S519: Evaluation of Information Systems

1
S519 Evaluation of Information Systems

• Social Statistics
• Ch3 Difference

2
Last week

• Social statistics
• Descriptive statistics
• Inferential statistics
• Mean, median and mode

3
This week

• Range
• Standard deviation
• Variance
• Using Excel to calculate them

4
The whole story

• Descriptive statistics
• Centrality tendency (average)
• Measurement of variability (variability)
• AverageVariability describe the
  characteristics of a set of data

5
Measures of variability

• Variability
• How scores differ from one another
• Three sets of data
• 7, 6, 3, 3, 1
• 3, 4, 4, 5, 4
• 4, 4, 4, 4, 4
• Variability the difference from the mean

6
Measures of variability

• Three ways
• Range
• Standard deviation
• Variance

7
Range

• The most general measure of variability
• How far apart scores are from one another

Range highest score lowest score
What is the range for 98, 86, 77, 56, 48
8
Standard deviation

• Standard deviation (SD)
• Average deviation from the mean (average distance
  from the mean)
• Represents the average amount of variability

9
Exercise
Lab

• Calculate standard deviation
• 5, 8, 5, 4, 6, 7, 8, 8, 3, 6
• By hand
• Using excel (STDEV())

10
STDEV and STDEVP

• STDEV is standard deviation for sample (biased
  SD)
• STDEVP is standard deviation for population
  (unbiased SD)
• If your dataset is the whole population, use
  STDEVP to calculate standard deviation
• If you dataset is the sample of something, use
  STDEV to calculate standard deviation

11
STDEV and STDEVP
STDEV
STDEVP
12
Why n or n-1?

• To be conservative
• STDEV
• This is the standard deviation for sample
• Take n-1 in order to make STDEV a bit larger than
  it would be.
• If we have err, we compensate by overestimating
  the STDEV

13
Why n or n-1?
Sample size Numerator in standard deviation formula Denominator Population standard deviation STDEVP (dividing by n) Denominator Sample standard deviation STDEV (dividing by n-1) Difference between STDEVP and STDEV
10 500 7.07 7.45 0.38
100 500 2.24 2.25 0.01
1000 500 0.7071 0.7075 0.0004
14
What to remember

• Standard Deviation (SD) the average distance
  from the mean
• The larger SD, the more different data are from
  one another
• Since mean is sensitive to extreme scores, so do
  SD
• If SD0, this means that there is no variability
  in the set of scores (they are all identical in
  value) this happens very rarely.

15
Variance

• Variance (Standard Deviation)2

16
Exercise
Lab

• Calculate variance in Excel
• 8, 8, 8, 7, 6, 6, 5, 5, 4, 3
• Var() ? STDEV
• Varp() ? STDEVP

17
SD vs. variance

• Often appears in the Results sections of
  journals
• They are quite different
• Variance is squared SD

18
SD vs. variance
mean
Average distance to mean(22211123)/101.4
SD 1.76 Variance 3.1
19
Exercise 1 (S-p78-problem2)
Lab

• Calculate range, STDEV and STDEVP and variance by
  hand or calculator
• 31, 42, 35, 55, 54, 34, 25, 44, 35
• Use Excel to do that.

20
Exercise 2 (S-p79-problem4)
Lab
Height Weight
53 156
46 131
54 123
44 142
56 156
76 171
87 143
65 135
45 138
44 114
57 154
68 166
65 153
66 140
54 143
66 156
51 173
58 143
49 161
48 131

• Problem 4 in S-p79
• Calculate the variation measures for height and
  weight

21
Exercise 3 (S-p79-problem5)
Lab
Western Airlines Flight Report            
             
  Thursday Friday Thursday Friday Thursday Friday
Morning Flights To Kansas To Kansas To Philadelphia To Philadelphia To Providence To Providence
Number of passengers 258 251 303 312 166 176
             
  Thursday Friday Thursday Friday Thursday Friday
Evening Flights To Kansas To Kansas To Philadelphia To Philadelphia To Providence To Providence
Number of passengers 312 331 321 331 210 274
             
22
Exercise 3 (S-p79-problem5)
Lab

• Look at problem 5
• Write a half page summary report to your boss
• Form a group to discuss it