1. Some Key Ingredients for Inferential Statistics
Chapter 4
Some Key Ingredients for Inferential Statistics
The Normal Curve, Probability, and Population Versus Sample
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

2. Inferential Statistics
Methods used by social and behavioral scientists to go from results of research studies to conclusions about theories or applied procedures
What most of statistics entails
Beyond mere descriptive statistics
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

3. The Normal Curve Bell-shaped Unimodal Symmetrical
Exactly half of the scores above the mean
Exactly half of the scores below the mean
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

4. The Normal Curve
There are known percentages of scores above or below any given point on a normal curve
34% of scores between the mean and 1 SD above or below the mean
An additional 14% of scores between 1 and 2 SDs above or below the mean
Thus, about 96% of all scores are within 2 SDs of the mean (34% + 34% + 14% + 14% = 96%)
Note: 34% and 14% figures can be useful to remember
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

5. Normal Curve Table
Normal curve table gives the precise percentage of scores between the mean (Z score of 0) and any other Z score.
Can be used to determine
Proportion of scores above or below a particular Z score
Proportion of scores between the mean and a particular Z score
Proportion of scores between two Z scores
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

6. Normal Curve Table Continued
By converting raw scores to Z scores, can be used in the same way for raw scores.
Can also use it in the opposite way
Determine a Z score for a particular proportion of scores under the normal curve
Table lists positive Z scores
Can work for negatives too
Why? Because curve is symmetrical
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

7. Steps for Figuring Percentage Above or Below a Z Score
Convert raw score to Z score, if necessary
Draw a normal curve
Indicate where Z score falls
Shade area you’re trying to find
Make rough estimate of shaded area’s percentage
Find exact percentage with normal curve table
Check to verify that it’s close to your estimate
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

8. Steps for Figuring a Z Score or Raw Score From a Percentage
Draw normal curve, shading approximate area for the percentage desired
Make a rough estimate of the Z score where the shaded area starts
Find the exact Z score using normal curve table
Check to verify that it’s close to your estimate
Convert Z score to raw score, if desired
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

9. Probability Abbreviated as p, as in “p < .05”
Expected relative frequency of a particular outcome
Probability = possible successful outcomes divided by all possible outcomes
Represented as
Proportion (number between 0 and 1)
Percentage (between 0% and 100%)
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

10. Probability and Frequency Distributions
For any frequency distribution the percentage of scores in a particular region corresponds to the probability of selecting a score from that region.
For example, the normal curve
Histogram to the right
10 out of 50 people scored 7 or higher.
Thus, the probability of randomly selecting a person with a score of 7 or higher is 10/50, or .20
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

11. Sample vs. Population Sample Population
Relatively small number of instances that are studied in order to make inferences about a larger group from which they were drawn
Population
The larger group from which a sample is drawn
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

12. Sample vs. Population Examples
a. pot of beans
b. larger circle
c. histogram
Sample
a. spoonful
b. smaller circle
c. shaded scores
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall

13. Why Study Samples? Often not practical to study an entire population
Instead, researchers attempt to make samples representative of populations
Random selection
Each member of population has an equal chance of being sampled
Good but difficult
Haphazard selection
Take steps to ensure samples do not differ from the population in systematic ways
Not as good but much more practical
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall