Ψ420 Ainsworth Stat Review Handbook Andrew Ainsworth Psych 420Ψ420 Ainsworth Data Subjects Aggression Difference Scores Locus of Control Video Type Gender Class Level Age Major 1 -10 18 Non-aggressive Female Junior 20 Psychology 2 -13 6 Non-aggressive Female Freshman 18 Biology 3 2 9 Non-aggressive Female Freshman 18 Biology 4 -3 8 Aggressive Female Sophomore 20 Art 5 16 17 Aggressive Female Freshman 19 Child Development 6 -9 8 Aggressive Female Senior 23 Psychology/Biology 7 0 10 Non-aggressive Female Junior 33 Health Administration 8 3 11 Non-aggressive Male Freshman 18 Business 9 2 11 Non-aggressive Male Sophomore 20 Journalism 10 -7 9 Aggressive Female Junior 20 Psychology 11 -6 11 Aggressive Female Sophomore 19 Psychology/Child Development 12 2 9 Aggressive Male Freshman 19 English Literature 13 3 16 Non-aggressive Female Junior 20 Physical Therapy 14 -21 6 Non-aggressive Female Freshman 18 Political Science 15 -4 10 Non-aggressive Male Senior 21 Computer Science 16 3 8 Non-aggressive Female Freshman 18 Accounting 17 -5 10 Non-aggressive Female Freshman 18 Undecided 18 -9 8 Non-aggressive Male Sophomore 19 Biology 19 -9 14 Aggressive Male Junior 20 Psychology 20 -6 11 Aggressive Female Sophomore 19 Health Science 21 3 10 Aggressive Female Freshman 19 Child Development 22 -10 6 Non-aggressive Female Senior 23 Biology 23 6 11 Non-aggressive Male Sophomore 19 Criminology 24 -13 14 Non-aggressive Female Sophomore 19 Physical Therapy 25 -5 9 Aggressive Male Sophomore 20 Undecided 26 -5 5 Aggressive Female Sophomore 21 Undecided 27 -1 14 Aggressive Male Junior 20 Psychology 28 -15 9 Aggressive Female Junior 23 Psychology 29 1 12 Aggressive Female Freshman 22 Biology 30 4 15 Aggressive Female Freshman 18.5 UndecidedΨ420 Ainsworth Mean and Standard Deviation xXN=∑ 22() xxNSample SDN22()1xxEstimated Population SD−==∑∑∑NN−−∑ 22 30 -106 2026( ) 11236Nxxx====∑∑∑ ()()2211063.533330106112362026 20262026 374.533330 30 30 30 301651.466755.0489 7.419530106112362026 202630 30 30 1 292026 374.5333 1651.466756.9471 7.5429 29NNXsample SDestimated population SD−−==−−−−−======−−−==−−====63 Subjects DV DV2 1 -10 100 2 -13 169 3 2 4 4 -3 9 5 16 256 6 -9 81 7 0 0 8 3 9 9 2 4 10 -7 49 11 -6 36 12 2 4 13 3 9 14 -21 441 15 -4 16 16 3 9 17 -5 25 18 -9 81 19 -9 81 20 -6 36 21 3 9 22 -10 100 23 6 36 24 -13 169 25 -5 25 26 -5 25 27 -1 1 28 -15 225 29 1 1 30 4 16 Σx = -106 Σx2 = 2026Ψ420 Ainsworth Percentile Rank ().5*10030.5*10030*100Rank −− 5.5.166716.6717PRPRPR====≈ Subjects DV Rank Percentile 1 -10 5.5 17 2 -13 3.5 10 3 2 22 72 4 -3 17 55 5 16 30 98 6 -9 8 25 7 0 19 62 8 3 25.5 83 9 2 22 72 10 -7 10 32 11 -6 11.5 37 12 2 22 72 13 3 25.5 83 14 -21 1 2 15 -4 16 52 16 3 25.5 83 17 -5 14 45 18 -9 8 25 19 -9 8 25 20 -6 11.5 37 21 3 25.5 83 22 -10 5.5 17 23 6 29 95 24 -13 3.5 10 25 -5 14 45 26 -5 14 45 27 -1 18 58 28 -15 2 5 29 1 