1.  Two basic types Descriptive  Describes the nature and properties of the data  Helps to organize and summarize information Inferential  Used in testing hypothesis (e.g., differences between groups, relationships between variables) Statistics

2. Describing Individual Differences  Measures of Central Tendency  Measures of Variability  Distribution of the data

3.  Measures of Central Tendency Mean  average score of all observations in distribution Median  midpoint of all scores in distribution Mode  most frequently occurring score in distribution Descriptive Statistics

4.  Measures of Variability Range  subtract the lowest from the highest score and add 1 Standard Deviation  measure of the “spread” of the scores around the mean Descriptive Statistics

5. ∑(x i – x) 2 n-1 √ Calculating the standard deviation (1 – 3) 2 + (2 – 3) 2 + (3 – 3) 2 + (4 – 3) 2 + (5 – 3) 2 5 - 1 √ (-2) 2 +(-1) 2 +(0) 2 + (1) 2 + (2) 2 5 - 1 √ 4 + 1 + 0 + 1 + 4 4 √ 1 2 3 4 5 15 3 Sum Mean Data 10 4 √ 2.5 √ 1.58

6. Frequency Plots ScoresTalliesFrequency 6I1 5III3 4IIII4 3IIIII5 2III3 1II2 0 2 Frequency Distribution

7. Descriptive Statistics  Distribution of the data Shapes of distribution curves  Bell (normal distribution) The bell curve has desirable statistical properties A number of inferential statistics “assume” data is normally distributed  Skewed Curves Negative Skew - tail of the curve is to the left Positive Skew - tail of the curve is to the right

8.  Properties of a normal distribution Measures of central tendency are the same  mean = median = mode We know percentage of scores that fall within   1 standard deviation (68%)   2 standard deviations (95%)   3 standard deviations (99%) Normal Distributions

10.  The extent to which one variable can be understood on the basis of another Two properties of correlation coefficient  direction (positive or negative)  magnitude (strength of the relationship) Correlation

11. r =.95 Positive Correlation

12. r =.00 No Correlation

13. Negative Correlation r = -.95 LowHigh Low High

14. Data Set 3 Example Scatter Plot