Notes on Quantitative Research

Research involves an investment and enables you to develop new knowledge and understanding (Higher Education Funding Council for England, 1999).
What is RESEARCH?
- (The transcript poses the question, establishing the context for definitions that follow.)

It is a systematic process of obtaining information about the world using numerical data and applying statistical treatment to support or refute alternate knowledge claims (Creswell, 2003).

Focus: collection of data so that information can be quantified and subjected to statistical analysis to support or refute knowledge claims.
Purpose: to provide evidence that can corroborate or challenge existing or alternative knowledge claims.

Quantitative research design is the most reliable and valid way of drawing conclusions, allowing new hypotheses to be formed or existing ones to be disproved.
Larger sample sizes from a population lead to more reliable and valid generalizations.

Quantitative research can be costly, difficult and time-consuming because many researchers are not mathematicians.

The following are major categories used to classify quantitative research designs and approaches.

Allows researchers to identify cause-and-effect relationships between variables.
Can distinguish placebo effects from treatment effects.

Pre-experimental designs have the least internal validity.
Example: single-group, pre-test–post-test design — measures the group two times, before and after the intervention.

In quasi-experimental designs, researchers can collect more data by scheduling additional observations or by using more existing measures.
Quasi-experiments are often used to evaluate social programs.

A true experimental design controls for both time-related and group-related threats to validity.
Two defining features: two or more differently treated groups and random assignment to these groups.
These features require control over the experimental treatment and the power to place subjects in groups.

Main purpose: observe, describe and document aspects of a situation as it naturally occurs.
Sometimes serves as a starting point for hypothesis generation or theory development.

A non-experimental design used when the researcher intends to provide a quantitative description of trends, attitudes, or opinions of a population by studying a sample of that population (Creswell, 2003).
Descriptive survey aims to describe behaviors and gather people’s perceptions, opinions, attitudes, and beliefs about a current issue in education.
These descriptions are summarized by reporting the number or percentage of persons reporting each response.
The survey is the primary method used to gather such data.

Descriptive survey research aims to describe behaviors and gather people’s perceptions, opinions, attitudes, and beliefs about a current issue in education. These descriptions are then summarized by reporting the number or percentage of persons reporting each response.
The survey is the primary method used to gather such data or information from people.

Correlational research is a quantitative method designed to show the relationships between two or more variables.
It consists of only one group of individuals (e.g., fifth-grade students) and two or more variables that are not manipulated or controlled by the researcher (e.g., reading scores and IQ).

Obtain scores from two variables for each subject, then use them to calculate a correlation coefficient.
The term bivariate implies that the two variables are correlated (variables are selected because they are believed to be related).
Example: Children of wealthier (var 1), better educated (var 2) parents earn higher salaries as adults.

Use correlation coefficient to show how one variable (the predictor variable) predicts another (the criterion variable).
Example: Which high school applicants should be admitted to college?

Prediction studies: All of these variables can contribute to the overall prediction in an equation that adds together the predictive power of each identified variable.
Formula (typical representation):
$\hat{Y} = \beta0 + \beta1 X1 + \cdots + \betap X_p + \varepsilon$
Note: The transcript describes a equation that adds together the predictive power of each identified variable.

Nonexperimental designs used to investigate causal relationships.
They examine whether one or more pre-existing conditions could have caused subsequent differences in groups of subjects.
Researchers attempt to discover whether differences between groups result in observed differences in the independent variables.
Example: What is the effect of home schooling on the social skills of adolescents?

Involves comparing and contrasting two or more samples of study objects on one or more variables, often at a single point in time.
Specifically used to compare two distinct groups based on attributes such as knowledge level, perceptions, attitudes, physical or psychological symptoms.
Example: A comparative study on the health problems among rural and urban older people from Cebu.

Seeks to address or judge in some way by providing information about something beyond what might be gleaned from mere observation or investigation of relationships.
Example: A test of children in school is used to assess the effectiveness of teaching or the deployment of a curriculum.

In this approach, the implementation of a variety of methodologies is a critical part of achieving the goal of developing a scale-matched approach.
Data from different disciplines can be integrated to enhance understanding.

Links to foundational principles:
- Measurement and quantification as the basis for statistical analysis.
- Internal validity (especially in true vs. quasi- and pre-experimental designs).
- Generalizability of findings with larger samples.
Real-world relevance:
- Experimental vs. non-experimental designs inform program evaluation and policy decisions (e.g., evaluating social programs, curriculum effectiveness).
- Descriptive surveys provide snapshot-style data about populations.
- Correlational and predictive studies inform expectations and planning, though causality must be inferred with caution in non-experimental designs.
Ethical and practical implications:
- Random assignment and control improve causal inference but may be difficult or unethical in some contexts.
- Non-experimental designs can describe and predict but cannot definitively establish causation.
- Costs and expertise requirements can influence study feasibility and validity.

Reading scores and IQ as variables in correlational research (single-group example).
Wealthier and better-educated parents predicting higher adult salaries (bivariate example).
High school GPA as part of predicting college GPA, with additional predictors contributing to a combined predictive equation.
Home schooling and social skills as an Ex-Post Facto example.
Rural vs. urban health problems among older people in Cebu as a comparative example.
Teaching effectiveness or curriculum deployment as the focus of evaluative research.

Correlation coefficient (two variables X and Y):
$r = \frac{N\sum XY - (\sum X)(\sum Y)}{\sqrt{[N\sum X^2 - (\sum X)^2][N\sum Y^2 - (\sum Y)^2]}}$
Multiple regression (prediction of Y from multiple predictors):
$\hat{Y} = \beta0 + \beta1 X1 + \cdots + \betap X_p + \varepsilon$