Introduction to Quantitative Methods & Analysis

Session 1 & 2

IntroductionResearch is the process of finding solutions to a problem after a thorough study and analysis of the situational factors

Researchcan be defined as the search forknowledge, or as any systematic investigation, with an open mind, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using ascientific method.

The systematic and objective process of generating information for aid in making management decisionsThe function which links the consumer, the customer, and public to the Problems through INFORMATION

Scientific MethodThe scientific methodis a body oftechniquesfor investigatingphenomena, acquiring new knowledge, or correcting and integrating previous knowledge.To be termed scientific, a method of inquiry must be based on empiricalandmeasurableevidence subject to specific principles of reasoning.The analysis and interpretation of empirical evidence (facts from observation or experimentation) to confirm or disprove prior conceptions.

Basic research Applied researchResearch Types

Deductive and inductive theoryDeductivism:theory --> dataexplicit hypothesis to be confirmed or rejectedquantitative research

Inductivism:data --> theorygeneralizable inferences from observationsqualitative research /grounded theory

Qualitative vs. Quantitative ResearchQualitative Research

To gain a qualitative understanding of the underlying reasons and motivations

Small number of non-representative cases

Unstructured

Non-statistical

Develop an initial understandingObjective

Sample

Data Collection

Data Analysis

OutcomeQuantitative Research

To quantify the data and generalize the results from the sample to the population of interest

Large number of representative cases

Structured

Statistical

Recommend a final course of action

Quantitative researchmeasurement of variables

common research designs: surveys and experiments

numerical and statistical data

deductive theory testing

positivist epistemology

objectivist view of reality as external to internal actors

Theoretical FrameworkA theoretical framework represents your beliefs on how certain phenomena (or variables or concepts) are related to each other (a model) and an explanation on why you believe that these variables are associated to each other (a theory).

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Theoretical FrameworkBasic steps:Identify and label the variables correctlyState the relationships among the variables: formulate hypothesesExplain how or why you expect these relationships

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VariablesAny concept or construct that varies or changes in value Main types of variables:Dependent variableIndependent variableModerating variable Mediating variable (or intervening)

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(In)dependent VariablesDependent variable (DV)Is of primary interest to the researcher. The goal of the research project is to understand, predict or explain the variability of this variable.

Independent variable (IV)Influences the Dependent Variable in either positive or negative way. The variance in the Dependent Variable is accounted for by the Independent Variable.

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*ModeratorsModerating variable Moderator is qualitative (e.g., gender, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of relation between independent and dependent variable.

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The Moderating VariableIs one that has a strong contingent effect on the independent variable-dependent variable relationship.

The presence of the moderating variable modifies the original relationship between the independent and dependent variables.*

The Intervening VariableIs one that surfaces between the time the independent variables start operating to influence the dependent variable and the time their impact is felt on it.*

Theoretical FrameworkHaving examined the different kinds of variables that could operate in a situation and how the relationships among these can be established, it is now possible to see how we can develop the conceptual model or the theoretical framework for our research. *

Theoretical FrameworkThe theoretical framework is the foundation on which the entire research project is based.

It is a logically developed, described, and elaborated network of associations among the variables deemed relevant to the problem situation.*

The components of the theoretical frameworkThe variables considered relevant to the study should be clearly defined.

A conceptual model that describes the relationships between the variables in the model should be given.

A clear explanation of why we expect these relationships to exist.*

ModelsAn analytical model is a set of variables and their interrelationships designed to represent, in whole or in part, some real system or process. In verbal models, the variables and their relationships are stated in prose form. Such models may be mere restatements of the main tenets of a theory.

Graphical ModelsGraphical models are visual. They are used toisolate variables and to suggest directions ofrelationships but are not designed to providenumerical results.AwarenessUnderstanding: EvaluationPreference

Mathematical models explicitly specify therelationships among variables, usually inequation form.

Where y = degree of preference= model parameters to be estimated statistically Mathematical Models

HypothesisA proposition that is empirically testable. It is an empirical statement concerned with the relationship among variables.

Good hypothesis:Must be adequate for its purposeMust be testableMust be better than its rivalsCan be:DirectionalNon-directional*

Statistics Descriptive Statistics

Inferential statistics

StatisticsDescriptive StatisticsGives numerical and graphic procedures to summarize a collection of data in a clear and understandable way

Inferential Statistics Provides procedures to draw inferences about a population from a sample

Graphs and tablesTablesColumn chartsBar chartsLine chartsPie chartsXY (Scatter) chartsArea chartsDoughnut chartsRadar chartsSurface chartsBubble chartsStock chartsCylinder, Cone, or Pyramid charts

Descriptive MeasuresCentral Tendency measures. They are computed to give a center around which the measurements in the data are distributed.

Variation or Variability measures. They describe data spread or how far away the measurements are from the center.

Relative Standing measures. They describe the relative position of specific measurements in the data.

Measures of Central TendencyMean: Sum of all measurements divided by the number of measurements.

Median: A number such that at most half of the measurements are below it and at most half of the measurements are above it.

Mode: The most frequent measurement in the data.

Numerical descriptions Let y denote a quantitative variable, with observations y1 , y2 , y3 , , yn

a. Describing the center

Median: Middle measurement of ordered sample

Mean:

Variance (for a sample)Steps:Compute each deviationSquare each deviationSum all the squaresDivide by the data size (sample size) minus one: n-1

The standard deviation

It is defines as the square root of the varianceIn the previous exampleVariance = 6Standard deviation = Square root of the variance = Square root of 6 = 2.45

Describing variabilityRange: Difference between largest and smallest observations (but highly sensitive to outliers, insensitive to shape)

Standard deviation: A typical distance from the mean

The deviation of observation i from the mean is

The variance of the n observations is

The standard deviation s is the square root of the variance,

Properties of the standard deviation: s 0, and only equals 0 if all observations are equal s increases with the amount of variation around the mean Division by n - 1 (not n) is due to differences between mean and median s depends on the units of the data (e.g. measure Rs vs $)Like mean, affected by outliers

Empirical rule: If distribution is approx. bell-shaped, about 68% of data within 1 standard dev. of mean about 95% of data within 2 standard dev. of mean all or nearly all data within 3 standard dev. of mean

PercentilesThe p-the percentile is a number such that at most p% of the measurements are below it and at most 100 p percent of the data are above it.Example, if in a certain data the 85th percentile is 340 means that 15% of the measurements in the data are above 340. It also means that 85% of the measurements are below 340

Notice that the median is the 50th percentile

Example of Tchebichevs Rule

Suppose that for a certain data is :Mean = 20

Standard deviation =3Then:

A least 75% of the measurements are between 14 and 26

At least 89% of the measurements are between 11 and 29

Bivariate descriptionUsually we want to study associations between two or more variables (e.g., how does number of close friends depend on gender, income, education, age, working status, rural/urban, religiosity)Response variable: the outcome variableExplanatory variable(s): defines groups to compare

Ex.: number of close friends is a response variable, while gender, income, are explanatory variables

Response var. also called dependent variableExplanatory var. also called independent variable

Summarizing associations:Categorical vars: show data using contingency tables Quantitative vars: show data using scatterplotsMixture of categorical var. and quantitative var. (e.g., number of close friends and gender) can give numerical summaries (mean, standard deviation) or side-by-side box plots for the groups

Ex. General Social Survey (GSS) data Men: mean = 7.0, s = 8.4 Women: mean = 5.9, s = 6.0Shape? Inference questions for later chapters?

********Draw picture showing insensitivity of range to shape