Research designs and statistical interpretation
Introduced| English |
|---|
| random assignment/ˈrændəm əˈsaɪnmənt/ |
| interaction effect/ˌɪntəˈrækʃn ɪˈfekt/ |
A decision before an answer
- Random assignment and random sampling sound alike but licence completely different conclusions.
- Your goal: Classify designs by assignment and measurement structure.
Classify the design
- A true experiment manipulates an independent variable with random assignment of participants to conditions; between-subjects designs give different people to each condition, within-subjects designs measure the same people in every condition and need counterbalancing. A quasi-experiment lacks full assignment, and a correlational study does not manipulate an independent variable. Correlation alone does not establish causation or temporal order.
- Random assignment supports internal validity (causal inference); random sampling supports external validity (generalisability). They answer different questions.
Each participant learns a list using exactly one of three rehearsal strategies. The design is:
Different participants serve in each condition, with the strategy manipulated between them.
Match the test
- Match analysis to design, measurement scale and assumptions. Two independent quantitative groups may suit an independent-samples t-test; paired data require a paired analysis.
- Factorial designs often use analysis of variance; categorical counts may suit a chi-square test when expected-count assumptions hold. Correlation or regression examines specified associations; neither alone establishes causation.
Counts of students choosing each of three majors, broken down by gender, are best analysed with:
The data are categorical counts in a 2×3 table, df=(2−1)(3−1)=2.
Read the effects
- A main effect averages one factor across the other factor. An interaction means one effect depends on the other factor.
- Nonparallel sample means suggest an interaction pattern, but variability and the design are needed for population inference. Interactions can exist when averaged main effects cancel; lack of significance is not proof of no effect.
Fictional mean scores are: task A, novices 4 and experts 8; task B, novices 8 and experts 4. Compute marginal means and describe the pattern. Novice marginal mean=(4+8)/2=6; expert marginal mean=(8+4)/2=6. Task A marginal mean=(4+8)/2=6; task B marginal mean=(8+4)/2=6. The task contrast reverses by expertise, an interaction pattern despite equal marginal means. Means alone do not establish a population interaction; variability, design and inference are needed.
A 2×3 contingency table has ____ degrees of freedom.
(rows−1)(columns−1)=(2−1)(3−1)=2.
Weigh the evidence
- Mean age 26 with most students 25 or younger is compatible with right skew, but does not uniquely determine distribution shape. Statistical significance is not effect size.
- A p-value is a probability of results at least as extreme under the specified null model and assumptions, not the probability the null is true. Type I and Type II errors depend on design and decision thresholds.
Drawing a causal conclusion from a correlational design, or reporting a significant interaction as if it were a main effect of one factor.
Which answer fits this case?
Classify designs by assignment and measurement structure
Random sampling from a population is what licenses a causal conclusion.
Random assignment licenses causal inference; random sampling supports generalisability.
Keep the distinctions
- interaction effect 交互作用 — The dependence of one factor's effect on the level of another factor.
- random assignment 随机分配 — Allocating participants to conditions by chance to support causal inference.
- Classify designs by assignment and measurement structure.
- Choose the statistical test that matches design and data type.
- Interpret main effects, interactions and distributional evidence.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.