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

Mean=Sum of all scores

Total number ofscores

• 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

TOTALSSS

33.00

31.00

29.00

27.00

25.00

23.00

21.00

19.00

17.00

15.00

12.00

7.00

Co

un

t

10

8

6

4

2

0

Median Modes

Histogram

TOTALSSS

35.0

32.5

30.0

27.5

25.0

22.5

20.0

17.5

15.0

12.5

10.0

7.5

16

14

12

10

8

6

4

2

0

Std. Dev = 6.20

Mean = 21.6

N = 74.00

=14+15+16Mode

Another Example

Mean = 18.9

Median = 21

Mode = 32

Bar Chart

BIMODAL

35.00

32.00

30.00

28.00

26.00

24.00

22.00

19.00

16.00

13.00

8.00

6.00

4.00

2.00

Co

un

t

10

8

6

4

2

0

Histogram

BIMODAL

35.0

32.5

30.0

27.5

25.0

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

2.5

Histogram

Fre

qu

en

cy

14

12

10

8

6

4

2

0

Std. Dev = 11.73

Mean = 18.9N = 74.00

Describing Distributions

• Normal

• Bimodal

• Negatively skewed

• Positively skewed

• Platykurtic (no neck)

• Leptokurtic (leap out)

TOTALSSS

35.032.5

30.027.5

25.022.5

20.017.5

15.012.5

10.07.5

16

14

12

10

8

6

4

2

0Std. Dev = 6.20

Mean = 21.6

N = 74.00

SAMEMEAN

23.022.021.020.019.0

Histogram

Fre

quen

cy

30

20

10

0Std. Dev = 1.16

Mean = 21.6

N = 74.00

Median = 22Mode = 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 = |X-X|

N

Measure of Variability

Variance =s

Standarddeviation

2

N - 1

2

(X-X)

SDN - 1

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