1. Intro to Research Methods
SPH-X590  Summer 2015
Data Analysis: Methodological Big Picture
Statistical Analysis
Probability, Inference & Estimation
Notation

2. Presentation Outline Review Statistical Analysis Structure of Research
Dimensions of Research
Research Process
Study Designs
Statistical Analysis
Types of Statistics: Descriptive and Inferential
Notation

3. The Structure of Research: Deduction
The “Hourglass" Notion of Research
Begin with broad questions narrow down, focus in.
Operationalize
OBSERVE
Analyze Data
Reach Conclusions
Generalize back to Questions

4. The Scientific Method Problem/Question Observation/Research
Formulate a Hypothesis
Experiment
Collect and Analyze Results
Conclusion
Communicate the Results

5. The Empirical Research Process:D
EDUCT ION
T H E OR Y
Step 1
Identification of Area of Study: Problem Formulation
Step 2
Literature Review: Context
Step 3
Research Objectives to Hypotheses: Content to Methodology
Concepts to Variables
Step 4
Study Design I: Data Collection Methods
Research Design: experimental, quasi-experimental, or non-experimental
Time & Unit of Analysis
Step 5
Procedures: Sampling, Assignment, Recruitment, & Ethics
Step 6
Collection: Instruments, Materials, & Management
Step 7
Study Design II: Analysis
Statistical Approaches & Analytical Techniques
Sample Size & Power
Step 8
Results: Dissemination
Publication, Presentation, & New Application

6. The Dimensions of Empirical Research: A movement from the theoretical to analytical
Theories
Postulates
Propositions
Hypotheses
Deductive
Reasoning
SCIENTIFIC METHOD
Analysis
Data Collection
Constructs
Variables
Concepts
Measurement

7. Describe Characteristics
Data Analysis: In the Big Picture of Methodology
Question to Answer
Hypothesis to Test
Theory
Note: Results of empirical scientific studies always begin with the Descriptive Statistics, whether results conclude with Inferential Statistics depends of the Research Objectives/ Aims
Study Design:
Data Collection Method & Analysis
Inferential Statistics
Causal Inference
Test Hypothesis, Conclusions, Interpretation, & Identification Relationships
Collect Data:
Measurements, Observations
Data Extraction
Data
Storage
Descriptive Statistics
Describe Characteristics
Organize, Summarize, &
Condense the Numbers
Decision:
Statistics?

8. Data Analysis: Types of Statistics
Descriptive Statistics
Summarization & Organization of variable values/scores for the sample
Inferential Statistics
Inferences made from the Sample Statistic to the Population Parameter.
Able to Estimate Causation or make Causal Inference
Isolate the effect of the Experimental (Independent) Variable on the Outcome (Dependent) Variable

9. Data Analysis: Descriptive Statistics
Descriptive Statistics are procedures used for organizing and summarizing scores in a sample so that the researchers can describe or communicate the variables of interest.
Note: Descriptive Statistics apply only to the sample: says nothing about how accurately the data may reflect the reality in the population
Use Sample Statistics to “infer” something about relationships in the entire population: assumes sample is representative of population.
Descriptive Statistics summarize 1 variable: aka Univariate Statistics
Mean, Median, Mode, Range, Frequency Distribution, Variance and Standard Deviation are the Descriptive Statistics: Univariates

10. Data Analysis: Inferential Statistics
Inferential Statistics are procedures designed to test the likelihood of finding the same results from one sample with another sample drawn from the same population: in fact, mathematically tests whether the sample results would be obtained if all possible samples from the population were tested.
Attempts to rule out chance as an explanation for the results: that results reflect real relationships that exist in the population and are not just random or only by chance.
Before you can describe or evaluate a relationship using statistics, you must design your study so that your research question can be addressed.
This is Methodology: where theory meets Data Collection Methods & Data Analysis.

11. Data Analysis: Statistics Notation
Capitalization
In general, capital letters refer to population attributes (i.e., parameters); and lower-case letters refer to sample attributes (i.e., statistics).
For example,
P refers to a population proportion;
and p, to a sample proportion.
X refers to a set of population elements;
and x, to a set of sample elements.
N refers to population size;
and n, to sample size.
Greek vs. Roman Letters
Like capital letters, Greek letters refer to population attributes.
Their sample counterparts, however, are usually Roman letters.
For example,
μ refers to a population mean;
and x, to a sample mean.
σ refers to the standard deviation of a population;
and s, to the standard deviation of a sample.

12. Data Analysis: Statistics Notation
Population Parameters
By convention, specific symbols represent certain population parameters.
Notation
μ refers to a population mean.
σ refers to the standard deviation of a population.
σ2 refers to the variance of a population.
P refers to the proportion of population elements that have a particular attribute.
Q refers to the proportion of population elements that do not have a particular attribute, so Q = 1 - P.
ρ is the population correlation coefficient, based on all of the elements from a population.
N is the number of elements in a population.
Sample Statistics
By convention, specific symbols represent certain sample statistics.
Notation
x refers to a sample mean.
s refers to the standard deviation of a sample.
s2 refers to the variance of a sample.
p refers to the proportion of sample elements that have a particular attribute.
q refers to the proportion of sample elements that do not have a particular attribute, so q = 1 - p.
r is the sample correlation coefficient, based on all of the elements from a sample.
n is the number of elements in a sample.

13. Data Analysis: Summation/ Sigma Notation
Summation Notation is shorthand that relies on Greek alphabet and mathematical symbols to indicate how to process values: aka formulae.
 = summation
X = Variable
What do each of these mean? X
Add up the values of X
X + 2 versus (X + 2)
Add up the values of X and add 2 to the Sum,
Add 2 to each value of X and then Sum the values
X2 versus (X)2
Square each value of X and then Sum
Sum the values of X and then Square the Sum
(X + 2)2 versus (X2 + 2)
Add 2 to each value of X, square the value, then Sum the squared values
Square each value of X, add 2 to the value, then Sum the values

14. Data Analysis: Summation/ Sigma Notation
X : Independent Variable, typically
Y: Dependent Variable, typically
N= Size of the Population
n= Size of the Sample
≤ ≥ ≠ = : Equalities or Inequalities
± × ÷ + - : Mathematical Operators
α: alpha, refers to constant/ intercept
µ: mu, sample mean
β: beta coefficient/ standardized
δ: sigma, sample standard deviation
δ2: sigma squared, sample variance