What is a longitudinal design?

• A longitudinal design measures the same people repeatedly over time
• Focus is on timing, not just group comparison
• Key idea: tracking change or prediction across time
• Can be experimental or non-experimental
  • Non-experimental (surveys, cohorts) are more common
• Used to understand
  • How behaviour or psychology changes
  • How earlier variables predict later outcomes

Longitudinal vs cross-sectional

• Cross-sectional
  • Different people measured once
  • Faster and cheaper
  • Cannot track true change
  • Vulnerable to cohort effects
• Longitudinal
  • Same people measured multiple times
  • Slower and more expensive
  • Can track real change and temporal order
• Cross-sequential
  • Combines both approaches
  • Multiple age groups followed for shorter periods

Key longitudinal terms

• Cohort
  • A group of people with shared characteristics
  • Example: all first-year psych students in 2022
• Waves
  • The different time points of measurement
• Pre–post design
  • Simplest longitudinal design
  • One group measured before and after something

Two types of longitudinal questions

Change over time

• Question type
  • Does something change over time?
• Same variable measured repeatedly
• Independent variable
  • Time
• Dependent variable
  • The construct of interest (e.g. anxiety, happiness, symptoms)
• Examples
  • Does anxiety change before and after public speaking?
  • Does academic self-efficacy change across a semester?
• Appropriate analyses
  • Numeric DV: paired t-test (two time points)
  • Categorical DV: McNemar’s test (two time points)
  • More than two time points: advanced models (later years)

Predicting over time

• Question type
  • Does something measured earlier predict something later?
• Different variables measured at different times
• Independent variable
  • Predictor measured at Time 1
• Dependent variable
  • Outcome measured at Time 2
• Examples
  • Does childhood self-esteem predict adult happiness?
  • Do early personality traits predict later health?
• Important reminder
  • Prediction ≠ causation
• Appropriate analyses
  • Numeric variables: correlation
  • Categorical variables: chi-square test of independence
  • Advanced models may control for confounds

Experimental longitudinal designs

• Often randomised controlled trials (RCTs)
• Participants randomly assigned to conditions
• Outcome measured later in time
• Examples
  • Therapy effects measured one year later
  • Study-skills intervention measured at graduation
• Stronger support for causal conclusions

Change over time with numeric data

• Same numeric variable measured at two time points
• Analysis
  • Paired t-test
• Null hypothesis
  • Mean difference = 0
• Key assumption
  • Difference scores are approximately normally distributed
• Effect size
  • Cohen’s d = mean difference / SD of differences
• Interpretation
  • Significant result → evidence of change over time
  • Non-significant result → no evidence of change

Change over time with categorical data

• Same categorical variable measured twice
• Data are dependent (same people)
• Chi-square test of independence is NOT appropriate
• Correct analysis
  • McNemar’s test
• Focus
  • Whether the proportion before equals the proportion after
• Only the off-diagonal cells matter (people who changed)

McNemar’s test

• Used when
  • Two dependent categorical variables
  • Binary outcomes (yes/no)
• Hypotheses
  • H0: proportion before = proportion after
  • H1: proportions differ
• Test statistic
  • Based on people who changed categories
• Interpretation
  • Significant result → proportions changed over time
• Effect size
  • Can use Cohen’s W
  • Small effects are common, even if significant

Predicting over time with numeric data

• Use correlation
• Looks at whether higher scores at Time 1 relate to higher or lower scores at Time 2
• Important
  • Focus on patterns across time
  • Directionality is clearer than cross-sectional data
  • Still not proof of causation

Predicting over time with categorical data

• Use chi-square test of independence
• Variables are measured at different times but are independent
• Example
  • Early exposure (yes/no) predicting later outcome (yes/no)

Longitudinal design considerations

• Cohort effects
  • Differences may reflect generation, not development
• Test–retest effects
  • Improvement may be due to familiarity, not real change
• Attrition (drop-out)
  • Common in long studies
  • Check whether drop-outs differ from retained participants
• Time and resources
  • Longitudinal research is expensive and slow
• Retrospective data
  • Asking people to recall past experiences
  • Easier, but vulnerable to recall bias

Choosing the correct test in longitudinal designs

• Same people, numeric outcome, two time points
  • Paired t-test
• Same people, categorical outcome, two time points
  • McNemar’s test
• Different variables over time, numeric
  • Correlation
• Different variables over time, categorical
  • Chi-square test of independence

So Overall…

• Longitudinal designs track people over time
• Two main question types
  • Change over time
  • Predicting over time
• The design determines the analysis
• Dependent data require different tests than independent data
• Longitudinal research helps clarify temporal order, but not always causation
• Always match your conclusions to your method