20 65 30 4 28 92 -21 -15 -13 -13 -10 -10 -9 -9 -9 -7 -6 -6 -5 -5 -5 -4 -3 -1 0 1 2 2 2 3 3 3 3 4 6 16 -> Score 1 2 3.5 3.5 5.5 5.5 8 8 8 10 11.5 11.5 14 14 14 16 17 18 19 20 22 22 22 25.5 25.5 25.5 25.5 28 29 30 -> RankΨ420 Ainsworth Z-scores Subjects DV z-scores1 -10 -0.86 2 -13 -1.25 3 2 0.73 4 -3 0.07 5 16 2.59 6 -9 -0.72 7 0 0.47 8 3 0.87 9 2 0.73 10 -7 -0.46 11 -6 -0.33 12 2 0.73 13 3 0.87 14 -21 -2.31 15 -4 -0.06 16 3 0.87 17 -5 -0.19 18 -9 -0.72 19 -9 -0.72 20 -6 -0.33 21 3 0.87 22 -10 -0.86 23 6 1.26 24 -13 -1.25 25 -5 -0.19 26 -5 -0.19 27 -1 0.34 28 -15 -1.52 29 1 0.60 30 4 1.00 10 ( 3.5333)7.5463.856936512.86xxSD−===−−−− zzzz = −Ψ420 Ainsworth Transforming Scores to a Different Scale New scale score = ()SD z x+ a. SAT 100, 500100( .87) 50087 500 413SD xss===−+=− + = b. Stanford-Binet Intelligence Test 16, 10016( .87) 10013.92 100 86.08 86SD xss===− +=−+= ≈ Subjects DV z-scores1 -10 -0.86 2 -13 -1.25 3 2 0.73 4 -3 0.07 5 16 2.59 6 -9 -0.72 7 0 0.47 8 3 0.87 9 2 0.73 10 -7 -0.46 11 -6 -0.33 12 2 0.73 13 3 0.87 14 -21 -2.31 15 -4 -0.06 16 3 0.87 17 -5 -0.19 18 -9 -0.72 19 -9 -0.72 20 -6 -0.33 21 3 0.87 22 -10 -0.86 23 6 1.26 24 -13 -1.25 25 -5 -0.19 26 -5 -0.19 27 -1 0.34 28 -15 -1.52 29 1 0.60 30 4 1.00Ψ420 Ainsworth Area Under a Normal Curve Assuming a normal curve a. The area between two scores on opposite sides of the distribution -10 3 -.86 .87 The area from the mean to -.86 is the same as the area from the mean to +.86. The area from the mean to +.86 = .3051. The area from the mean to .87 = .3078. The two areas together equals .3051 + .3078 = .6129. b. The are between two scores on the same side of the distribution. -14.341 The area from 0 to 1.00 = .3413. The area from 0 to .34 = .1331. The area from .34 to 1.00 = .3413 - .1331 = .2082. Subjects DV z-scores1 -10 -0.86 2 -13 -1.25 3 2 0.73 4 -3 0.07 5 16 2.59 6 -9 -0.72 7 0 0.47 8 3 0.87 9 2 0.73 10 -7 -0.46 11 -6 -0.33 12 2 0.73 13 3 0.87 14 -21 -2.31 15 -4 -0.06 16 3 0.87 17 -5 -0.19 18 -9 -0.72 19 -9 -0.72 20 -6 -0.33 21 3 0.87 22 -10 -0.86 23 6 1.26 24 -13 -1.25 25 -5 -0.19 26 -5 -0.19 27 -1 0.34 28 -15 -1.52 29 1 0.60 30 4 1.00Ψ420 Ainsworth Correlation Coefficient Correlation between Change in aggression (DV) and Locus of control (LOC) 2222315, 106=3625, 2026821, 30,( ) 99225, ( ) 11236 XYXYXY NXY==−==− ===∑∑∑∑∑∑∑ ()( )[][]()( )222222()()/() ()( 821) 315 -106 / 30(315) (-106)3625- 2026-30 30( 821) ( 1113)3625-3307.5 2026-374.53292317.5 1651.47292.4033724.1144XY X Y NrXYXYNNrrrr−= −−  −−=   −−−====∑∑∑∑∑∑∑ Subjects (X) LOC (Y) DV (X)(Y) X2 Y2 1 18 -10 -180 324 1002 6 -13 -78 36 1693 9 2 18 81 4 4 8 -3 -24 64 9 5 17 16 272 289 2566 8 -9 -72 64 81 7 10 0 0 100 0 8 11 3 33 121 9 9 11 2 22 121 4 10 9 -7 -63 81 49 11 11 -6 -66 121 36 12 9 2 18 81 4 13 16 3 48 256 9 14 6 -21 -126 36 44115 10 -4 -40 100 16 16 8 3 24 64 9 17 10 -5 -50 100 25 …