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: $d = \frac{M<em>1 - M</em>2}{s_{p}}$
  • Where $M<em>1, M</em>2$ 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.