Psychology 3020: Class 2 Notes - Terminology and Types of Data

Course Information and Overview

• Course Title: Psychology 3020: Statistics in Psychology
• Lecture Topic: Class 2: Terminology, Types of Data
• Term: Fall 2026
• Instructor: Dr. Donna Dueker
• Institution: California State University, Los Angeles (CSULA)
• Course Reading Schedule:
  • Date: $8/24$
  • Topic: Course Introduction and Overview; Introduction to Data
  • Assigned Readings: Chapter 1 IMS; Chapter 1 Modern Dive
  • Date: $8/26$
  • Topic: More about Data: Types of variables, relationships, sources of data
  • Assigned Readings: Chapter 1 IMS; Chapter 1 Modern Dive
• Textbook Access: Required textbooks (IMS and Modern Dive) are accessible via ATI.
• Core Learning Objectives:
  • Define statistics and key foundational concepts: data, parameter, population, and statistic.
  • Classify types of data and variables: quantitative, qualitative, categorical, and discrete.
  • Distinguish between the four levels of data measurement: nominal, ordinal, interval, and ratio.
  • Differentiate between descriptive statistics and inferential statistics.
  • Explain the methodology distinction between an observational study and an experimental study.

Fundamental Definitions of Statistics

• Definition of Statistics: A scientific and mathematical discipline dedicated to the collection, organization, descriptive analysis, interpretation, and statistical inference of numerical and categorical data.
• Applied Questions Addressed by Statistics:
  • Distance studies: How far do students at CSULA travel to campus?
  • Comparative group analysis: Is the distance traveled by CSULA students significantly different from students attending CSULB?
  • Prevalence estimation: What percentage of college students use electronic cigarettes?
  • Longitudinal trend tracking: How has the use of e-cigarettes changed over time?
  • Relational analysis: Is there a relationship between body weight and hours spent engaged in physical activity?
• Role of Statistics in Research Methodology:
  • Formulating precise research questions.
  • Defining testable hypotheses.
  • Determining appropriate sample size requirements.
  • Deciding participant selection protocols.
  • Analyzing collected data and effectively presenting empirical findings.

Branches of Statistics

• Descriptive Statistics:
  • Definition: Statistical methods used to summarize, organize, and present data features in a clear, quantitative manner without making inferences beyond the specific sample observed.
  • Examples:
  • The average (mean) weight of U.S. women aged $21\text{ to }65$.
  • The total population count of LA County and the exact proportion in each ethnic group.
  • Categorizing participant smoking status into groups: never smoker, former smoker, and current smoker.
• Inferential Statistics:
  • Definition: Statistical procedures that draw conclusions, test hypotheses, and make predictions or generalizations about a broader target population based on sample data.
  • Examples:
  • Testing whether individuals who smoke have a statistically significant higher rate of lung cancer than non-smokers.
  • Testing whether women living in LA County are on average heavier than the overall national average for women in the United States.

Core Terminology: Populations, Samples, Parameters, and Statistics

• Population:
  • Definition: The complete set of all individuals, objects, or scores of interest in a study.
  • Practical Constraint: Populations are generally too large to measure or evaluate in their entirety due to resource and time limits.
• Sample:
  • Definition: A subset of individuals or observations drawn directly from the target population.
  • Random Sample: A selection method where every member of the population has an equal chance of being included. Random selection helps ensure the sample is representative of the population.
  • Convenience Sample: A selection method based on easily accessible or readily available subjects.
• Parameter:
  • Definition: A numerical measurement that describes a specific characteristic of a population.
  • Nature: Usually unknown fixed values that researchers attempt to estimate through statistical inference.
  • Symbol Example: Population mean, denoted as $\mu$.
• Statistic:
  • Definition: A numerical measurement describing a characteristic of a sample.
  • Nature: Calculated directly from sample observations and varies across different drawn samples.
  • Symbol Example: Sample mean, denoted as $\bar{x}$.
• Interrelationship Process:
  • Sampling: The process of selecting a subset from the population.
  • Inference: The statistical process of drawing conclusions about population parameters based on sample statistics.

Practice Scenarios: Population, Sample, Parameter, and Statistic

• Allergy Prevalence Study:
  • Scenario: Of the U.S. adult population, a sample of $1200$ randomly selected adults resulted in $33.2\%$ reporting an allergy.
  • Target Population: All U.S. adults (the entire population of adults in the United States).
  • Selected Sample: The $1200$ randomly selected adults.
• Geese Study at Airport:
  • Scenario: In studying the effects of geese near an airport, a random sample of Canada geese includes $12$ males.
  • Classification: Sample Statistic (describes a subset sample of Canada geese).
• Cloned Sheep Study:
  • Scenario: In a study of all cloned sheep, it is found that their average age is $2.7\,\text{years}$.
  • Classification: Population Parameter (describes the entirety of all cloned sheep).

Data and Variable Classifications

• Data: Information obtained by measuring or observing specific properties or traits of target objects, individuals, or events.
• Variable: A characteristic or property that differs or varies from one individual or observation to the next.
• Importance of Data Types: Statistical methods can only be applied to specific data types. Using inappropriate methods yields invalid conclusions.
• Primary Data Divisions:
  • Quantitative Data:
  • Definition: Data consisting of numbers that represent actual counts or physical measurements.
  • Examples: Heights, weights, pulse rate, age, body temperatures, credit hours completed, test scores, average rainfall.
  • Qualitative Data (Categorical Data):
  • Definition: Data consisting of labels, names, or non-numeric categories that describe specific traits.
  • Trait: Typically non-numeric, but can include numerical codes (such as identification numbers) where mathematical calculations hold no value.
  • Examples: Eye color, gender, religious preference, binary Yes/No responses, hometown, favorite food, identification numbers (e.g., Social Security Number SS#, GHC#).

