Psychometrics and Statistical Concepts

Discussion of psychometrics, focusing on central concepts.
- Topics include normal distribution and percentile ranks.
- Reassurance: The statistical portion is simpler than expected.

Legal, cultural, and ethical implications of testing will be revisited.
- Summarized key points from chapter 2 in Cohen to facilitate understanding without unnecessary reading.

Explanation of why normal distribution can be assumed for most tests.
- Reference to slide 29 as key material.

Familiar Concepts from PSYC 202: Recognition of measurement scales.
- Importance of understanding types of scales: Continuous vs. Discrete.
- Continuous Scale: Can take any value (e.g., 1.0, 1.1, 1.2).
- Discrete Scale: Only whole numbers (e.g., 10 or 11 goals).
Error in Measurement: Sources of error when administering tests.
- Factors affecting scores: testee’s mood, environmental conditions, and test attitudes.
Nominal and Ordinal Scales:
- Nominal Scales: Categorization without order (e.g., gender).
- Ordinal Scales: Rank order (e.g., Likert scales).
Many tools used are Likert scales (ordinal), but can be treated as interval scales for statistical analysis.

Treatment of Likert scales for statistical purposes:
- Minimum of five to seven points for validity in analysis.
- Average scores are calculated for interpretation.
- Must cite references when justifying this approach in academic reports.

Overview of major IQ tests: Wechsler Adult Intelligence Scale, Stanford-Binet, and Wechsler Intelligence Scale for Children.
- Emphasis on how IQ scores relate to percentile ranks and normal distribution.
- Discussion of implications of various IQ scores (e.g., IQ of 100 at the 50th percentile).
- Clarifications about the meaning of different IQ levels.

Understanding conversion of raw scores using:
- Mean and Standard Deviation.
- Example: Raw score of 21 out of 26 with mean of 15 and standard deviation of 3.
Calculation of Z-scores for transformation:
- Formula: Z = \frac{(X - \text{mean})}{\text{SD}}
- Interpretation of Z-scores relative to percentile ranks.

Need for context when interpreting raw scores.
- Example: Understanding norms and benchmarks for comparison.
Differentiate between raw scores and what they signify in terms of expected outcomes or standing against population norms.

Familiarity with different distributions: Normal, Positive Skew, Negative Skew, and Uniform distributions.
Key statistics defined:
- Mean, Median, Mode: Important measures of central tendency.
- Standard Deviation: Measure of variability within a dataset.
Understanding skewness and kurtosis, especially regarding validity of scores.

Assumption of normality in larger samples (30+).
- Encouragement not to stress about normality but to rely on the central limit theorem for sample sizes over 30.

Types of transformations explained:
- Linear Transformations: E.g., Z-scores.
- Nonlinear Transformations: Changes shape of original distribution but maintains ranks.
- Importance of understanding rank versus distance measures in interpreting scores.

Explanation of correlation:
- Positive and negative correlations.
- Relationship between correlation and causation.
- Practical example with outdoor work and skin cancer incidences to illustrate predictiveness versus causation.
Pearson correlation focus for report work, citing significance levels.

Detailed understanding of percentile ranks in interpretation of scores.
- Example provided for practical applications and comparisons.
Reiteration of the importance of meta-analyses as strong statistical sources in reports.

Review of test manual tables for Wechsler scale.
- Interpretation based on scaled scores.
- Emphasis on using specific tables for correct context (e.g., age-specific norms).
Open Q&A conclusion to address any uncertainties regarding the material covered in lecture.