## NR 512 – Spatial Statistical Modeling

## Exercise #2 – Centrographic Statistics in ArcMap

Centrographic statistics are simple descriptive statistics often use for exploratory data analysis in spatial statistics. Centrographic statistics such as Mean Center, Standard Distance, Standard Distance Ellipse and their weighted counterparts can be used to assist in hypothesis development and spatial distribution characterization for spatially referenced datasets.

This goal of today’s lab is to demonstrate how we can use ArcMap 10 to quickly calculate centrographic statistics.

**The dataset: **Today you will be working with a sample dataset that is described in Chapters 2 and 3 of the Isaaks book, which is available on Canvas. The data are spatially referenced across a 10 X 10 grid and containing measurements of two covariates: V and U.

The database is named ‘lab1_data.csv’. This is the same dataset from last week’s lab.

**Exercise 1 – Being Organized:**

- Think about where on your computer you would like to store your project materials. Create a class directory there, with sub directories for associated lab materials.
- Make sure that the lab1_data.csv is stored in your newly created lab2 directory within your spatial stats class directory. You can rename the data to ‘lab2_data.csv’ if you like.

**Exercise 2 – Adding data into ArcMap10:**

- Start ArcMap10
- Use the Add Data option to load the ‘lab2_data.csv’ as a table into ArcMap.
- To show the XY coordinates, right click on the loaded table in ArcMap’s table of contents and select Display XY Data…
- Convert the csv points to a shapefile by right clicking on it in ArcMap’s table of contents, navigated to the Data options and selecting Export Data. Save the shapefile with an appropriate name in your lab2 directory and load the shapefile back to the map.
- Ask the instructor for help on steps 2, 3, and 4 if you are having trouble.

**Exercise 3 – Calculating Centrographic Statistics via the Spatial Statistics Toolbox**

ArcMap’s spatial statistics toolbox contains statistical tools for analyzing the distribution of geographic features: finding the geographic center, identifying statistically significant spatial clusters (hot spots) or outliers, assessing overall patterns of clustering or dispersion, and so on. Spatial statistics differ from traditional statistics in that space and spatial relationships are an integral and implicit component of their mathematics. The tools in the Spatial Statistics toolbox demonstrate a variety of statistical operations appropriate for analyzing geographic data.

Open ArcMap’s Spatial Statistics Toolbox and explore the variety of spatial statistics tools available.

As you conduct each of these assessments, turning off some layers or color coordinating across weighting features might help you understand patterns within the data.

- Use the mean center tool to calculate the mean center of the lab2 dataset.

Report the mean center coordinates: X:_______, Y:________

- Use the weighted mean center tool to calculate mean center of the lab2 dataset weighted by the
.*V covariate*

Report the mean center coordinates of the ** V covariate**: X:_______, Y:________

- Use the weighted mean center tool to calculate mean center of the lab2 dataset weighted by the
.*U covariate*

Report the mean center coordinates of the ** U covariate**: X:_______, Y:________

- Describe the difference in the weighted mean center of the
*V and U covariates:*

___________________________________________________________________________________________________________________________________________________

How are these 2 distributions related?

___________________________________________________________________________________________________________________________________________________

What basic hypotheses could this inform?

___________________________________________________________________________________________________________________________________________________

- Use the Standard Distance tool to calculate the standard distance of the lab2 dataset.

Report the standard distance and your assumptions: _______________________________

- Use the weighted Standard Distance to calculate standard distance of the lab2 dataset weighted by the
.*V covariate*

Report the weighted standard distance of the ** V covariate:** ____________________________

Do you see any directionality in the weighted Standard Distance?

- Use the weighted Standard Distance to calculate standard distance of the lab2 dataset weighted by the
.*U covariate*

Report the weighted standard distance of the ** U covariate:** _____________________________

Do you see any directionality in the weighted Standard Distance?

Compare the standard distance between the ** V and U covariates. **Which covariate is more variable? How do you know this?

- Use the Directional Distribution tool to calculate the Standard Deviational Ellipse of the lab2 dataset.

Dose the Standard Deviational Ellipse look any different than the Standard Distance, Why or

Why not? Consider the data’s spatial arrangement:

- Use the weighted Directional Distribution tool to calculate Standard Deviational Ellipse of the lab2 dataset weighted by the
and then again by the*V covariate*.*U covariate*

Report the weighted Standard Deviational Ellipse of the *V covariate: *

Rotation: ______________ X-axis: ______________ Y-axis: ______________

Report the weighted Standard Deviational Ellipse of the *U covariate:*

Rotation: ______________ X-axis: ______________ Y-axis: ______________

Compare the Standard Deviational Ellipse between the ** V and U covariates. **Which covariate is more variable?

Do you see any directionality in the weighted Standard Deviational Ellipses?

Is there a difference in directionality between Standard Deviational Ellipses of the *V and U **covariates?
*

Describe how the outputs from the Standard Deviational Ellipse might link to the concepts of isotropic and anisotropic data that we talked about:

Describe the difference you see and discuss a possible hypothesis:

We will talk about many of the other tools contained in the Spatial Statistics Toolbox, both in ArcMap and in R, as we move through the semester.