Module 1 – Introduction to Statistics (Psychological Statistics)

Module Context

  • Module 1: Introduction to Statistics (Psychological Statistics / PSYSTAT)
  • Delivery mode: Synchronous; 5 hrs-week, scheduled for one week.
  • Instructor: Mrs. Gina T. Montalla – College of Arts & Sciences, San Mateo Municipal College.
  • Timeline: Initiated July 14 2025, completed July 19 2025.

Learning Objectives

  • Enumerate the four philosophical/scientific methods of studying truth.
  • Define & contrast key pairs:
    • Observational vs Experimental research
    • Descriptive vs Inferential statistics
  • Define foundational terms: population, sample, variable, statistic, parameter.
  • Explain the importance of random sampling.
  • Differentiate the four measurement scales: nominal, ordinal, interval, ratio.
  • Differentiate & exemplify continuous vs discrete variables.

Statistics, Science & Observation

  • Psychological statistics = application of mathematical formulas, theorems, numbers & laws to psychological data.
  • Provides tools for modelling the science of mind & behavior; aids in discovering what is typical or normal for a group.
  • Visual displays (graphs, pie charts, frequency distributions, scatterplots) help spot patterns otherwise missed.
  • General purposes:
    • Organize & summarize information so researchers “see what happened.”
    • Provide a basis for justified conclusions.

Core Definitions

  • Statistics (discipline): body of methods for collecting, organising, presenting, analysing & interpreting data.
  • Statistics (data): facts/figures such as average income, crime rate, birth rate, etc.
  • Four functional stages:
    • Collection – gathering information.
    • Organisation/Presentation – textual, tabular, graphical summarising.
    • Analysis – application of statistical techniques.
    • Interpretation – drawing conclusions.

Population & Sample

  • Population (N): totality of elements/individuals of interest.
  • Sample (n): subset chosen to represent the population.
  • Relationship: sample is studied ➔ inference about population.

Parameter vs Statistic

  • Parameter: numerical/nominal characteristic of a population (usually unknown, fixed). Example: population mean \mu.
  • Statistic: numerical characteristic computed from a sample; estimator of the parameter. Example: sample mean \bar{x}.

Variables & Data

  • Variable: attribute with varying values across individuals (age, gender, temperature).
  • Data/Datum: measurements or observations on variables.

Variable Classifications

  • Discrete: separate, indivisible categories; no values between. Ex: number of students, gender.
  • Continuous: infinite possible values between any two points; divisible into fractional parts. Ex: height, weight, time.

Data Classifications

  • Metric (Measurement) Data – obtained via measuring; yields numbers on a scale (height, scores).
  • Enumeration (Count) Data – obtained by counting; yields whole numbers (number of households).
  • Categorical (Qualitative) Data – grouped by categories/qualities (attitudes, SES).

Scales of Measurement

  • Nominal
    • Labels only; mutually exclusive categories; no quantitative value.
    • Examples: religion, civil status, nationality.
  • Ordinal
    • Rank order; intervals undefined.
    • Examples: class standing, clothing sizes (S/M/L), Likert-type positions if treated strictly.
  • Interval
    • Ordered, equal intervals, arbitrary zero.
    • Can speak of how much more but not meaningful ratios.
    • Examples: IQ scores, °C/°F temperature, standardised test scores.
  • Ratio
    • Ordered, equal intervals, absolute (true) zero; allows ratios (“twice as heavy”).
    • Examples: age, height, weight, reaction time.

Choosing a scale:

  • Fit must match variable nature & desired precision.
  • When several scales fit, prefer the highest level – affords richer info & more powerful statistical tests.

Descriptive vs Inferential Statistics

  • Descriptive: techniques that summarise/organise raw scores (tables, graphs, mean, SD).
  • Inferential: techniques that use sample data to make generalisations/decisions about populations (hypothesis tests, confidence intervals).

Error Concepts

  • Sampling Error: natural, random discrepancy between a sample statistic and its corresponding population parameter; size unknown, bounded by margin of error in random sampling.
  • Non-Sampling Error: errors from data-collection process other than sampling itself (selection bias, questionnaire wording, recording mistakes, non-response). Potentially introduces systematic bias.

