Chapter 3

Measurement and Measures of Association

Course Details

  • Course Code: PSYC 385

  • Course Title: Psychological Test

  • Semester: Fall 2025

Outline

  • Measurement and Describing Data

  • Measures of Central Tendency and Variability

  • Normal Curve and Standard Scores

  • Correlation and Inferences

  • Meta-analysis

Learning Objectives

  • Objective 1: Be able to interpret the basic descriptions of data and the potential implications of sample characteristics.

  • Objective 2: Interpret correlational results and the potential implications.

  • Objective 3: Understand common standardization techniques.

Scales of Measurement

  • Nominal: Categorization or classification

    • Example: DSM-5-TR

  • Ordinal: Classifications but also rank ordered

    • Example: Level of severity

  • Interval: Equal intervals between numbers

    • Examples: Temperature, SAT scores

  • Ratio: Has a true zero unlike the others

    • Example: Time

  • Most psychological tests are often treated as interval levels for statistical purposes.

Describing and Comparing Data Distributions

  • A set of test scores arrayed from a test or study.

  • Raw Score: A straightforward numerical accounting of performance.

  • Frequency Distribution: All scores listed alongside the number of times each score occurred.

Frequency Distributions

  • May be presented in tabular form.

  • Grouped Frequency Distribution: Displays scores in class intervals rather than actual test scores.

Example of Grouped Frequency Distribution

Class Interval

Frequency (f)

95-99

1

90-94

2

85-89

2

80-84

3

75-79

3

70-74

2

65-69

0

60-64

1

55-59

0

50-54

2

45-49

0

40-44

0

Graphical Representations

  • A Histogram is a graph with vertical lines drawn at the true limits of each test score or class interval, forming a series of contiguous rectangles.

Measures of Central Tendency

  • Central Tendency: A statistic that indicates the average or midmost score between extreme scores in a distribution.

  • Mean: Sum of observations divided by the number of observations.

  • Median: The middle value in a distribution; particularly useful when outliers are present.

  • Mode: The most frequently occurring score in a distribution.

    • If two scores occur most frequently, the distribution is termed bimodal.

Visual Representation

  • Diagrams illustrating median, mean, and mode in various distributions.

Measures of Variability

  • Variability: An indication of the degree to which scores are scattered or dispersed within a distribution.

  • Distributions may have the same mean but different variabilities, affecting interpretations.

Key Measures of Variability

  • Range: The difference between the highest and lowest scores.

  • Interquartile Range (IQR): Difference between the third (Q3) and first (Q1) quartiles of a distribution.

  • Variance: The arithmetic mean of the squares of the differences between scores in a distribution and their mean.

  • Standard Deviation (SD): The square root of the variance, representing typical distances of scores from the mean.

Skewness and Kurtosis

  • Skewness: The extent of asymmetry in a distribution.

    • Positive skew: Clustering of scores near the low end.

    • Negative skew: Clustering of scores near the high end.

  • Kurtosis: The peakedness of a distribution.

    • Platykurtic: Relatively flat.

    • Leptokurtic: Relatively peaked.

    • Mesokurtic: Intermediate form.

Types of Distributions

  • Normal Distribution: Bell-shaped curve.

  • Bimodal Distribution: Two modes present.

  • Skewed Distributions: Positive or negative skew, differing forms such as J-shaped curve or rectangular distribution.

The Normal Curve

  • A mathematically defined, smooth bell-shaped curve that is symmetrical and follows a specific frequency distribution pattern.

  • Area under the normal curve can be divided into sections based on standard deviations.

Standard Scores

  • Purpose: To compare scores across different distributions or studies and to normalize skewed data.

  • Z-score: A score indicating how many standard deviations a raw score is above or below the mean; mean = 0.

  • T-score: A standard score where the mean is set at 50 and the standard deviation at 10.

Application of Standard Scores

  • Useful for comparing individuals and different studies.

  • Particularly beneficial for highly skewed data.

Example Study

  • Study Title: Modifying Instructions on the Posttraumatic Stress Disorder Checklist for Military Populations Does Not Change Symptom Reporting.

  • Authors: Lyndon A. Riviere, PhD, Edward N. Edens, PhD, among others.

  • Objective: Investigate whether modifications in instructions affect PTSD symptom reporting and prevalence rates.

  • Sample: 1691 soldiers randomly assigned to different versions of the PCL.

  • Findings: No statistically significant differences in PTSD symptom reporting across PCL versions.

Posttraumatic Stress Disorder Checklist (PCL)

  • Versions: PCL-Civilian, PCL-Specific stressor, PCL-Military.

  • Each version includes 17 items with variations in wording for military and civilian contexts.

  • Symptom Clusters: Intrusion, avoidance, hyperarousal; cutoff score of 50 indicates PTSD.

Sample Demographics and Combat Exposure

  • Data summarized showing mean ages, gender distribution, education level, race/ethnicity, rank, and marital status of participants in the study.

Correlation and Inference

  • Correlation describes the strength of the relationship between two variables.

  • Correlation Coefficients: Ranges from -1 to +1; zero indicates no correlation.

  • Positive Correlation: As one variable increases, so does the other.

  • Negative Correlation: As one variable increases, the other decreases.

  • Correlation does not imply causation but aids in hypothesis testing.

Methods of Correlation

  • Pearson r: For linear relationships between continuous variables; check for statistical significance typically at p < .05.

  • Spearman Rho: For small sample sizes or ordinal variables.

Scatterplots

  • Graphical representation of correlation; depict relationships between two variables.

  • Strong correlations are characterized by tightly clustered points.

Outliers

  • Outlier: An atypical data point lying far from other points in a scatterplot; can significantly affect correlations.

Meta-Analysis

  • Purpose: To examine relationships across multiple studies for a comprehensive view.

  • Outputs include a single estimate often represented as a correlation coefficient.

  • Important considerations include the variability of dropout rates among different studies on PTSD treatments.

Conclusion on Meta-Analysis

  • Highlights dropout from PTSD treatments; indicates that dropout is not necessarily correlated with the trauma focus of treatments, requiring further exploration.