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.