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Arden Miller, Ph.D

Professor of Psychology
Missouri State University


Psychological Statistical Methods




Unit 4: Concepts for Inferential Statistics

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Objectives and Lecture Notes
Reading Assignment: Aron Chapter 3

1. Conceptualize z scores as distance from the mean with standard deviation as the unit and transform raw scores, z-scores and standard scores from one score type to another.

2. Recognize how the normal distribution allows us to describe the percentage of scores that are above, below or between z-scores.

3. Complete score transformations from percentiles to z-scores and z-scores to percentiles using normal curve tables and calculators.

4.  Recognize parameters associated with populations and samples, and discuss issues of sampling in estimating population parameters from sample parameters.

5. Explain probability in terms of expected relative frequency, and use tables to find probabilities for scores above or below a z-score, or between two z-scores.

6. Briefly address the assumptions of the normal distribution and how that is likely to affect hypothesis testing.


1. Standard score transformation worksheet.

2. Score transformation tutorial.

3. QA: MFT z-scores, percentile ranks, etc.

4. z scores and probability tutorial

5. Normal curves for conceptualizing transformations

Project 2: SPSS z-scores.