Univariate Statistics PSYC6060

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Univariate Statistics PSYC6060

• Peter Hausdorf
• University of Guelph

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Agenda

• Overview of course
• Review of assigned reading material
• Sensation seeking scale
• Howell Chapters 1 and 2
• Student profile

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Course Principles

• Learner centered
• Balance between theory, math and practice
• Fun
• Focus on knowledge acquisition and application

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Course Activities

• Lectures
• Discussions
• Exercises
• Lab

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Terminology

• Random sample
• Population
• External validity
• Discrete
• Parameter

• Random assignment
• Sample
• Internal validity
• Continuous
• Statistic

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Terminology (contd)

• Descriptive vs inferential statistics
• Independent vs dependent variables

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Measurement Scales

• Nominal
• Ordinal
• Interval
• Ratio

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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
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Measures of Central Tendency The Mean
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Measures of Central Tendency The Mode

• Is the most common score (or the score obtained
  from the largest number of subjects)

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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.

N 1

Median Location
2
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Advantages
Mean

• 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

Mode
Median
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Disadvantages
Mean

• 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

Mode
Median
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Bar Chart
Modes
Median
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Histogram
Mode
141516
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Another Example

• Mean 18.9
• Median 21
• Mode 32

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Bar Chart
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Histogram
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Describing Distributions

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

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Median 22
Mode 23
Median 22
Mode 23
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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

X-X
E
N
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Measure of Variability
2
(X-X)
E

s
2
Variance
N - 1
2
Standard deviation
(X-X)
SD
E

N - 1
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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

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Mean Variance as Estimators

• Sufficiency
• Unbiasedness
• Efficiency
• Resistance

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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