i. introduction to data and statistics
DESCRIPTION
I. Introduction to Data and Statistics. A. Basic terms and concepts Data set - variable - observation - data value. CentralGulf States. age. > 65. < 19. $. Rent $. 53. 19. 34. 98. 25. TX. 34. 14. 58. 89. 78. LA. MS. 35. 65. 78. 25. 56. 25. 78. 65. 12. 89. AL. - PowerPoint PPT PresentationTRANSCRIPT
I. Introduction to Data and Statistics
A. Basic terms and concepts
Data set
- variable
- observation
- data value
5625786535
8912657825
7889581434
2598341953TX
> 65 $< 19 Rent $age
LA
AL
MS
CentralGulf States
B. Primary and Secondary data
1. Primary data
- original data
- collected for a specific purpose
- sample design and procedures
- time and $
2. Secondary data
- archival data
- agency or organization
- organized in a set format
- time and $
- data quality an issue
- sample design
C. Individual and spatially aggregated data
State 1
State 4State 3
State 2
State 1
State 4State 3
State 2
Region
Region
D. Discreet and Continuous data
1. Discreet
2. Continuous
E. Qualitative and Quantitative data
1. Qualitative (categorical)
Ex: land cover, sex, political party, race
2. Quantitative
Ex: population, precipitation, grades
II. Scales of Measurement
A. Nominal
B. Ordinal
C. Interval
D. Ratiofor comparison must use the same scale of measurement
A. Nominal
Name: George = 1, Wanda = 2, Bob = 3
Land Cover: Forested = 45, urban = 39, etc...
Climate regimes: polar = 1, temperate = 2, tropical = 3
Sex: Male = 1, Female = 2
- Mutually exclusive
- Exhaustive
Ex:
B. Ordinal
- ranked data
- arbitrary
- comparisons
- not a set interval between rankings
Ex:
Places rated (cities, beaches…)
Level of satisfaction (poor, ok, good)
C. Interval
- separated by absolute differences
- does not have an absolute zero
Ex:
- temperature
- elevation
D. Ratio
- separated by absolute differences
- absolute zero
Ex:
- precipitation
- tree growth
- income
III. Graphing procedures (univariate)
A. frequency histogramB. cumulative histogram
1000 50
A. frequency histogram
Freq.
(#, %)
income, grades
(-)
(+)(frequency polygon)
0 50
B. Cumulative frequency histogram
Cumu- lative Freq.
(#, %)
(-)
(+)
100
(cumulative frequency polygon)
IV. Descriptive Statistics (univariate)- summary of data characteristics- inferential; extend sample to a larger population
A. Measures of Central TendencyB. Measures of DispersionC. Measures of Shape
A. Measures of Central Tendency• attempt to define the most typical value of a larger data set
1. Mode2. Median3. Mean (average)
Mode (nominal only)• value that occurs most frequently
• only measure of central tendency appropriate for nominal level data• works better for grouped data, not raw values• many data sets will not have two exact data sets
2. Median• the middle value from a set of ranked observations• equal number of observations on either side• appropriate when data is heavily skewed• interval or ratio level data, not nominal
3. Mean (average), .xi / n• most commonly used value of central tendency• interval or ratio level data• sensitive to outliers• most easily understood• assumptions:
• unimodal• symmetric distribution
(-) (+)
0 100
mode
median
mean
Normal distribution
50
(-) (+)
0 10050
mode
median
mean
B. Measures of Dispersion• provide information about distribution of data
1. Range2. Standard deviation3. Coefficient of variation
1. Rangedifference between largest and smallest value
• simplest measure of dispersion• easy to calculate• can be misleading
• ignores all other values• does not take into account clustering of data
2. Standard deviation• the average deviation of each value from the mean
• based on the mean• better indicator of the dispersion of the entire sample (in comparison to the range)• scale dependent value
3. Coefficient of variation• standard deviation / mean
• allows you to compare dispersion independent of scale• should be used to make comparisons where there are differences in mean
(-) (+)
15 8550
Range: 85 - 15 = 70
1000
Std. dev. ~ .xi - X
X = 50
C.V. = Std. dev. / mean
C.V. = Std. dev. / mean
C. Measures of Shape
1. Skewness2. Kurtosis
Leptokurtic
Mesokurtic
Platykurtic
(-) skew(+) skewSymmetrical
(bell shaped)
I.D. Xi Yi
A 2.8 1.5B 1.6 3.8C 3.5 3.3D 4.4 2.0E 4.3 1.1F 5.2 2.4G 4.9 3.5
Mean Center
0 6
4 B (1.6, 3.8)
A (2.8, 1.5)
C (3.5, 3.3)
D (4.4, 2.0)
E (4.3, 1.1)
G (4.9, 3.5)
F (5.2, 2.4)
54321
1
2
3
0 6
B (1.6, 3.8)
A (2.8, 1.5)
C (3.5, 3.3)
D (4.4, 2.0)
E (4.3, 1.1)
G (4.9, 3.5)
F (5.2, 2.4)Mean Center (3.81, 2.51)
54321
1
2
3
4
I.D. Xi Yi f (w)
A 2.8 1.5 5B 1.6 3.8 20C 3.5 3.3 8D 4.4 2.0 4E 4.3 1.1 6F 5.2 2.4 5G 4.9 3.5 3
Weighted Mean Center
0 6
B (20)
A (5)
C (8)
D (4)
E (6)
G (3)
F (5)
54321
1
2
3
4
I.D. Xi Yi f (w) w Xi wYi
A 2.8 1.5 5 14 7.5B 1.6 3.8 20 32 76C 3.5 3.3 8 28 26.4D 4.4 2.0 4 17.6 8.0E 4.3 1.1 6 25.8 6.6F 5.2 2.4 5 26 12G 4.9 3.5 3 14.7 10.5
0 6
B (20)
A (5)
C (8)
D (4)
E (6)
G (3)
F (5)
54321
1
2
3
4
Weighted MeanCenter (3.10, 2.88)
Correlation
1. Directionnegative or positive
2. Strength of relationshipperfect, strong, weak, no
- Bivariate relationship
Scattergrams
(-) (+)
(+)
Positive (direct) correlation
(-) (+)
(+)
Negative (inverse) correlation
(-) (+)
(+)
Perfect correlation
(-) (+)
(+)
Strong correlation
(-) (+)
(+)
Weak correlation
(-) (+)
(+)
No correlation ??
(-) (+)
(+)
Controlled Correlation
(-) (+)
(+)
Controlled correlation (clumping)
(-) (+)
(+)
(-) (+)
(+)
Threshold
(-) (+)
(+)
Curvilinear