excel

Percentage of Children in Households Without the Internet

Kids with No Internet at Home: Data Processing for US Census Mapping

In this post I’ll demonstrate some essential data processing steps prior to joining census American Community Survey (ACS) tables downloaded from data.census.gov to TIGER shapefiles, in order to create thematic maps. I thought this would be helpful for students in my university who are now doing GIS-related courses from home, due to COVID-19. I’ll illustrate the following with Excel and QGIS: choosing an appropriate boundary file for making your map, manipulating geographic id codes (GEOIDs) to insure you can match data file to shapefile, prepping your spreadsheet to insure that the join will work, and calculating new summaries and percent totals with ACS formulas. Much of this info is drawn from the chapters in my book that cover census geography (chapter 3), ACS data (chapter 6), and GIS (chapter 10). I’m assuming that you already have some basic spreadsheet, GIS, and US census knowledge.

For readers who are not interested in the technical details, you still may be interested in the map we’ll create in this example: how many children under 18 lack access to a computer with internet access at home? With COVID-19 there’s a sudden expectation that all school children will take classes remotely from home. There are 73.3 million children living in households in the US, and approximately 9.3 million (12.7%) either have no computer at home, or have a computer but no internet access. The remaining children have a computer with either broadband or dial-up at home. Click on the map below to explore the county distribution of the under 18 population who lack internet access at home, or follow this link: https://arcg.is/0TrGTy.

arcgis_webmap

Click on the Map to View Full Screen and Interact

Preliminaries

First, we need to get some ACS data. Read this earlier post to learn how to use data.census.gov (or for a shortcut download the files we’re using here). I downloaded ACS table B28005 Age by Presence of a Computer and Types of Internet Subscription in Household at the county-level. This is one of the detailed tables from the latest 5-year ACS from 2014-2018. Since many counties in the US have less than 65,000 people, we need to use the 5-year series (as opposed to the 1-year) to get data for all of them. The universe for this table is the population living in households; it does not include people living in group quarters (dormitories, barracks, penitentiaries, etc.).

Second, we need a boundary file of counties. You could go to the TIGER Line Shapefiles, which provides precise boundaries of every geographic area. Since we’re using this data to make a thematic map, I suggest using the Cartographic Boundary Files (CBF) instead, which are generalized versions of TIGER. Coastal water has been removed and boundaries have been smoothed to make the file smaller and less detailed. We don’t need all the detail if we’re making a national-scale map of the US that’s going on a small screen or an 8 1/2 by 11 piece of paper. I’m using the medium (5m) generalized county file for 2018. Download the files, put them together in a new folder on your computer, and unzip them.

TIGER Line shapefile

TIGER Line shapefile

CBF shapefile

CBF shapefile

GEOIDs

Downloads from data.census.gov include three csv files per table that contain: the actual data (data_with_overlays), metadata (list of variable ids and names), and a description of the table (table_title). There are some caveats when opening csv files with Excel, but they don’t apply to this example (see addendum to this post for details). Open your csv file in Excel, and save it as an Excel workbook (don’t keep it in a csv format).

The first column contains the GEOID, which is a code that uniquely identifies each piece of geography in the US. In my file, 0500000US28151 is the first record. The part before ‘US’ indicates the summary level of the data, i.e. what the geography is and where it falls in the census hierarchy. The 050 indicates this is a county. The part after the ‘US’ is the specific identifier for the geography, known as an ANSI / FIPS code: 28 is the state code for Mississippi, and 151 is the county code for Washington County, MS. You will need to use this code when joining this data to your shapefile, assuming that the shapefile has the same code. Will it?

That depends. There are two conventions for storing these codes; the full code 0500000US28151 can be used, or just the ANSI / FIPS portion, 28151. If your shapefile uses just the latter (find out by adding the shapefile in GIS and opening its attribute table), you won’t have anything to base the join on. The regular 2018 TIGER file uses just the ANSI / FIPS, but the 2018 CBF has both the full GEOID and the ANSI FIPS. So in this case we’re fine, but for the sake of argument if you needed to create the shorter code it’s easy to do using Excel’s RIGHT formula:

Excel formula: RIGHT

The formulas RIGHT, LEFT, and MID are used to return sub-strings of text

The formulas reads X characters from the right side of the value in the cell you reference and returns the result. You just have to count the number of characters up to the “S’ in the “US”. Copy and paste the formula all the way down the column. Then, select the entire column, right click and chose copy, select it again, right click and choose Paste Special and Values (in Excel, the little clipboard image with numbers on top of it). This overwrites all the formulas in the column with the actual result of the formula. You need to do this, as GIS can’t interpret your formulas. Put some labels in the two header spaces, like GEO_ID2 and id2.

