Week 3 Day 1 LEC

Standardizing Psychological Variables

• Need for Standardization: In psychology, various Likert scales (e.g., depression and optimism) measure different constructs that require standardization for meaningful comparison.

• Metrics Comparison: Different psychological constructs represent different types of information; standardizing scores allows comparison between diverse constructs.

Importance of Standard Scores

• Standard Scores: To facilitate comparisons, we transform original metrics into standardized scores such as z-scores and t-scores.

• Significance of Effect Sizes: An understanding of how far scores differ from one another in standardized units leads to the calculation of effect sizes, crucial for determining group differences.

Overview of Standardized Scales

• Types of Scores:

  • z-scores: Set mean to 0 and standard deviation to 1.

  • t-scores: Commonly used with mean set to 50 and standard deviation set to 10.

• Universal Metric Example: IQ tests use a mean of 100 and a standard deviation around 15 to express rankings in cognitive ability.

Calculating z-scores

• Calculation Formula:

  • Formula: $z = \frac{X - \bar{X}}{s}$$$ z = \frac{X - \bar{X}}{s} $$ where

  • $X$: Raw score

  • $\bar{X}$: Mean

  • $s$: Standard deviation

• Example: For a population mean of 24 and a standard deviation of 12, a raw score of 30 would have a z-score of 0.5, indicating it is half a standard deviation above the mean.

Utilizing the CES Depression Scale

• Depression Scale Interpretation: The Center for Epidemiologic Studies Depression Scale (CES-D) uses a 20-item questionnaire to assess depression, summing scores from 0 to 3.

• Clinical Interpretations:

  • Low scores indicate subclinical depression while higher scores (e.g., above 29) indicate clinically elevated depression levels.

Standardized Mean Difference and Effect Size

• Standardized Mean Difference: Refers to the mean difference expressed in standardized units (z-scores) to compare group differences.

• Cohen's d: Represents the effect size, calculated as:

  • Formula: $$ d = \frac{\bar{X}1 - \bar{X}2}{s_{pooled}} $$

  • Where $s_{pooled}$$$ s_{pooled} $$ is the pooled standard deviation of both groups.

• Interpreting Cohen's d:

  • Values interpreted as:

  • Small: $d < 0.2$$$ d < 0.2 $$

  • Medium: $0.2 \leq d < 0.5$$$ 0.2 \leq d < 0.5 $$

  • Large: $d \geq 0.8$$$ d \geq 0.8 $$

Effect Size in Practical Use

• Practical Significance: Understanding effect sizes enables researchers to evaluate the strength and practical significance of their findings.

• Visual Representation: Graphs illustrate scores on different psychological constructs and aid in understanding differences in distributions and effect sizes.

Z Scores vs. T Scores

• z-score Usage: More frequently used in practice, especially with larger sample sizes when population standard deviation is known.

• t-scores: Relevant when working with smaller samples or when the population standard deviation is unknown.

• Distribution: Converting scores into z-scores or t-scores does not change the score distribution but merely re-labels the axes for comparison.

Conclusion

• Standardization Importance: Standardizing psychological metrics through transformations informs assessment, diagnosis, and treatment decisions in clinical psychology. Effect sizes provide a crucial metric for interpreting the implications of research findings effectively.

• Flexibility with Metrics: Researchers can choose between different standardized scores (z or t) based on study design and statistical requirements, ensuring a consistent framework for analysis.