research methodology and data analysis felix famoye central michigan university, usa currently a...

Research Methodology and Data Analysis

Felix FamoyeCentral Michigan University, USA

Currently a Fulbright Scholar, Unilag

Presented by Felix Famoye04/19/23 1

Thanks to Workshop Organizers

• Thanks for the Invitation• My research area is Statistics

• Additional thanks to Dean, SPGS, Unilag


Outline of the talk

• Introduction• Research Types• Sub-sections of Research Methodology• Data Analysis• Conclusion/Final Comments


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:


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 AnalysisSub-section’s choice depends on research type.

04/19/23 Presented by Felix Famoye 5

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.


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.


Types of Qualitative Research:

• Historical research, allows one to discuss past and present events. The method investigates the why and how of 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 solve algebraic equations.


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 on how students solve algebraic equations.


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.


• Statistics is widely used in quantitative

research.

• Quantitative method can be divided into four types:odescriptive researchocorrelational researchocausal-comparative researchoexperimental research


Jokes: [http://www.btinternet.com/~se16/hgb/statjoke.htm]

• How many statisticians does it take to change a light bulb? 1-3, alpha = 0.05.

• There is no truth to the allegation that statisticians are mean. They are just your standard normal deviates.

• Did you hear about the statistician who invented a device to measure the weight of trees? It’s referred to as the log scale.

• Did you hear about the statistician who was thrown in jail? He now has zero degrees of freedom.


http://www.btinternet.com/~se16/hgb/statjoke.htm

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).


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/[(N – 1)B2/4 + pq], where N =

population size, B = error bound, p = 0.5]


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.


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.


Data Collection Methods:• If you do not have adequate training in this

area (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.


Data Collection Methods continued:

• Data from surveys and experiments are called primary data.

• Data obtained from a source are called secondary data.

• For examples, humanities, social sciences, public health, law and education are most likely to use surveys.

• Also for examples, agriculture, physical and biological sciences, medical sciences are most likely to conduct experiments.


Some data collection methods are:• Personal interviews• Telephone interviews• Direct observation• Self-administered questionnaires (Mailed or

handed out, especially in convenience sample)


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.


Data Analysis• Will data be analyzed qualitatively or

quantitatively?• The choice will depend on data collection

methods and the sample size.• Describe the types of data analysis or

modeling that will be done.• Address each research question by describing

the type of statistical tests that will be performed.

• Include the name of the software used.


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.


More Jokes:• The only time a pie chart is appropriate is at a

baker's convention. • Old statisticians never die, they just undergo a

transformation.• How do you tell one bathroom full of

statisticians from another? Check the p-value. • Did you hear about the statistician who made

a career change and became a surgeon specializing in ob/gyn? His specialty was histerectograms.


Data Types• Generally speaking, statistical techniques are

often 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 areNominal- data are non-numeric group labelsOrdinal- values are ranked categories


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.


Statistics (descriptive and inferential) Descriptive statistics (Numeric and Graphic):• These includes summary statistics (mean,

median, standard deviation, frequency) and graphic tools (pie charts, bar charts, histograms, box plots, scatter plots)

For nominal data: Use frequency, crosstabs, bar charts 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.


Estimation and Tests (Inferential statistics):

• This is used to make comparisons between two or more groups or study relationships.

• These include point estimation, confidence interval or interval estimation, and hypothesis testing.


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-way

analysis 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 a repeated measure ANOVA for more than two periods.


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.


If you are interested in modeling a response variable using predictor variables

• For nominal data, use Logistic regression model if the response is a binary variable (that is only two possible values such as yes or no). If the response has more than two categories, use multinomial logistic regression.

• For count data, use Poisson regression model if the response follows a Poisson distribution. In general, one can use log-linear models for ordinal data.

• For continuous data, use regression analysis.


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 X’s is linear.• When assumptions do not hold, use

transformation or a non-parametric method.


Some Nonparametric Methods• Chi-square tests• For two independent samples comparison, use Mann-

Whitney U or Kolmogorov-Smirnov Z. This is similar to independent t-test.

• For K independent samples comparison, use Kruskal-Wallis H or Median. This is similar to ANOVA.

• For two related samples, use Wilcoxon or Sign test for quantitative data; McNemar for binary data and Marginal Homogeneity for multinomial data. This is similar to paired t-test.

• For K related samples, use Friedman or Kendall’s W measure of agreement or Cochran’s Q for binary data. This is similar to Repeated Measure ANOVA.


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 subsets of variables based on the similarity of cases.

Factor analysis combines similar variables together into a dimension that can be interpreted from the qualitative aspects of the study.


Conclusions/Final Comments• You bought an expensive clothing material. • Do you look for an apprentice tailor to sew the

material 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 not settle for less (anybody).

• Look for someone with adequate training in statistical methodology.

Mathematics Dept Statistical Consulting UnitPresented by Felix Famoye04/19/23 34

Conclusions/Final Comments continued:• When test shows a significant effect, a common

misunderstanding is that the hypothesis has been proven.

• In a statistical test, if the outcome is inconsistent with the research hypothesis, then the hypothesis is rejected.

• If the outcome is consistent with the research hypothesis, the data is said to support the hypothesis.

• Hypothesis is never proven but rather only supported by the analyzed data.


More Jokes:• A statistician can have his head in an oven and his feet

in ice, and he will say that on the average he feels fine.• Numbers are like people; torture them enough and

they will tell you anything. • Statistics in the hands of an engineer are like a

lamppost to a drunk-they are used more for support than illumination. (Bill Sangster, Dean of Engineering, Georgia Tech.)

• The statistics on sanity are that one out of every four Nigerians is suffering from some form of mental illness. Think of your three best friends. If they are okay, then it is you. (Rita Mae Brown, for Americans)


Thanks for your attention

This is the end of the presentation


research methodology and data analysis felix famoye central michigan university, usa currently a...

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