Sampling & Sample-Selection Techniques

  • Sampling = process of selecting a sample.
  • Sampling Technique = specific procedure for choosing sample members.

Probability Sampling (each element has known, non-zero chance)

  1. Simple Random Sampling (SRS)
    • Every element has equal chance; requires complete population list.
    • Tools: lotteries, random-digit tables, RNG.
  2. Systematic Sampling
    • Select every k^{th} element where k = \frac{N}{n}; start point random.
  3. Stratified Sampling
    • Divide population into homogeneous strata; perform SRS within each.
    • Allocation options: Equal vs Proportional.
  4. Cluster Sampling
    • Population split into heterogeneous clusters (often geographically); randomly select clusters & study all elements within chosen clusters.
  5. Multi-Stage Sampling
    • Combine stages (e.g., pick clusters, then households within clusters) until final units obtained.

Uses/Advantages of Probability Sampling

  • Minimises selection bias; supports valid generalisation & error estimation.
  • Ensures diversity & representativeness, especially in large/heterogeneous populations.

Non-Probability Sampling (chance of selection not equal/known)

  1. Convenience Sampling – sample units easiest to access (mall intercepts).
  2. Purposive/Judgemental Sampling – researcher selects units possessing specific characteristics (e.g., master’s-degree aspirants).
  3. Snowball Sampling – existing subjects recruit future subjects; useful for hidden or hard-to-reach populations (e.g., undocumented migrants, HIV patients).
  4. Quota Sampling – researcher sets target quotas for categories & samples until quotas filled (mimics stratification but without random selection).

Uses/Advantages of Non-Probability Sampling

  • Exploratory or pilot work where speed, cost, or limited frames matter.
  • Hypothesis generation when no prior info exists.
  • Acceptable under tight budget/time or where random access impossible.

Limitations

  • Potentially large bias; weak generalisability; absence of calculable sampling error.

Slovin’s Formula & Sample-Size Determination

  • Formula: n = \frac{N}{1 + N\alpha^{2}} where
    • n = required sample size
    • N = population size
    • \alpha = permissible error (level of significance)
  • Illustrative problem (given): N = 5000, \; \alpha = 0.05\; \Rightarrow\; n = 370.
  • Same method applied for varying populations (2 000; 10 000; 8 000) and different error tolerances (10 %, 7.5 %, 5 %, 2.5 %, 1 %).
  • Smallest possible sample is that which still yields acceptable error.

Learning Activities (Google Form)

  • Classify data as discrete/continuous.
  • Classify data as metric/enumeration/categorical.
  • Identify scales of measurement (nominal, ordinal, interval, ratio).
  • Decide if situations require descriptive or inferential procedures.
  • Compute sample sizes using Slovin’s formula for various scenarios.

Assignment Preview – Presentation of Data

  • Define & differentiate frequency distribution tables:
    • Simple Frequency
    • Complete Frequency
    • Relative Frequency
    • Cumulative Frequency
    • Cumulative Percentage
  • Illustrate graphs:
    • Bar Chart
    • Histogram
    • Frequency Polygon
    • Pie Chart
    • Ogive (cumulative frequency curve)

Ethical, Practical & Philosophical Notes

  • Random selection underpins unbiased inference; ethical obligation to represent population faithfully.
  • Non-sampling errors (question wording, low response) can invalidate findings despite perfect randomisation.
  • Choice of measurement scale affects both ethical clarity (do labels mislead?) and analytic power.

Connections & Real-World Relevance

  • Psychological researchers rely on stats to interpret test scores, treatment effects, or prevalence of behaviors.
  • Sampling methods replicate in market research, public-health studies, political polling.
  • Data-visualisation skills transfer to reporting insights for stakeholders.

References & Further Reading

  • Ferguson & Takane (1989) Statistical Analysis in Psychology and Education – foundational text on educational stats.
  • Gravetter & Wallnau (2012) Statistics for the Behavioral Sciences – widely used psychology stats guide.
  • Montero–Galliguez et al. (2016) Fundamentals of Statistical Analysis – local Philippine perspective.
  • Online: video resources on Prim’s algorithm, cryptocurrency, banking loans, stock-vs-bond differences.