4_Lecture4.2_Variability_0204_Spring11(1)

4_Lecture4.2_Variability_0204_Spring11(1) - deviation of a...

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1 PSY207 B Spring 2011 Psychological Statistics IV. Variability 4.1 Introduction 4.2 The Range and the Interquartile Range 4.3 Standard Deviation and Variance for a Population 4.4 Standard Deviation and Variance for Samples 4.5 More about Variance and Standard Deviation 4.6 Degrees of freedom Figure. Calculation of the Variance Average of the deviations Average of the squared deviations Average of standard distance =0 = Population Parameters Variance Standard Deviation Symbol Computation Sample Statistics Variance Standard Deviation Symbol Computation Why n-1?
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2 Degrees of Freedom (df) The number of values free to vary after certain restrictions are placed on the data Degrees of freedom (df) for a sample: n -1 Degrees of Freedom (df) Example: n = 3, M = 5, Σ X = 15 15 12 2 1 X 15 10 3 2 15 8 4 3 15 6 5 4 15 6 4 5 Σ X 6 15 3 6 The first 2 out of 3 scores were free to vary to have any values, but the final one was dependent on the values chosen for the first 2 df = n-1 = 3-1 = 2 What would happen to the mean and standard
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Unformatted text preview: deviation of a distribution if you . . . adding/subtracting a constant to every score? multiplying/dividing a constant to every score? Transformations of Scale Adding a constant to each score--The Mean is changed (is added by that constant)--The standard deviation is unchanged Multiplying each score by a constant--The Mean is changed (is multiplied by that constant)--Standard Deviation is also changed (is multiplied by that constant) What happens to the SD if adding or multiplying by a constant to each score? SD: added by the constant SD: multiplied by the constant X1 = 41, X2 = 43, Distance between scores = 2 If each score added by 3 New X1 = 41 + 3 = 44, New X2 = 43 + 3 = 46 Distance between new scores = 2 If each score multiplied by 2 New X1 = 41 x 2 = 82, New X2 = 43 x 2 = 86 Distance between new scores = 4 SD is unchanged SD is multiplied by 2 Summary...
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4_Lecture4.2_Variability_0204_Spring11(1) - deviation of a...

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