Some Nonparametric Methods
Chi-squaretests
For two independent samples comparison, use Mann-Whitney U or Kolmogorov-Smirnov Z. This is similar toindependent t-test.
For K independent samples comparison, use Kruskal-Wallis Hor Median. This is similar to ANOVA.
For two related samples, use Wilcoxonor Signtest forquantitative data; McNemarfor binary data andMarginal Homogeneity for multinomial data. This issimilar to paired t-test.
For K related samples, use FriedmanorKendalls W
measure of agreement or Cochrans Q for binary data.This is similar to Repeated Measure ANOVA.
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If you are interested in reducing the data
dimension
Use Cluster Analysis or Factor Analysis.
Cluster analysis can be applied to group variables
or cases. The cluster analysis for variables will
group the variables into small number of subsetsof variables based on the similarity of cases.
Factor analysis combines similar variables
together into a dimension that can be interpretedfrom the qualitative aspects of the study.
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Conclusions/Final Comments
You bought an expensive clothing material.
Do you look for an apprentice tailor to sew thematerial for you?
You look for an experienced tailor who is very
knowledgeable. When you decide to seek help for your data
collection and/or data analysis, you should notsettle for less (anybody).
Look for someone with adequate training instatistical methodology.
Mathematics Dept Statistical Consulting Unit
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Conclusions/Final Comments continued:
When test shows a significant effect, a common
misunderstanding is that the hypothesis has beenproven.
In a statistical test, if the outcome is inconsistentwith the research hypothesis, then the
hypothesis is rejected.
If the outcome is consistent with the researchhypothesis, the data is said to support the
hypothesis. Hypothesis is never proven but rather only
supported by the analyzed data.
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More Jokes:
A statistician can have his head in an oven and his feetin ice, and he will say that on the average he feels fine.
Numbers are like people; torture them enough andthey will tell you anything.
Statistics in the hands of an engineer are like a
lamppost to a drunk-they are used more for supportthan illumination. (Bill Sangster, Dean of Engineering,Georgia Tech.)
The statistics on sanity are that one out of every fourNigerians is suffering from some form of mental illness.Think of your three best friends. If they are okay, thenit is you. (Rita Mae Brown, for Americans)
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Thanks for your attention
This is the end of the presentation
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