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

2. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

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

4. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

5. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

6. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

7. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

8. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

9. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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%)

10. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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

11. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Sample vs. Population Sample –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

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

13. Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall 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