Experimental Methods: Statistics & Correlation Mr. Koch AP Psychology Andover High School

Statistics Types: Distributions: Descriptive – describe data Inferential – mathematical procedures that help psychologists make inferences about what data mean Distributions: Frequency distribution Histogram Percentile rank

Central Tendencies Mean (M) – arithmetic average (1122333444455555) = 56/16 = 3.5 Median – halfway point in a set of data (1122333444455555) = middle #(s) Mode – score that occurs most frequently 5 = most frequent #

Variation Range = gap between highest and lowest scores (5-1) Standard Deviation (SD) Calculate each difference (deviation) between each score and the mean Square these deviations Find their average Find the square root of this average Use a “normal curve” to interpret results

Deviation from the Mean (40) Standard deviation gauges whether scores are packed together or dispersed because it uses information from each score. (The true basis for curving a test.) M = 160/4 = 40 Sum of (deviations)² = 46 SD = √{[sum of (deviations)²]/number of scores} = √(46/4) = 3.4 Test Scores Deviation from the Mean (40) Deviation Squared 36 -4 16 38 -2 4 41 +1 1 45 +5 25

The Normal (aka Bell) Curve

Negatively skewed Bell Curve Positively skewed Bell Curve

Inferential Statistics Statistical significance Calculation of the likelihood a result happens by chance Most use 5% (arbitrary) as standard for determining significant difference between means p < .05 Principles: Representative samples are better than biased samples More cases are better than fewer Less variable observations are more reliable than highly variable observation

Correlation Scatter plot Correlation coefficient r = +1.00 One set of scores goes up in direct proportion to the other r = 0.00 Scores unrelated r = -1.00 One set of scores goes up as the other goes down

Examples + (positive) - (negative) Child abuse / aggressiveness Education / income Studying / grades - (negative) Self esteem / depression Age / hours of sleep Stress / health Correlation DOES NOT prove causation Only proves relationship, not cause and effect

Correlation “Illusory Correlations”: A perceived correlation that really does not exist Examples: “lucky” penny = wishes come true Arthritis and cold weather Pregnant cravings and sex of baby