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Descriptive Statistics & Research Methods – Lecture 1 Vocabulary

Introduction & Rationale for Statistics in Psychology

  • Lecturer: Dr William Coventry (first of two statistics lectures in PSYC 01/2002)

  • Core message

    • Psychology prides itself on being a “hard science” because of its rigorous statistical methodology.

    • Mastery of statistics is indispensable for honours projects, theses, and any research career.

    • Although stats may feel intimidating, psychological statistics are usually “not too mathematical.”

  • Practical advice

    • “Own it and get on top of it.” Early competence pays dividends later.

    • Textbook study is still required; lecture covers only selected chapters.

Lecture Roadmap (Descriptive Statistics Only)

  • Distinction: Descriptive vs Inferential Statistics (inferential to be covered next lecture)

  • Topics today

    1. Quantitative vs Qualitative methods

    2. Experimental research design basics

    3. Statistical tools: t-tests and correlations

    4. Fundamental descriptive measures (central tendency, variability, graphs, effect sizes)

Quantitative vs Qualitative Methods

  • Quantitative

    • Numerical data, statistical analysis

    • Primary focus in undergraduate psychology; unique among many social-science disciplines

  • Qualitative

    • Narrative, thematic, non-numerical

    • Valuable but less emphasised in core psych stats units

  • Real-world note: Multidisciplinary labs often hire psych graduates for their superior statistical training.

Experimental Research Design (Randomised Controlled Trials)

  • Purpose: Establish cause → effect

  • Structure

    • Multiple conditions: ≥1 experimental vs ≥1 control group

    • Random assignment to minimise pre-existing group differences

    • Manipulation applied only to experimental group

    • Pre- and post-testing of dependent variables

  • Terminology

    • Independent Variable (IV) = manipulated or grouping factor

    • Dependent Variable (DV) = outcome that “depends on” IV

  • Ethical / practical note: Sometimes RCTs are impossible (e.g., withholding a life-saving drug); alternatives include observational or correlational designs.

Independent vs Dependent Variables (Metaphor)

  • Fertiliser & Plants example

    • IV: Application of fertiliser (yes/no)

    • DV: Plant growth (height, biomass)

    • DV value “depends on” the IV manipulation

Example Study: “IQ Is a Muscle” Intervention

  • Research Question: Does telling children that intelligence is malleable improve mathematics performance?

  • Groups

    • Experimental: Received sessions framing IQ as a “muscle that gets stronger with use.”

    • Control: Received sessions on memory/academic topics (equal contact time; no growth-mindset content).

  • DV: Math grades (continuous)

  • IV: Group membership (categorical: experimental vs control)

  • Result (single-time-point view)

    • Experimental group’s mean math score > Control’s mean math score

    • “Nothing more to it”—illustrates simplest use of t-test

Importance of Multiple Time-Points & Baseline Equivalence

  • Actual study recorded 3 time points (pre-intervention, immediate post, later post)

    • Baseline showed near-equal math scores (though experimental slightly higher—weakens causal claim slightly)

    • Post-intervention divergence supports effect of manipulation

  • Take-home: Pre-test measures allow stronger inference of causality.

  • Additional follow-up (Time 4) would reveal whether effects persist.

Variable Types & Their Statistical Consequences

  • Categorical (Discrete) Variables

    • Distinct groups/levels (e.g., male/female/non-binary; pass/fail/credit/distinction/HD)

    • For t-tests, ideal when variable has exactly 2 levels

  • Continuous Variables

    • Numeric continuum (e.g., 0!\text{–}!100 exam mark, height in cm)

  • Golden rule for beginners

    • Two continuous vars → Correlation

    • One categorical (2-level) + one continuous → t-test

Statistical Tool 1: t-Tests

  • Purpose: Test whether the means of two independent groups differ

  • Inputs

    • IV: Categorical (2 groups)

    • DV: Continuous

  • Calculation considers

    1. Difference of group means (\bar X1 - \bar X2)

    2. Spread around those means (pooled variance s^2_p)

    3. Formula (simplified): t = \dfrac{\bar X1 - \bar X2}{SE} where SE = standard error

  • Interpretation

    • Larger mean gap + smaller within-group variance ⇒ larger |t| (more “impressive”)

    • Visual cue: Less overlap of score distributions strengthens result

Statistical Tool 2: Correlation (r)

  • Definition: Single number summarising linear association between two continuous variables

  • Range: -1 \le r \le 1

    • r = 0 → no linear relation

    • r = +1 → perfect positive; r = -1 → perfect negative

  • Strength (|r|)

    • Rough guidelines: |r| ≈ 0.1 weak, 0.3 moderate, \ge 0.5 strong

  • Direction

    • Positive: Variables move together (↑ drinks → ↑ hangover severity)

    • Negative: Variables move opposite (↑ drinks → ↓ driving ability)

  • Each scatter-plot dot = one participant (paired scores on X & Y axes)

  • Effect size role: Correlation itself is an effect-size metric.

Worked Examples for Correlation

  1. Drinks vs Hangover Severity

    • Positive correlation; more drinks, worse hangover.

  2. Drinks vs Driving Skill

    • Negative correlation; more drinks, poorer driving.

  3. Vitamin D vs COVID-19 Severity

    • Hypothesis predicted negative correlation (high vitamin D → mild COVID).

    • Empirical finding: r \approx -0.06 (statistically tiny, “miserable”).

    • RCT meta-analysis likewise shows no meaningful protective effect of vitamin D supplementation.

Descriptive Statistics: The Big Picture

  • Aim: Summarise data before any inferential claims

  • Core measures

    • Central tendency: Mean, median, mode

    • Variability: Range, variance (s^2), standard deviation (s)

    • Effect sizes: Correlation (r), Cohen’s d, etc.

    • Graphs: Histograms, scatter-plots, box-plots

  • Philosophical note

    • Over-complex statistics can obscure insights; clear graphics often suffice (Gerd Gigerenzer).

    • Psychology remains a “hard science” even when using simple descriptive visuals.

Ethical & Philosophical Implications Discussed

  • RCT feasibility & ethics (e.g., denying a potentially life-saving treatment is unethical; parallels with smoking & lung cancer research)

  • Proper use of p-values; misuse leads to misunderstandings—topic for next lecture

  • Encouragement to balance statistical sophistication with transparent data storytelling

Connections to Future Content

  • Next lecture = Inferential Statistics (p-values, significance tests, deeper use of t-tests & correlations)

  • Understanding today’s foundations makes later concepts (e.g., ANOVA, regression) much easier.

Key Takeaways & Study Tips

  • Master t-tests & correlations first; they are “everywhere” in psychological science.

  • Always identify variable type (categorical vs continuous) before choosing a test.

  • Use multiple pre/post measurements to bolster causal inference in experiments.

  • Remember that effect size and practical significance matter as much as (or more than) p-values.

  • Reinforce learning via external tutorials and practise interpreting scatter-plots & group means.

Quick Formula Reference

  • t-test (independent): t = \dfrac{\bar X1 - \bar X2}{\sqrt{\dfrac{s1^2}{n1} + \dfrac{s2^2}{n2}}}

  • Pearson correlation: r = \dfrac{\sum (Xi - \bar X)(Yi - \bar Y)}{\sqrt{\sum (Xi - \bar X)^2 \; \sum (Yi - \bar Y)^2}}

Closing Remarks

  • Descriptive stats are the foundation; inferential stats build on them.

  • Upcoming session will “trample” misconceptions about p-values and significance.

  • Until then, focus on understanding basic group comparisons, variable types, and interpreting scatter-plots.