2 Criteria for Good Visual Displays ClarityData is represented in a way closely integrated with their numerical meaning.PrecisionData is not exaggerated.EfficiencyData is presented in a reasonably compact space.
7 Measures of Central Tendency: Determining The Median Arrange scores in orderDetermine the position of the midmost score: (N+1)*.50Count up (or down) the number of scores to reach the midmost positionThe median is the score in this (N+1)*.50 position
8 Measures of Central Tendency: The Arithmetic Mean The balancing point in the distributionSum of the scores divided by the number of scores, or
9 Measures of Central Tendency: The Mode The most frequently occurring scoreProblem: May not be one unique mode
10 Symmetry and Asymmetry Symmetrical (b)Asymmetrical or SkewedPositively Skewed (a)Negatively Skewed (c)
11 Comparing the Measures of Central Tendency If symmetrical: M = Mdn = MoIf negatively skewed: M < Mdn MoIf positively skewed: M > Mdn Mo
12 Measures of Spread: Types of Ranges Crude Range: High score minus Low scoreExtended Range: (High score plus ½ unit) minus (Low score plus ½ unit)Interquartile Range: Range of midmost 50% of scores
13 Measures of Spread: Variance and Standard Deviation Variance: Mean of the squared deviations of the scores from its meanStandard Deviation: Square root of the variance
14 Summary Data for Computing the Variance and Standard Deviation Raw scoresX - M(X – M)22-394-115783X = 30(X – M) = 0(X – M)2 = 24M = 5
15 Descriptive vs. Inferential Formulas Use descriptive formula when:One is describing a complete population of scores or eventsSymbolized with Greek lettersUse inferential formula when:Want to generalize from a sample of known scores to a population of unknown scoresSymbolized with Roman letters
16 Variance: Descriptive vs. Inferential Formulas Descriptive FormulaInferential FormulaCalled the “unbiased estimator of the population value”
18 Values of x (for df =5) for Five Different Confidence Intervals CIxt(x) (for df = 5)99.9%.0016.8799%.014.0395%.052.5790%.102.0280%.201.48
19 The Normal Distribution Standard Normal Distribution: Mean is set equal to 0, Standard deviation is set equal to 1
20 Standard Scores or z-scores Raw score is transformed to a standard score corresponding to a location on the abscissa (x-axis) of a standard normal curveAllows for comparison of scores from different data sets.
21 Raw Scores (X) and Standard Scores (z) on Two Exams Student ID and genderExam 1Exam 2Average of z1 and z2 scoresX1 scorez1 scoreX2 scorez2 score1 (M)42+1.7890+1.21+1.502 (M)9-1.0440-1.65-1.343 (F)28+0.5892+1.33+0.964 (M)11-0.8750-1.08-0.985 (M)8-1.13496 (F)15-0.5363-0.33-0.437 (M)14-0.6268-0.05-0.348 (F)25+0.3375+0.35+0.349 (F)+1.6189+1.16+1.3810 (F)20-0.1072+0.18+0.04Sum ()212688Mean (M)21.268.8SD ()11.691.017.470.98