Describing Behavior Chapter 4

Data Analysis Two basic types  Descriptive Summarizes and describes the nature and properties of the data  Inferential What is the likelihood the results in the sample actually occur in the population  (e.g., differences between groups, relationships between variables)

Describing Individual Differences Measures of Central Tendency Measures of Variability Distribution of the data

Mean  average score of all observations in distribution Median  midpoint of all scores in distribution Mode  most frequently occurring score in distribution Measures of Central Tendency

Range  subtract the lowest from the highest score Standard Deviation  measure of the “spread” of the scores around the mean – Variance  square of the standard deviation Measures of Variability

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

Data Distributions

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

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%) Properties of a Normal Distribution

The extent to which one variable can be understood on the basis of another  Properties of correlation coefficient direction (positive or negative) magnitude (strength of the relationship) Correlation

r =.95 Positive Correlation

r =.00 No Correlation

r = -.95 LowHigh Low High Negative Correlation

Correlation: A Review

Distribution for Example M = 3.00 SD = 1.10