Quantitative Data: Discrete vs. Continuous

• Continuous Data:
  • Definition: Quantitative data resulting from infinitely many possible values on a continuous numerical scale without gaps, jumps, or interruptions.
  • Nature: Can take on any decimal or fractional value within a continuum.
  • Examples:
  • Clinical markers: pH of a sample, patient cholesterol levels.
  • Physical dimensions: Weight ($3.25\,\text{kg}$), distance ($1.32\,\text{miles}$), length ($7.25\,\text{inches}$).
  • Age timeline: Age changing continuously over time (e.g., James's age progressing smoothly from $25\,\text{years}$ to $25.3\,\text{years}$, $25.5\,\text{years}$, $25.8\,\text{years}$, and $26\,\text{years}$).
• Discrete Data:
  • Definition: Quantitative data where the number of possible values is finite or countable ($0, 1, 2, 3, \dots$).
  • Nature: Values jump in distinct steps with gaps in between permissible values.
  • Examples:
  • Biological counts: Number of bacteria colonies in a culture.
  • Discrete counts: $5\text{ kids}$, $96\text{ workers}$, $3\text{ laptops}$.

Qualitative Data: Nominal vs. Ordinal

• Nominal Data:
  • Definition: Categorical data that consist of names, labels, or categories with no natural or logical ordering scheme.
  • Characteristics: Cannot be meaningfully arranged from low to high.
  • Examples: Gender (Male, Female, Trans), blood groups (A, B, AB, O), hair color (Black, Red, Blonde, Brown).
• Ordinal Data:
  • Definition: Categorical data that can be arranged in a meaningful order or rank hierarchy.
  • Characteristics: Relative ranking exists, but exact differences between data ranks cannot be calculated or are meaningless.
  • Examples: Disease severity (mild, moderate, severe illness), house price categories (low, moderate, high).

Levels of Measurement

• Four Hierarchy Levels of Measurement:
  • Nominal Level:
  • Definition: Data consist of categories, names, or labels only.
  • Properties: No order, no mathematical operations, no natural zero point.
  • Ordinal Level:
  • Definition: Data can be arranged in relative ranks or ordered series.
  • Properties: Order exists; mathematical differences between ranks are meaningless or impossible to measure.
  • Interval Level:
  • Definition: Ordered numerical data where differences between any two values are meaningful and equal across the scale.
  • Properties: Meaningful differences; lacks a natural zero starting point (zero is arbitrary and does not signify complete absence).
  • Example: Temperature in Celsius or Fahrenheit ($0^\circ\text{C}$ does not mean "no temperature").
  • Ratio Level:
  • Definition: Interval level measurement with an additional natural zero starting point.
  • Properties: Meaningful differences; natural zero indicates complete absence of the trait; ratios between values are mathematically valid ($200\,\text{lbs}$ is twice as heavy as $100\,\text{lbs}$).
  • Examples: Weight, height, distance, income.

Practice Scenarios: Data Types and Levels of Measurement

• Scenario 1: Number of kittens in a litter
  • Classification: Quantitative Discrete Data (countable whole numbers).
• Scenario 2: Mean length of broad-billed hummingbirds ($3.25\,\text{inches}$)
  • Classification: Quantitative Continuous Data; Ratio Level of Measurement (continuous measurement with absolute zero).
• Scenario 3: Volume of milk given by a group of cows
  • Classification: Quantitative Continuous Data; Ratio Level of Measurement (continuous liquid volume).
• Scenario 4: Letter grades in a class (e.g., A, B, C, D, F)
  • Classification: Qualitative Data; Ordinal Level of Measurement (ordered rank without equal intervals).
• Scenario 5: Colors used in a plant genetics experiment
  • Classification: Qualitative Data; Nominal Level of Measurement (unranked categories).
• Scenario 6: Postal Zip codes
  • Classification: Qualitative Data; Nominal Level of Measurement (numeric codes acting as arbitrary labels).
• Scenario 7: Blood types (A, B, AB, O)
  • Classification: Qualitative Data; Nominal Level of Measurement (unranked biological categories).
• Scenario 8: Weights of pregnant women measured in pounds
  • Classification: Quantitative Continuous Data; Ratio Level of Measurement (continuous physical mass with a natural zero).
• Scenario 9: Conference attendee income gathered as upper, middle, and low levels
  • Classification: Qualitative Data; Ordinal Level of Measurement (ranked socioeconomic levels without numeric precision).

Research Methodology: Observational Studies vs. Experiments

• Observational Study:
  • Definition: A research methodology in which specific characteristics are observed and measured without any attempt to intervene, modify, or manipulate the subjects being studied.
  • Core Trait: Non-experimental, passive data gathering in natural settings.
• Experimental Study (Experiment):
  • Definition: A research methodology in which a treatment or manipulation is applied to subjects, followed by observation and measurement of the treatment effects.
  • Core Trait: Active manipulation of variables to determine cause-and-effect relationships.