Variables and Scales of Measurement

• Statistics is a step-by-step science requiring data.
• Statistics relies on data rather than just logic.
• Definition in plural sense: a set of numerical figures.
• Examples of numerical figures: population count, vital statistics like birth/mortality rates, COVID-19 cases per province, average lifespan of Filipinos, and the percentage of Filipinos in favor of same-sex marriage.
• COPAIData: Collection and Organization, Presentation, Analysis, Interpret.

Uses of Statistics:

• Describe general characteristics of a population: Filipinos' top Valentine's Day gifts were money, love, and flowers.
• Compare different subpopulations: Filipino women outlive men by six years but have higher obesity rates.
• Explain phenomena: In 2023, 247 newborns were named Argus, based on 7 records analyzed from 2022 by PSA.
• Predict future phenomena: Males with longer index fingers are 33% more likely to develop prostate cancer.
• Correlate relationships: the divorce rate in Maine and margarine consumption have a positive correlation.
• Study cause-and-effect: Each absence from STAT 166 decreases the final grade by 6 points.
• Statistics is a useful tool in decision-making.

Basic Concepts in Statistics:

• Population: all elements under consideration in a statistical study.
• Sample: a subset of the population.
• Example of population vs sample: A study on voting behavior covering all registered Filipino voters (population) and a subset of them (sample).
• Variable: a characteristic of interest that assumes different values for different elements.
• Observation: a realized value of a variable.
• Data: a collection of observations.

Types of Variables:

• Qualitative Variables: use labels or names for categories; e.g., sex of students or support for marijuana legalization.
• Quantitative Variables: are measurable or countable; e.g., household size or cups of rice consumed per meal.

Levels of Measurement:

• Measurement: process of determining the value or label of a variable.
• Nominal (equality): numbers classify elements into distinct categories of equal importance, e.g., sex of students.
• Ordinal (greater than or less than): numbers classify elements into distinct, ranked categories, organizing them by magnitude; e.g., UP student classification.
• Interval (difference or sum): numbers classify elements into distinct categories with a fixed unit of measurement, but no true zero; e.g., daily temperature.
• Ratio (all algebraic operations): numbers classify elements into distinct categories with a fixed unit of measurement and an absolute zero; e.g., time in military hours.
• Level of measurement impacts the selection of appropriate statistical tools for data analysis.

Parameter vs. Statistic:

• Parameter: summarizes a population characteristic.
• Statistic: summarizes a sample characteristic.

Major Areas in Statistics:

• Descriptive: techniques organize, summarize and present data from a sample or population.
• Inferential: techniques analyze sample data to make generalizations about the population it came from.

The Research Process:

• A set of activities social scientists use to answer questions, examine ideas, or test theories.
• Examples of research questions: Does feminist theory on gender inequality persist in the Philippines? Why is ghosting so common to Filipinos?
• Empirical Research: based on verifiable evidence from direct experience.

Statistical Inquiry:

• Provides information (processed data) to solve a research problem.

Steps in Statistical Inquiry:

• Identify the problem and state the hypothesis.
• Plan the study.
• Collect the data.
• Explore data.
• Analyze and interpret results.
• Present results.
• Distinguishing factor is use of data that have been collected and analyzed in answering the research problem

Collecting Data:

• Methods include: Observation, Experiment, Use of documented data, Registration, and Survey.

OBSERVATION:

• Involves using senses to record behavior or phenomena in a natural setting, gathering nonverbal behavior.

EXPERIMENTATION:

• Features control and direct human intervention, isolating effects of a treatment on a variable.

USE OF DOCUMENTED DATA:

• Utilizes data from previous studies by private, government, or non-governmental agencies; e.g., PSA, BSP.

REGISTRATION:

• Enumerates and records vital statistics: birth, marriage, death, voter registration, sales inventory, etc.

SURVEY:

• Obtains data from individuals through verbal or written communication.
• Example: A coffee company interviewing shoppers about their favorite brand.
• The methods for data collection need to consider several factors such as the nature of the study, and resources, etc.

Kinds of Data Collected:

• Primary Data: acquired directly from the source.
• Secondary Data: acquired indirectly.

Methods of Conducting Surveys:

• Personal Interview: questions are asked and recorded directly on a questionnaire (PAPI - pencil and paper interview, or CAPI - computer-assisted personal interview).
• Telephone Interview: questions are asked and recorded over the phone.
• Self-administered Questionnaires: respondents complete the questionnaire themselves.
• Online Surveys: respondents submit answers via the internet or email.
• Mailed Questionnaire: questionnaires are mailed to the respondent. Focus Group Discussion: a moderator directs discussion among small groups using a guide.