Psychology and Statistics

1. Psychology and Statistics Interpreting Data (Ch. 1 Myers and Ch. 2 Barron’s)

2. Descriptive Statistics • Descriptive statistics – describes a set of data • Measures of Central Tendency • Goal is to determine the center of the distribution • Measures of Variation • Goal is to describe the diversity of the distribution

3. Measures of Central Tendency • MEAN - Average • MEDIAN – Middle, 50th % • MODE – Most frequently occurring score

4. Mean • Most frequently used measure of central tendency but can be distorted by outliers (extremes). If the distribution includes outliers, then the median is a better measure of central tendency. • Ex. 2, 7, 8, 9, 10, 18

5. Mean • If the distribution is not skewed it is called symmetrical. Outliers skew the distribution. If there are high positive outliers then the distribution is positively skewed. (more low scores than high scores) If there are very low outliers then the distribution is negatively skewed. (more high scores than low scores) Symmetrical Positively Skewed Negatively Skewed

6. Examples of Skewed Distributions • 39,000 penniless people • Geography Majors from UNC Chapel Hill class of 84?? • Test average 65

7. Measures of Variation • Range – the gap between the lowest and the highest score

8. Distribution of ValueStandard Deviation • THE BELL CURVE (IQ) + or – 1 Standard Deviation = 15 pts. Remember Standard Deviation measures the distance from the mean. Mean of IQ = 100 What score is +1 SD? What score is – 1 SD? + and – 1 SD of IQ scores includes 68% What score is + 2 SD? What score is – 2 SD? + and – 2 SD of IQ scores includes 95%

9. Z Scores and Standard Deviation • Z scores measure the distance of a score from the mean in units of standard deviation. If the score is below the mean its z score is negative. If it Is above the mean then the z score is positive. • Consider this example. Mean of 100. Joe scores 90 and has a z score of -1. Sarah scores a 105. What is her z score?

10. Inferential Statistics • Inferential Statistics determines if the findings can be applied to a larger population from which the sample was selected. • It is a goal of the researchers for the sample to be representative of the population • The extent to which the sample differs from the population is known as sampling error. • Statistical tests yield p values. The smaller the p-value the more significant the results. The cutoff for findings being statistically significant is p = .05. This means that there is a 5% chance that the findings were by chance. P-value never equals 0 because we can never be 100% certain that our findings were not due to chance.

11. Statistical Significance • When is the difference significant? • Psychologists are conservative when it comes to declaring some research statistically significant. • Statistical significance – When the difference observed is not likely to have occurred by chance. • When samples averages are reliable and the difference between them is large then the difference has statistical significance • When it is 5% or less likely to have occurred by chance, then psychologist will say that there is statistical significance. • Be wary of statistical significance in homogeneous samples – (these samples are homogeneous and not practical to life application)

12. Statistics can Lie • Examples of Statistics being used for selfish purposes of politicians and/or corporations. • Video: • ECU study changing NC school start times • Global Warming Studies funded by Exxon. • NC HWY 74 By Pass studies and impact on the environment. • Health Care Debate - Lies, Lies and Statistics