Psychological Statistics Notes

Module 5: Standardizing Variables

Attendance Check

  • Enter attendance # for Quiz 4/15: 3

iClicker Session

  • Testing out iClicker functionality with options: A. Present B. Present

Outline of Module 5

  1. Standardized Mean Difference Effect Size
  2. Standardized Scales in Psychology
  3. Z-Scores
  4. Study Questions
  5. Jamovi and RStudio Analyses

Standardized Scores

  • Physical variables like age, height, weight have clear metrics.
  • Psychological variables often default to sum scores without inherent metrics.
  • Standard scores (e.g., z-scores, T-scores) facilitate easier interpretation of psychological data.

Common Standard Tests

IQ Tests
  • Mean: 100, Standard Deviation: 15
  • Standardized Scale: IQ Standard Score with +1 SD, +2 SD, +3 SD representing 115, 130, and 145 respectively.
GRE Subtests
  • Mean: 150, Standard Deviation: 9
Personality Inventories (MMPI & NEO)
  • Use T-scores: Mean = 50, SD = 10

T-Scores Explained

  • T-scores indicate the score's relative position in a distribution:
    • Example: Is T above or below 50?
    • Provides a clearer comparison across different personality traits.

T-Scores vs. Z-Scores

  • T-scores set mean to 50 and SD to 10.
  • Z-scores set mean to 0 and SD to 1. The transformation allows for comparisons with unknown population parameters.

CES-D Depression Scale

  • 20-item self-report questionnaire measures depressive symptoms.
  • Scoring scale: 0 (Rarely) to 3 (Most/all the time).
  • Example questions cover various aspects of depression like appetite, sleep, and feelings of worthlessness.

Z-Score Formula

  • Captures the raw score’s deviation from the mean.
  • Formula: z = \frac{X - \mu}{\sigma} where:
    • X = raw score
    • \mu = mean of the distribution
    • \sigma = standard deviation

Rule of Thumb for Normal Data

  • In a normal distribution, 95% of scores fall within ±2 SD from the mean, critical for determining margins of error and statistical significance.

Standardized Mean Difference (Cohen's d)

  • Indicates effect size by comparing means of two groups in standard deviation units:
    • Use: d = \frac{M1 - M2}{s_{p}}
    • Where M1, M2 are the means of the two groups and s_{p} is the pooled standard deviation.

Effect Size Guidelines (Cohen's d)

  • Negligible: |d| < 0.20
  • Small: 0.20 ≤ |d| < 0.50
  • Moderate: 0.50 ≤ |d| < 0.80
  • Large: |d| ≥ 0.80

Data Analysis Using Jamovi and RStudio

  • R packages like ggplot2 and psych are utilized for visualizing and analyzing data such as CES-D scores across groups.
  • Example analysis shows differences in CES-D scores for malignant vs non-malignant diagnoses—with an example output indicating a standardized mean difference of 0.45, a small effect size.

Study Questions

  1. Convert a T score of 75 (mean 50, sd 10) to a z-score.
  2. Analyze the implications of a z-score of -2 from a Beck score baseline.
  3. Calculate and interpret effect size for a treatment impacting anxiety.
  4. Reflect upon the magnitude of a change in pain scores from a new pain management program with a standardized mean difference of 0.25.