à topics not...last updated: 2017.07.05 introduction to quantitative research what determines...

Last updated: 2017.07.05

Introduction to Quantitative Research What determines whether research is quantitative or qualitative? à Research topics do NOT determine whether research is qualitative or quantitative. à Instead, the research question’s focus, the type of data collected, the method of sampling, and the methods used to analyze the data determine whether qualitative or quantitative.

Qualitative Quantitative 1. Focus Cases – individuals, groups,

institutions Variables – something that can take on different values or attributes

2. Data Nonnumeric – oral interviews, text,

observations

Numerical

3. Sampling Purposive – typical cases, extreme cases, snowball, confirming and disconfirming cases

Random – representative and generalizable

4. Analyses Methods of interpreting the meaning

of symbolic content (e.g., language)

Use statistical methods (e.g., descriptive, inferential) to interpret numerical data

à Qualitative methods emphasize meaning making, or the variety of ways that people conceptualize phenomena. Language provides a window into people’s thoughts, experiences, and motivations, but also requires interpretation by the researcher. Intersubjectivity – the idea that language allows us to see / understand / know the world from another’s perspective. à But…, can we ever really know what someone else knows? This is a complicated issue, so be wary of simple answers such as “Yes” or “No.” à Quantitative methods emphasize discrete conceptualizations of phenomena (not necessarily objective) that afford shared meaning-making, but require context to be meaningful. This is why statistics ≠ math.


The Qualitative-Quantitative Dynamic, Mixed-methods, Triangulation • Using both qualitative and quantitative research methods on a phenomenon of interest

Exploration à Measurement/Instrumentation à Explanation/Revision

(mostly qualitative) (mostly quantitative) (mostly qualitative)

RVR, Figure 3.7, p. 83 Scientific vs. Nonscientific* Characteristics of Scientific and Nonscientific (Everyday) Approaches to Knowledge

Nonscientific Scientific

Approach Intuitive Empirical (direct observation, demonstrable)

Observation Casual, uncontrolled Systematic, controlled, replicable

Reporting Biased, subjective Unbiased, objective, public

Concepts Ambiguous Clear, operational specificity

Instruments Inaccurate, imprecise Accurate, precise (verifiable)

Measurement Not valid and/or reliable Valid and reliable

Hypotheses Untestable Testable

Attitude Uncritical, accepting Critical, skeptical

*Based on Shaughnessy, Zechmeister, and Zechmeister (2003, p. 15)


Formal Fallacies of Logic Affirming the consequent (converse error)

1. If P, then Q. 2. Q. 3. Therefore, P.

The argument is invalid because the conclusion (#3) can be false even when #1 and #2 are true. That is, since P was never asserted to be the only sufficient condition for Q, other factors could also account for Q while P is false. Two examples adapted from Wikipedia:

1. If Bill Gates owns Apple, then he is rich. 2. Bill Gates is rich. 3. Therefore, Bill Gates owns Apple.

Clearly you can be rich without owning Apple.

1. If I have the flu, then I have a sore throat. 2. I have a sore throat. 3. Therefore, I have the flu.

Here again, there are many different reasons for having a sore throat (kareoke anyone?!?). à No single approach to research can answer every important policy or practice question. Qualitative research is useful for generating theory, building models, and uncovering causal processes. Quantitative research is useful for describing representative estimates and determining how likely it is that a given outcome is due to chance.


Quantitative Methods

1. What are statistics? à “Statistics” represent a collection of procedures and principles for gathering data and analyzing information.

2. What is the difference between math and statistics?

à Statistics places math in “context.” That is, statistics never speaks for themselves; they always needs a good translator.

3. So, what does it mean to place math in context? Statistics Without a Problem to Solve


Statistics without a frame of reference

What are Statistics? 1. Descriptive Statistics

The use of graphical and numerical summaries of data to describe the results of an experiment or and observational study.

Examples:

How much do MSU graduates earn? How many eggs do Humpback turtles lay? How popular is President Trump?

2. Inferential Statistics

The use of a sample to draw inferences about a population

How likely are MSU male graduates earn more than female graduates? Is the Michigan lottery fair? How likely is it to rain?


