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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Ch. 10: Summarizing the Data

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Criteria for Good Visual Displays Clarity Data is represented in a way closely integrated with their numerical meaning. Precision Data is not exaggerated. Efficiency Data is presented in a reasonably compact space.

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Frequency Distribution Example

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Bar Graphs Example

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Stem-and-Leaf Chart StemsLeaves 827 7049 62669 5126 417 37

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Back-to-Back Stem-and-Leaf Chart DepressionStemsHypomania 258 16 55431100124

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Measures of Central Tendency: Determining The Median Arrange scores in order Determine the position of the midmost score: (N+1)*.50 Count up (or down) the number of scores to reach the midmost position The median is the score in this (N+1)*.50 position

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Measures of Central Tendency: The Arithmetic Mean The balancing point in the distribution Sum of the scores divided by the number of scores, or

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Measures of Central Tendency: The Mode The most frequently occurring score Problem: May not be one unique mode

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Symmetry and Asymmetry Symmetrical (b) Asymmetrical or Skewed Positively Skewed (a) Negatively Skewed (c)

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Comparing the Measures of Central Tendency If symmetrical: M = Mdn = Mo If negatively skewed: M < Mdn Mo If positively skewed: M > Mdn Mo

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Measures of Spread: Types of Ranges Crude Range: High score minus Low score Extended Range: (High score plus ½ unit) minus (Low score plus ½ unit) Interquartile Range: Range of midmost 50% of scores

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Measures of Spread: Variance and Standard Deviation Variance: Mean of the squared deviations of the scores from its mean Standard Deviation: Square root of the variance

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Summary Data for Computing the Variance and Standard Deviation Raw scoresX - M(X – M) 2 2-39 41 4 1 500 724 839 X = 30 (X – M) = 0 (X – M) 2 = 24 M = 5

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Descriptive vs. Inferential Formulas Use descriptive formula when: One is describing a complete population of scores or events Symbolized with Greek letters Use inferential formula when: Want to generalize from a sample of known scores to a population of unknown scores Symbolized with Roman letters

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Variance: Descriptive vs. Inferential Formulas Descriptive Formula Inferential Formula Called the unbiased estimator of the population value

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Confidence Interval for a Mean

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Values of x (for df =5) for Five Different Confidence Intervals CIxt (x) (for df = 5) 99.9%.0016.87 99%.014.03 95%.052.57 90%.102.02 80%.201.48

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall The Normal Distribution Standard Normal Distribution: Mean is set equal to 0, Standard deviation is set equal to 1

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall 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 curve Allows for comparison of scores from different data sets.

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Rosnow, Beginning Behavioral Research, 5/e. Copyright 2005 by Prentice Hall Raw Scores (X) and Standard Scores (z) on Two Exams Student ID and gender Exam 1Exam 2Average of z 1 and z 2 scores X 1 scorez 1 scoreX 2 scorez 2 score 1 (M)42+1.7890+1.21+1.50 2 (M)9-1.0440-1.65-1.34 3 (F)28+0.5892+1.33+0.96 4 (M)11-0.8750-1.08-0.98 5 (M)8-1.1349-1.13 6 (F)15-0.5363-0.33-0.43 7 (M)14-0.6268-0.05-0.34 8 (F)25+0.3375+0.35+0.34 9 (F)40+1.6189+1.16+1.38 10 (F)20-0.1072+0.18+0.04 Sum ( ) 212068800 Mean (M)21.2068.800 SD ( ) 11.691.017.471.00.98

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