I. Introduction to Data and Statistics A. Basic terms and concepts Data set - variable - observation - data value

TX > 65$< 19Rent $age LA AL MS Central Gulf 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

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. Ratio for 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 histogram B. cumulative histogram

A. frequency histogram Freq. (#, %) income, grades (-) (+) (frequency polygon)

050 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 Tendency B. Measures of Dispersion C. Measures of Shape

A. Measures of Central Tendency attempt to define the most typical value of a larger data set 1. Mode 2. Median 3. 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), .x i / n most commonly used value of central tendency interval or ratio level data sensitive to outliers most easily understood assumptions: unimodal symmetric distribution

(-) (+) 0100 mode median mean Normal distribution 50

(-) (+) mode median mean

B. Measures of Dispersion provide information about distribution of data 1. Range 2. Standard deviation 3. Coefficient of variation

1. Range difference 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

(-) (+) Range: = Std. dev. ~ .x i - X X = 50 C.V. = Std. dev. / mean

C. Measures of Shape 1. Skewness 2. Kurtosis

Leptokurtic Mesokurtic Platykurtic

(-) skew (+) skew Symmetrical (bell shaped)

Mean Center

06 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)

06 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)

Weighted Mean Center

06 B (20) A (5) C (8) D (4) E (6) G (3) F (5)

06 B (20) A (5) C (8) D (4) E (6) G (3) F (5) Weighted Mean Center (3.10, 2.88)

Correlation 1. Direction negative or positive 2. Strength of relationship perfect, 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