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Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph Agenda • • • • • Overview of course Review of assigned reading material Sensation seeking scale Howell Chapters 1 and 2 Student profile Course Principles • Learner centered • Balance between theory, math and practice • Fun • Focus on knowledge acquisition and application Course Activities • • • • Lectures Discussions Exercises Lab Terminology • • • • • Random sample Population External validity Discrete Parameter • • • • • Random assignment Sample Internal validity Continuous Statistic Terminology (cont’d) • Descriptive vs inferential statistics • Independent vs dependent variables Measurement Scales • • • • Nominal Ordinal Interval Ratio Sensation Seeking Test Defined as: “the need for varied, novel and complex sensations and experiences and the willingness to take physical and social risks for the sake of such experiences” Zuckerman, 1979 Measures of Central Tendency: The Mean Mean = Sum of all scores Total number of scores X = EO N Measures of Central Tendency: The Mode • Is the most common score (or the score obtained from the largest number of subjects) Measures of Central Tendency: The Median • The score that corresponds to the point at or below which 50% of the scores fall when the data are arranged in numerical order. Median Location = N+1 2 Advantages Mean – can be manipulated algebraically – best estimate of population mean Mode – unaffected by extreme scores – represents the largest number in sample – applicable to nominal data Median – unaffected by extreme scores – scale properties not required Disadvantages Mean – influenced by extreme scores – value may not exist in the data – requires faith in interval measurement Mode – depends on how data is grouped – may not be representative of entire results Median – not entered readily into equations – less stable from sample to sample Bar Chart 10 Median Modes 8 6 4 Count 2 0 7.00 15.00 12.00 TOT ALSSS 19.00 17.00 23.00 21.00 27.00 25.00 31.00 29.00 33.00 Histogram Mode =14+15+16 16 14 12 10 8 6 4 2 Std. Dev = 6.20 0 N = 74.00 Mean = 21.6 7.5 12.5 10.0 TOTALSSS 17.5 15.0 22.5 20.0 27.5 25.0 32.5 30.0 35.0 Another Example Mean = 18.9 Median = 21 Mode = 32 Bar Chart 10 8 6 4 Count 2 0 2.00 6.00 4.00 BIMODAL 13.00 8.00 19.00 16.00 24.00 22.00 28.00 26.00 32.00 30.00 35.00 Histogram Histogram 14 12 10 8 6 Frequency 4 Std. Dev = 11.73 Mean = 18.9 N = 74.00 2 0 2.5 7.5 5.0 BIMODAL 12.5 10.0 17.5 15.0 22.5 20.0 27.5 25.0 32.5 30.0 35.0 Describing Distributions • • • • • • Normal Bimodal Negatively skewed Positively skewed Platykurtic (no neck) Leptokurtic (leap out) 16 N = 74.00 Mean = 21.6 Median = 22 Mode = 23 14 12 10 8 6 4 2 Std. Dev = 6.20 0 7.5 12.5 10.0 17.5 15.0 TOTALSSS 22.5 20.0 27.5 25.0 32.5 30.0 35.0 Histogram 30 N = 74.00 Mean = 21.6 20 Median = 22 Frequency 10 Mode = 23 Std. Dev = 1.16 0 19.0 20.0 SAMEMEAN 21.0 22.0 23.0 Measures of Variability • Range - distance from lowest to highest score • Interquartile range (H spread) - range after top/bottom 25% of scores removed |X-X| E • Mean absolute deviation = N Measure of Variability Variance Standard deviation (X-X) E s = N-1 2 2 SD = E(X-X) N-1 2 Degrees of Freedom • When estimating the mean we lose one degree of freedom • Dividing by N-1 adjust for this and has a greater impact on small sample sizes • It works Mean & Variance as Estimators • • • • Sufficiency Unbiasedness Efficiency Resistance Linear Transformations • Multiply/divide each X by a constant and/or add/subtract a constant Rules • Adding a constant to a set of data adds to the mean • Multiplying by a constant multiplies the mean • Adding a constant has no impact on variance • Multiplying by a constant multiplies the variance by the square of the constant