PSYC331 – Statistics for Psychologists

PSYC331 - Statistics for Psychologists (First Semester 2024/2025)

Course Instructors

  • Instructor: John E. K. Dotse, PhD

  • Office Location: Main Building, Psychology

  • Office Hours: Wednesdays, 10.30 am – 12.30 pm

  • Email: jekdotse@ug.edu.gh

Course Structure

Lecture 1: Introduction to Statistics

Instructions

  • Mode of teaching: Face-to-face.

  • All students should procure calculators.

  • Teaching assistants will be available for tutorial assistance.

  • Attend all lectures, as the course is technical and involves self-practice in computations.

Assessment and Grading

  • Assessment Format: Both online and paper-based.

  • Tests:

    • Test 1: Interim Assessment (online, MCQ) - Weight: 25%

    • Test 2: Interim Assessment (online, MCQ) - Weight: 25%

    • Test 3: Final Exam (paper-based) - Weight: 50%

  • Dates and times for tests, as well as any changes, will be communicated via the SAKAI platform and during lectures.

Reading List

  • Opoku, J. Y. (2007). Tutorials in Inferential Social Statistics. (2nd Ed.). Accra: Ghana Universities Press. Pages 3 – 22.

Inferential Statistics Observations

  • A solid grounding in statistics is essential for research in the social sciences.

  • Characteristics:

    • Technical yet manageable.

    • Statistics are not mathematics; focused on data analyses with basic calculations.

    • Crucial for data analytics in research projects.

Example Computation

  • Computational formula for Independent t-test.

Course Outline

  • Descriptive statistics.

  • Inferential statistics.

  • Properties/levels of measurement scales.

  • Summation notations.

  • Computation of mean and standard deviation.

What is Statistics?

  • Definition: A branch of mathematics concentrating on the organization, analysis, and interpretation of numerical groups (Aron, Coups, & Aron, 2014).

  • Branches of Statistical Methods:

    • Descriptive Statistics: Used to summarize and describe quantitative data.

    • Inferential Statistics: Techniques to draw conclusions about a population based on sample data.

Descriptive Statistics

Overview

  • Summarize and describe quantitative data, providing an overall picture of samples.

  • Examples of Summarized Measures: Mean, mode, median, variance, and standard deviation.

Measures of Central Tendency

  • Definition: Indicate the typical score in a sample.

  • Types:

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

    • Median: The middle score when ordered from lowest to highest.

    • Mode: The most frequently occurring score.

    • Quartiles: Data division into four equal parts.

Measures of Dispersion/Variation

  • Purpose: Indicate how variable scores are in distribution.

  • Types:

    • Range: Difference between the highest and lowest scores.

    • Variance: Average squared deviation of scores from the mean.

    • Standard Deviation: Square root of the variance; it reflects variability of scores around the mean.

Implications of Descriptive Statistics

  • Allow for educated guesses about population trends based on summarized data.

  • Cannot definitively indicate exact circumstances within the population.

Inferential Statistics

Overview

  • Techniques for estimating population attributes based on sample data.

  • Assumption: Well-selected samples represent the population.

Key Concepts

  • Sample Statistic: Estimate computed from a sample.

  • Population Parameter: Estimate derived from entire population, typically denoted by Greek letters (e.g., $\mu$ for mean).

  • Sample Statistics: Denoted by Latin letters (e.g., $\bar{x}$ for sample mean, $s$ for sample standard deviation).

Generalization from Sample to Population

  • Inferences can be made about population parameters using sample statistics.

Conceptual Visuals

  • Illustration showing multiple samples taken from a population (e.g., faces).

Variables

  • Definition: Characteristics capable of taking various values.

  • Types:

    • Continuous Variables: Numeric with infinite values (e.g., time).

    • Discrete Variables: Numeric with countable values (e.g., number of students).

    • Categorical Variables: Group data into finite categories (e.g., gender).

Measurement Scales

Properties

  • Measurement Scale Properties:

    • Identity: Numbers assigned for identification, not for mathematical operations (e.g., 1 = male, 2 = female).

    • Magnitude: Ordered relationship among values; can compare instances (higher, lower).

    • Equal Intervals: Uniform distance between points on a scale (e.g., temperature).

    • Absolute Zero Point: Indicates absence of an attribute being measured (e.g., 0 siblings).

Types of Measurement Scales

  • Ratio Scale: Highest level; all four properties present (e.g., height, weight).

  • Interval Scale: Lacks absolute zero; measures on a continuum (e.g., temperature in Celsius).

  • Ordinal Scale: Orders distinct categories without magnitude (e.g., satisfaction level).

  • Nominal Scale: Classifies into distinct categories without order (e.g., gender).

Exercises on Measurement Scales

Example Situations

  1. GRE Scores - Continuous interval scale.

  2. Children classified by reading level - Ordinal scale.

  3. PTSD symptom survey - Nominal scale.

  4. Student hall preferences - Nominal scale.

Statistical Testing

Types of Tests by Measurement Scale

  • Scale -> Tests:

    • Ratio: Parametric tests (e.g., t-test, F-test).

    • Interval: Non-parametric tests (e.g., Mann-Whitney U).

    • Ordinal: Non-parametric tests (e.g., Wilcoxon).

    • Nominal: Non-parametric tests (e.g., Chi-Square).

Summation Notations

Definitions

  • Summation Symbol (Σ): Used to indicate sum of a set of values.

  • Sum of a Set: Example with numbers: $2, 3, 5, 7, 11$ with $ ext{x}_i$ notation.

Exercises

  1. Sum of Squares (ΣX²): Squaring individual numbers and summing.

  2. Square of the Sum (ΣX)²: Adding values and squaring resultant sum.

  3. Product Sums (ΣXY): Determining sum of products of two variables.

Variability Measures

Mean Calculation

  • Calculate the mean: Sum divided by the number of observations:
    \text{Mean} = \frac{\text{Sum of observations}}{N}

Standard Deviation and Variance Calculations

  • Standard Deviation: Measure of dispersion from mean. Use variance to compute:

    • Variance formula for population and sample calculations:
      \sigma^2 = \frac{\Sigma(X - \mu)^2}{N}
      s^2 = \frac{\Sigma(X - \bar{x})^2}{n - 1}

  • Calculate variability for individual scores: Squaring differences from mean, summing results

Example Calculations

  • Compute standard deviation from score set (e.g., 2, 4, 6, 8, 10, 12) using defined formulae.

Conclusion

  • Mastery of descriptive and inferential statistics is critical for effective data analysis in psychological research. Individual performance on assessments will demonstrate understanding of these fundamental statistical concepts.