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In this tutorial, we will use the year of 1790, 1870 and 2010 of the States’ Population as the weighting, and we can see the population changing trend across the states.

1790

1. On the right side of the Map Window, in the Catalog pane, expand the Databases folder.
2. Expand the GeographicDistribution.
3. Right-click the USStatesPopTimeline feature class and select Add to New Map.
4. In the Contents pane to the left of the Map Window, right-click the USStatesPopTimeline layer and select Attribute Table.

Now you can see that this table has the population data from year 1790 to 2010 (every 10 years) for the total 51states.

1. Close the Attribute Table.

At this point, you wish to find in the year of 1790 which state is accessible to the most people in the whole region. You will do so using a spatial statistics tool in the Toolbox.

1. In the Analysis tab, click the Tools button. In the Geoprocessing pane to the right of the Map Window, search for ‘Central Feature’. Select Central Feature (Spatial Statistics Tools).
2. For the ‘Input Feature Class’, use the drop-down menu, select USStatesPopTimeline.
3. Click the Brows button next to the ‘Output Feature Class’ menu. Make sure that the file is in the GeographicDistributionData geodatabase and name it USStatesPopTimeline_CentralFeature_1790.
4. In ‘Weight Field,’ select Pop1790.
5. Leave other fields as default.
6. Ensure your Geoprocessing pane appears as shown below. Select Run.

1870

As the Geoprocessing pane doesn’t reset after the tool is complete, it is easy to rerun tools.

1. For ‘Output Feature Class’, rename the layer ‘USStatesPopTimeline_CentralFeature_1870’.
2. In ‘Weight Field,’ select Pop1870.
3. Leave other fields as default.
4. Ensure your Central Feature window appears as shown below. Select Run.

2010

1. In ‘Weight Field,’ select Pop2010.
2. For ‘Output Feature Class’, rename the layer ‘USStatesPopTimeline_CentralFeature_2010’.
3. Leave other fields as default.
4. Ensure your Central Feature window appears as shown below. Select Run.

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The mean center is the average x and y coordinate of all the features in the study area. It's useful for tracking changes in the distribution or for comparing the distributions of different types of features.

1790

1. In the Geoprocessing pane, click the Back Arrow. In the search bar, search for ‘Mean Center’. Select Mean Center (Spatial Statistics Tools).
2. For the ‘Input Feature Class’ drop-down menu, select USStatesPopTimeline.
3. In ‘Output Feature Class,’ rename the layer ‘USStatesPopTimeline_MeanCenter_1790’.
4. In ‘Weight Field,’ select Pop1790.
5. Leave other fields as default.
6. Ensure your Geoprocessing pane appears as shown below. Select Run.

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You may hear of the standard deviation within a dataset, but if you want to measure the compactness of a distribution in a map, the following tool would come as handy.

1790

1. In the Geoprocessing pane, click the Back Arrow. In the search bar, search for ‘Standard Distance’. Select Standard Distance (Spatial Statistics Tools).
2. For the ‘Input Feature Class’ drop-down menu, select USStatesPopTimeline.
3. In ‘Output Feature Class’, rename the layer ‘USStatesPopTimeline_StandardDistance_1790’.
4. In the ‘Circle Size’ drop-down menu, leave it as 1 standard deviation.
5. In ‘Weight Field,’ select Pop1790.
6. Leave other fields as default.
7. Ensure your Standard Distance window appears as shown below. Select Run.

2010

1. Rename the ‘Output Feature Class’ menu ‘USStatesPopTimeline_StandardDistance_2010’.
2. In ‘Weight Field,’ select Pop2010.
3. Leave other fields as default.
4. Ensure your Standard Distance window appears as shown below. Select Run.

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Besides the compactness of the distribution, we can choose to find the directional trend, which calculate the standard distance separately in the x and y directions. These two measures define the axes of an ellipse encompassing the distribution of features, which is referred to as the standard deviational ellipse. The ellipse allows you to see if the distribution of features is elongated and hence has a particular orientation.

1790-1SD

1. In the Geoprocessing pane, click the Back Arrow. In the search bar, search for ‘Directional Distribution. Select Directional Distribution (Standard Deviational Ellipse) (Spatial Statistics Tools).
2. For the ‘Input Feature Class’ drop-down menu, select USStatesPopTimeline.
3. In ‘Output Feature Class’, rename the layer ‘USStatesPopTimeline_DirectionalDistribution1_1790’.
4. In the ‘Circle Size’ drop-down menu, leave it as 1 standard deviation.
5. In ‘Weight Field,’ select Pop1790.
6. Leave other fields as default.
7. Ensure your Standard Distance window appears as shown below. Select Run.

1790-2SD

1. In the ‘Ellipse Size’ drop-down menu, change to 2 standard deviations.
2. In ‘Weight Field,’ make sure Pop1790 is selected.
3. Leave other fields as default.
4. Ensure your Directional Distribution window appears as shown below. Select Run.

2010-1SD

1. Rename the ‘Output Feature Class’ ‘USStatesPopTimeline_DirectionalDistribution1_2010’.
2. In ‘Ellipse Size’, select 1 standard deviation.
3. In ‘Weight Field,’ select Pop2010.
4. Leave other fields as default.
5. Ensure your Directional Distribution window appears as shown below. Press OK.

2010-2SD

1. Rename the ‘Output Feature Class’ ‘USStatesPopTimeline_DirectionalDistribution2_2010’.
2. In ‘Ellipse Size,’ change to 2 standard deviations.
3. In ‘Weight Field,’ select Pop2010.
4. Leave other fields as default.
5. Ensure your Directional Distribution window appears as shown below. Press OK.

You can see that the trend from the population distribution of 1790 to 2010.

The trend for a set of line features is measured by calculating the average angle of the lines. The statistic used to calculate the trend is known as the directional mean. The Linear Directional Mean tool lets you calculate the mean direction or the mean orientation for a set of line.

1. Click the X on the top right corner of the Geoprocessing pane.
2. In the Catalog pane, expand the Databases folder, and expand the GeographicDistributionData geodatabase. Drag the InnerLoopRoadsDissolved and the HoustonFreewaysDissolved feature classes into the Map Display.
3. In the Contents pane, right-click on the InnerLoopRoadsDissolved layer and click Zoom to Layer.
4. In the Analysis tab, click on the Tools button. In the Geoprocessing search bar, search for ‘Linear Directional Mean’. Select Linear Directional Mean (Spatial Statistics Tools).
5. For the ‘Input Feature Class’ drop-down menu, select InnerLoopRoadsDissolved.
6. In ‘Output Feature Class’, rename it ‘innerLoopRoadsDissolved_DirectionalMean’.
7. Leave other fields as default.
8. Ensure your Linear Directional Mean pane appears as shown below. Select Run.

Roads

Freeways

1. In the ‘Input Feature Class’ drop-down menu, select HoustonFreewaysDissolved.
2. In ‘Output Feature Class’, rename it ‘HoustonFreewaysDissolved_DirectionalMean’.
3. Leave other fields as default.
4. Ensure your Linear Directional Mean pane appears as shown below. Select Run.

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