Representative sampling, statistical-test selection and sociometric mapping of classroom relationships.
Three Core Concepts
Concept 01
Probability vs. Non-Probability Sampling
Core principle/rule: Sampling reduces bias in educational studies. A sample is strictly representative only when selected through probability methods, where every individual has a known, non-zero chance of selection.
Probability Sampling · Random
Simple Random: Every member has an equal chance—for example, drawing lots.
Stratified Random: Divide the population into strata by a characteristic such as gender or grade, then randomly sample within each subgroup.
Cluster Sampling: Randomly select intact groups—whole classrooms or schools—rather than individual students.
Non-Probability · Non-Random
Purposive / Judgmental: Researcher handpicks subjects for expertise or relevance.
Snowball Sampling: Existing subjects recruit others among acquaintances; useful for hard-to-reach groups such as high-school dropouts.
Quota Sampling: Researcher fills predetermined subgroup quotas by convenience, without random selection.
Concept 02
Parametric vs. Non-Parametric Tests
Core principle/rule: The choice of statistical test depends strictly on the shape of the data distribution and its NOIR measurement scale.
Parametric Tests
Mathematically powerful; make strict assumptions about population parameters. Data must follow a Normal Distribution and use Interval or Ratio scales.
t-test: comparing means of two groups
ANOVA: comparing means of three or more groups
Pearson correlation
Non-Parametric Tests
“Distribution-free”; make no normality assumption. Used for heavily skewed data or Nominal or Ordinal scales.
Chi-Square: nominal frequency data
Mann–Whitney U: non-parametric alternative to t-test
Spearman Rank correlation: ordinal rankings
Concept 03 · Jacob Moreno
Sociometry
Core principle/rule: Sociometry is a highly specific quantitative method developed by Jacob L. Moreno to measure social dynamics, interpersonal relationships and peer acceptance within a defined group such as a classroom.
Key facts
Mechanism: Ask students questions such as “Who are your three best friends in this class?” or “Who would you most like to work with on a project?”
Sociogram: Plot the data as a visual map using nodes and arrows to show the network of choices and rejections.
StarReceives disproportionately many positive choices; highly popular.
IsolateNeither chosen nor rejected; simply flies under the radar.
RejecteeExplicitly receives negative choices or peer rejections.
CliqueClosed subgroup of three or more members who mutually choose one another and exclude outsiders.