• The topics, methods and techniques in this exercise represent CORE concepts. They demonstrate a level of 'mastery' of Geospatial Analysis -- using GIS and related tools.  Listed below, in no particular order, are some of these analytical skills embedded in the exercise:

 
• Measuring Differences and Change: A basic requirement of comparison measurements is that they MUST be standardized, normalized, or dimensionless.  Comparisons based on RAW numbers are very rarely useful.
 
Some common examples are Density ( Number_of_Subjects / Unit_Area), Per Capita (like Percapita GNP), Proportions (like percentage), Ratios, Indexes,  and measures of Central Tendency (Mean/Average for normally or symetrically distributed variables, OR Median or Mode for skewed or oddly distributed data).

The basic 'formula' for Percent Change is:

    NewTotal - OldTotal / OldTotal     for example    105 - 100 / 100 = 0.05  or (if *100) 5 percent
 

• Using Maps to Generate/Test Hypotheses: If something is a 'geographic question' it should reveal some trend or pattern on the map.  If not, its just a question.  Sometimes the trend or pattern isn't obvious and requires using a standardized, normalized or dimensionless transformation of the data to become visible (as above).

Map Analysis and Comparison are basic geographic tools.  However, comparing HomeValue1990 with HomeValue2000 side-by-side may exhibit a confusing pattern.  Comparing PercentChange1990-2000 in HomeValues and PopulationChange side-by-side might suggest that areas with higher growth rates had larger increases in home prices -- or not!

Testing such a hypothesis may be a multi-step process:

• IF the maps show no similarities (i.e. Areas of High Growth have average or below-average change in prices), then REJECT the hypothesis .. end of story.
• IF there appears to be a trend, then use some statistical correlation technique to establish both the Strength of the Relationship AND the level of statistical significance.  This step would require the Attribute Table to be copied and used in a statistics program.  For really basic statistics (such as we might use), MS Excel spreadsheet has these functions built-in.
• Use whatever software/technique that works and is appropriate to the task.  The perfect GIS package has yet to be released.  Database programs, stat packages and spreadsheets all do some things better than ArcGIS.  All good GIS analysts can move data between programs to get results.

• A Note on Attribute Tables and Excel.  All ArcGIS attributes in Shapefiles are stored as dBase (.DBF) format.  Excel can open and save this type of file ... BUT things can go wrong and data can disappear   when saved.
This often happens when Formulas are used to calculate new fields.  Here are some tips/requirements when creating/calculating new data fields in Excel:
 
• Field Names must be in the 1st Row.  Names must begin with a letter (A,B,C..) , MUST BE LESS than 8 characters in length, cannot contain spaces OR special characters ($&^..)
• Formulas which reference other fields to calculate a new value (such as percent change) will not be saved correctly -- the .DBF file doesn't do formulas.
• An easy work-around for this problem is to highlight the entire spreadsheet and COPY to the clipboard.  Then open a New, Blank Worksheet and PASTE-SPECIAL the spreadsheet into the blank one -- using the option to copy ONLY VALUES (not formulas).  This will put all the stuff in potentially dBase-compatible format.
• I usually DELETE columns that already exist in the original attribute table (remember you're using a copy!!!), and only save the new columns and the Primary Key (county name, Tract number .. Feature ID) that you can use to LINK the new data to the existing table.
• Save AS dbase IV .DBF.

• Far and Near -- the geographer's friends.  Distance and Proximity are essential elements in many geospatial analyses. Either something is more, better, easier because it is close to something  .. OR it's better, safer, greener because it is far enough away from something else.  Buffering and Overlays are useful for analysing phenomena and establishing distance relationships. So too are distance gradients -- where the exact distance between features is known (or easily calculated).


IF you know an object's location in space (X,Y or Lat/Lon) and you know the location of another feature (such as the Peak Value Intersection [PVI] of an urban area), THEN you can calculate the distance between them (at least one measure -- 'as the crow flies.')

The distance between each Tract Centroid and the PVI can be calculated as the Hypotenuse of a Right Triangle (X and Y are at right angles to each other!)

                 Dist =  SquareRoot (  [ x₂ - x₁]² + [y₂ - y₁]²  )

This calculation can be done in either ArcGIS tables or Excel.

A Gradient can and should be graphed.  Excel again.  But, most distance gradients in the real world are NOT linear.  Usually some sort of curve -- Excel can try to draw those too .. but it is not necessary.
 

• Using Supplementary Materials.  Whatever data, maps and information you have is never enough to do a good job. Often you are asked to analyse a situation in a place with which you are totally unfamiliar.  For many of us West Coasters, Topeka, Kansas and Washington, D.C. are examples.   Thank heavens for the World-Wide Web!
Get a map (or two).  Is there a big park, public buildings, shopping center, sewage plant .. in areas that appear unusually rich or poor, dense, or otherwise exceptional?  If parts of the study area have missing data (like no people), delete them from the analysis. Don't let those Zeros bias the class intervals or graphs.
 
• Calculating an Index is a multi-step process.  Create intermediate fields and values.  Not only does this strategy simplify the 'formulas' and make it easier to find mistakes earlier (rather than later), but the intermediate values themselves may be potentially useful.
For example, in the 'Index of Dissimilarity' or so-called 'Segregation Index', you must calculate the proportion of African Americans  in each tract [ aa ] of ALL blacks in the city [AA].
 
PctAFAM = [aa/AA] x 100       *** Please note that this is NOT the same as PctBlack in the tract (which is aa/TotPop )


This can be a good map in itself -- How concentrated is  the AA population?

Likewise, the difference in proportions [aa/AA - other/OTHER] should be stored in a separate column PRIOR to finding the Absolute Value!  This makes a neat map -- Where in the City are the two groups MOST disproportionate?  Positive numbers mean "more blacks than would be expected" and negative "more non-blacks than would be expected" on the assumption of equally distributed populations.

Indexes themselves tend to be single numbers -- summarizing the findings for the city as a whole -- and have "known ranges" such as 0 to 100.
 

SegNdx = 1/2  x  SUM(  Abs( aa/AA - other/OTHER )  ) x 100

• The analysis is the fastest and easiest part of the project!  Trust me.  I guarantee that I have spent more hours putting these datasets together so that the analysis is straightforward than you have spent frustrated by dealing with it.  In fact, it is educational to learn how to put such datasets together and I will illustrate how to do just that -- using a smaller, simpler study area -- in a subsequent 'lecture.'  The same ratio -- data preparation to data analysis -- should be expected in all projects you undertake for the rest of your life.  Computers and the internet have made 'acquisition' easier .. but preparation still take the most time and effort.

Honestly, If I'd given you the same problem and required you to acquire and massage the info into usuable attribute tables .. We would probably never see eachother again