Lecture Chapter 3-1

Key Ingredients for Inferential Statistics

Learning Objectives

• Z Scores: Understand Z scores and transforming raw scores

• Distributions: Explain the normal curve in psychology research

• Sample vs Population: Define and understand their relationship

• Probability: Describe probability calculation procedures

• Non-Normal Populations: Actions if populations are not normal or samples are not random

• Research Presentation: How normal curves, samples, populations, and probabilities are presented in articles

Normal Distribution

• Characteristics: Unimodal, symmetrical; most scores near the center

• Extreme Scores: Fewer scores at the extremes of the curve

Areas Under the Normal Distribution

• Mean and Standard Deviations: Representation and percentage of scores between mean and standard deviations

• Z Scores: Used to determine the percentage of scores; tables illustrate this relationship

Normal Curve Table

• Distribution Information: Provides percentages between mean and Z scores, and in tails of distribution

• Notation of Scores: Highlighted values for examples in text

Steps for Figuring Areas Under the Normal Distribution

1. Convert raw score to Z score.

2. Draw the normal curve and identify the Z score.

3. Estimate the percentage of the shaded area.

4. Use the normal curve table for exact percentages.

Samples and Populations

• Definitions: Population is the entire group; sample is a subset for practical reasons

• Sampling Methods: Random vs. haphazard selection

Probability of an Event

• Probability Definition (p): Relative frequency of an outcome

• Calculation Steps: Determine successful outcomes, total outcomes, and divide.

• Probability Representation: Range from 0 (impossible) to 1 (certain) or 0% to 100%

Statistical Relevance of Z Scores

• Normal Distribution as Probability Distribution: Scores between Z scores represent probabilities.

• Symbols for Probability: p < .05 indicates significant probability thresholds.

Addressing Non-Normal Populations

• Controversies: Questions on normality and randomness of samples

Research Article Norms

• Z Scores & Normal Curves: Rarely discussed; relevant in methodology and statistics sections in articles.