Notes on Measurement Scales and Experimental Design

Measurement Scales and Statistical Reasoning

  • Data scales and how they shape analysis

    • Nominal data
    • Categories without intrinsic order
    • Examples: group labels, types of interventions, yes/no responses
    • Ordinal data
    • Ranks or ordered categories; the order matters but intervals are not guaranteed equal
    • Example from transcript: star ratings (e.g., excellent, good, fair, poor)
    • Key caution: do not assume equal spacing or treat as actual numeric values; averaging ordinal labels is inappropriate
    • Transcript note: assigning numbers like 4, 3, 2 to ordinal categories does not imply equal intervals or true numeric meaning
    • Interval data
    • Clearly defined, equal gaps between adjacent scores; but no true zero
    • Classic example: temperature scales (Celsius/Fahrenheit)
    • Equal meaning of each interval, but lack of a true zero complicates ratio interpretation
    • Ratio data
    • Interval data with a true zero point; allow meaningful ratios
    • Examples: weight, height, amount of weight loss
    • Transcript example: saying one person lost twice as much weight as another implies a ratio interpretation when a true zero exists
    • Practical takeaway
    • The scale determines what kinds of statistical analyses are appropriate
    • Ordinal data should not be averaged; interval/ratio data allow a wider set of arithmetic/statistical operations

  • Independent and dependent variables in research

    • Independent variable (IV)
    • The variable that is manipulated or used to define groups
    • Levels = distinct groupings or conditions under the IV
    • The example: gender as an IV with levels (e.g., male, female, non-binary/other)
    • Another example: time of class as an IV with levels (e.g., 10AM, 11AM)
    • Important distinction: the IV is the high-level concept; levels are the concrete groups within that concept
    • Dependent variable (DV)
    • The outcome or measurement collected to assess the effect of the IVs
    • Examples from transcript: GPA, first-exam score, weight loss, pain level, quality of life, activity/mobility

  • Designing with one or more independent variables

    • Single IV with multiple levels
    • Example: time of class with two levels (10AM and 11AM)
    • DV: exam score or GPA
    • Multiple IVs (factorial designs)
    • Example: IV1 = gender, IV2 = time of class
    • Allows exploration of interaction effects: whether the effect of one IV depends on the level of another IV
    • If more IVs are added, graphing becomes more complex; you may need to examine interactions (e.g., gender × time of class)
    • Levels vs IV terminology
    • IV = overarching factor (e.g., “time of class”)
    • Levels = actual groupings (e.g., 10AM, 11AM)
    • Repeated measures and time as an IV
    • Example: weight loss measured baseline, 2 weeks, 4 weeks, 8 weeks
    • IV = time; levels = {baseline, 2 weeks, 4 weeks, 8 weeks}
    • This allows studying change over time within subjects and between groups
    • Special case: no-diet control group
    • Could be added as a level of a diet-related IV to test whether any intervention differs from no intervention

  • Experimental design concepts and practical implications

    • Randomized Controlled Trial (RCT) vs cohort study
    • RCT: participants are randomly assigned to groups; high level of control; generally considered higher quality evidence
    • Transcript note: the discussed study is an RCT with randomization and two groups
    • Levels vs groups in RCTs
    • Treatment groups (the IV) have levels that define the different interventions
    • The outcome measures (DV) are what researchers compare across groups
    • Example from transcript (back pain study)
    • Intervention groups (two levels): 1) individualized physiotherapist-delivered intervention; 2) physiotherapist-delivered group-based exercise and medication
    • Primary outcome: pain reduction
    • Secondary outcomes: quality of life, ability to move/activity
    • Randomization: 206 participants, randomized assignment to the two groups
    • Other potential RCT design notes mentioned
    • Titles may state