How do we use statistics to describe data? à Univariate vs. Bivariate vs. Multivariate But definitions first…

Variable: Any characteristic of an individual that takes different values for different individuals Distribution: Describes the values a variable takes and how frequently these values occur. The distribution of a variable can be described graphically and/or numerically in terms of “shape”, “center” and “spread”. There are two types of variables: categorical and quantitative. The simplest variable is a categorical variable, which takes on only a few discrete values that usually have no natural numerical coding (e.g., yes/no, approve/dissaprove).

Quantitative variables can assume both a small (discrete – e.g., number of heads in 3 coin tosses) and large number of values (continuous – e.g., age, debt or income)


Univariate Considerations Shape, center, and spread help us to understand the nature of univarate data.

Measures of “Center”


Measures of “Spread”


Bivariate Considerations Statistical relationships occur when 2 or more variables tend to vary in a related way. Two variables are: • positively associated if increasing values of one occur with increasing values of the other. • negatively associated if increasing values of one occur with decreasing values of the other. • linearly associated if the points tend to lie in a straight line. A correlation summarizes the strength and direction of the linear relationship between two variables and can take on values from -1 to +1, where 0 = no linear relationship. We use different kinds of correlations to summarize different types of bivariate relationships • Two quantitative variables • Two categorical variables • One of each Examples of bivariate correlation.

But, shape still matters!! So always plot your data.


Relationships involving Categorical Variables For one categorical, one quantitative variable, the standard approach is to plot distributions of the quantitative variable at for each value of the categorical variable.

For two categorical variables, the distributions are described using 2-way tables.

Some take-home points about relationships between variables… 1. A relationship / association / correlation should not be confused with causation. 2. Correlations measure the strength of a linear relationship, which must be confirmed visually. (STOP HERE)


Multivariate Relationships Multiple Regression - Used to predict a criterion variable (Y) using a combination of predictors (X’s)

Y = β! + β!X! + β!X!

Earnings = β! + β!Education+ β!Experience

- Each coefficient (β) describes how much the criterion variable (Y) changes when the

predictor (X1) changes by one unit, holding all other predictors (e.g., X1) constant.

- R-squared is the proportion of variation in the criterion variable (Y) that is explained by

variation in all of the predictors combined. - Multicollinearity – when one predictor adds NO new information that cannot be obtained

from the other variables. Results in large SE of coefficients (less precision), which affects

Perfect Collinearity Multicollinearity - How many predictors can one regression model have? à Common rule = 1 per 10 observe

Little unique

Highly collinear


Other Multivariate Methods Exploratory Factor Analysis – empirically reduces number of correlated variables into fewer, less correlated factors Multilevel Models (Hierarchical Models) – account for nesting and allow researchers to simultaneously consider variables measured at different levels of analysis

Structural Equation Models Traditional Statistical Approaches Structural Equation Modeling (SEM) Highly inflexible default models No default model and few limitations on what

types of relations can be specified between variables. Thus, highly flexible.

Only observed (measured) variables Both observed (measured) and unobserved (latent) variables

Assume measurement occurs without error Specifies measurement error Vulnerabile to multicollinearity Resolves problems of multicollinearity by

specifying latent constructs Straightforward tests of model significance (p-value)

No straightforward tests to determine model fit. Instead, relies on multiple indicators (e.g., chi-square, CFI, RMSEA, etc.).


SEM Example Research Question: What is the association between deep processing, isolated factual knowledge, and course achievement? (from Schreiber et al., 2006) Logic Model – Perhaps we have theory- and research-based reasons for thinking that isolated factual knowledge has both a direct and indirect associations with course achievement.

How would test this? First, we need to measure deep processing and isolated knowledge. This is hard… Confirmatory Factor Analysis (measurement model) – Tests pattern of observed variables (e.g., compare for latent constructs (e.g., deep processing, isolated knowledge) models of relations between latent variables and measured variables


Second, after accounting for measurement error, we can test our structural model. Structural Model – Tests models of relations between latent variables and measured variables.

Other SEM-based Models Path Analysis – Tests models and relations among measured variables. Involves highly restrictive assumptions about measurement without error, no intercorrelation between error terms, and unidirectional flow among variables (i.e., no feedback loops). Latent growth curve models – estimate initial level (intercept), rate of change (slope), structual slopes, and variance.

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