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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 Measures of Central Tendency Mean Median average score of all observations in distribution midpoint of all scores in distribution Mode most frequently occurring score in distribution Measures of Variability Range Standard Deviation – subtract the lowest from the highest score measure of the “spread” of the scores around the mean Variance square of the standard deviation Calculating the standard deviation √ Data 1 2 3 4 5 Sum 15 Mean 3 √ ∑(xi – x)2 n-1 2+ (2)2 2+ (5 – 3)2 (1 – 3)2 +(-2) (2 –2 +(-1) 3)42 ++21(3+(0) –03) +10 +21+(1) +(442 –+ 3) 2.5 1.58 5 4-41 √ √ √√ 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 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%) Correlation 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) Positive Correlation Final Grade Points 350 r = .95 300 250 200 150 100 50 0 0 20 40 60 Exam Points 80 100 120 No Correlation Final Grade Points 350 r = .00 300 250 200 150 100 50 0 0 20 40 60 Exam Points 80 100 120 Negative Correlation High Turnover Intentions r = -.95 Low Low Job Satisfaction High Correlation: A Review Distribution for Example 50 40 M = 3.00 SD = 1.10 40 30 20 20 20 10 10 10 0 1 2 3 4 5

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