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 “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” Defined as: Zuckerman, 1979

Measures of Central Tendency: The Mean X = N O E Mean = Sum of all scores Total number of scores

Is the most common score (or the score obtained from the largest number of subjects) Measures of Central Tendency: The Mode

The score that corresponds to the point at or below which 50% of the scores fall when the data are arranged in numerical order. Measures of Central Tendency: The Median Median Location = N + 1 2

Advantages –can be manipulated algebraically –best estimate of population mean –unaffected by extreme scores –represents the largest number in sample –applicable to nominal data –unaffected by extreme scores –scale properties not required Mean Mode Median

Disadvantages –influenced by extreme scores –value may not exist in the data –requires faith in interval measurement –depends on how data is grouped –may not be representative of entire results –not entered readily into equations –less stable from sample to sample Mean Mode Median

Bar Chart Median Modes

Histogram = Mode

Another Example Mean = 18.9 Median = 21 Mode = 32

Bar Chart

Histogram

Describing Distributions Normal Bimodal Negatively skewed Positively skewed Platykurtic (no neck) Leptokurtic (leap out)

Median = 22 Mode = 23 Median = 22 Mode = 23

Measures of Variability Range - distance from lowest to highest score Interquartile range (H spread) - range after top/bottom 25% of scores removed Mean absolute deviation = E |X-X| N

Measure of Variability Variance =s Standard deviation 2 N - 1 E 2 (X-X) SD N - 1 E 2 (X-X) =

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 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 Rules