Excel: Paste Special

Copy a column, and use Paste Special – Values on top of that column to overwrite formulas with values

Subsets and Headers

It’s common that you’ll download census tables that have more variables than you need for your intended purpose. In this example we’re interested in children (people under 18) living in households. We’re not going to use the other estimates for the population 18 to 64 and 65 and over. Delete all the columns you don’t need (if you ever needed them, you’ve got them saved in your csv as a backup).

Notice there are two header rows: one has a variable ID and the other has a label. In ACS tables the variables always come in pairs, where the first is the estimate and the second is the margin of error (MOE). For example, in Washington County, Mississippi there are 46,545 people living in households +/- 169. Columns are arranged and named to reflect how values nest: Estimate!!Total is the total number of people in households, Estimate!!Total!!Under 18 years is the number people under 18 living in households, which is a subset of the total estimate.

The rub here is that we’re not allowed to have two header rows when we join this table to our shapefile – we can only have one. We can’t keep the labels because they’re too long – once joined, the labels will be truncated to 10 characters and will be indistinguishable from each other. We’ll have to delete that row, leaving us with the cryptic variable IDs. We can choose to keep those IDs – remember we have a separate metadata csv file where we can look up the labels – or we can rename them. The latter is feasible if we don’t have too many. If you do rename them, you have to keep them short, no more than 10 characters or they’ll be truncated. You can’t use spaces (underscores are ok), any punctuation, and can’t begin variables names with a number. In this example I’m going to keep the variable IDs.

Two odd gotchas: first, find the District of Columbia in your worksheet and look at the MOE for total persons in households (variable 001M). There is a footnote for this value, five asterisks *****. Replace it with a zero. Keep an eye out for footnotes, as they wreak havoc. If you ever notice that a numeric column gets saved as text in GIS, it’s probably because there’s a footnote somewhere. Second, change the label for the county name from NAME to GEO_NAME (our shapefile already has a column called NAME, and it will cause problems if we have duplicates). If you save your workbook now, it’s ready to go if you want to map the data in it. But in this example we have some more work to do.

Create New ACS Values

We want to map the percentage of children that do not have access to either a computer or the internet at home. In this table these estimates are distinct for children with a computer and no internet (variable 006), and without a computer (variable 007). We’ll need to aggregate these two. For most thematic maps it doesn’t make sense to map whole counts or estimates; naturally places that have more people are going to have more computers. We need to normalize the data by calculating a percent total. We could do this work in the GIS package, but I think it’s easier to use the spreadsheet.

To calculate a new estimate for children with no internet access at home, we simply add the two values together (006_E and 007_E). To calculate a new margin of error, we take the square root of the sum of the squares for the MOEs that we’re combining (006_M and 007_M). We also use the ROUND formula so our result is a whole number. Pretty straightforward:

Excel Sum of Squares

When summing ACS estimates, take the square root of the sum of the squares for each MOE to calculate a MOE for the new estimate.

To calculate a percent total, divide our new estimate by the number of people under 18 in households (002_E). The formula for calculating a MOE for a percent total is tougher: square the percent total and the MOE for the under 18 population (002_M), multiply them, subtract that result from the MOE for the under 18 population with no internet, take the square root of that result and divide it by the under 18 population (002_E):

MOE for percentage

The formula for calculating the MOE for a proportion includes: the percentage, MOE for the subset population (numerator), and the estimate and MOE for the total population (denominator)

In Washington County, MS there are 3,626 +/- 724 children that have no internet access at home. This represents 29.4% +/- 5.9% of all children in the county who live in a household. It’s always a good idea to check your math: visit the ACS Calculator at Cornell’s Program for Applied Demographics and punch in some values to insure that your spreadsheet formulas are correct.

You should scan the results for errors. In this example, there is just one division by zero error for Kalawao County in Hawaii. In this case, replace the formula with 0 for both percentage values. In some cases it’s also possible that the MOE proportion formula will fail for certain values. Not a problem in our example, but if it does the solution is to modify the formula for the failed cases to calculate a ratio instead. Replace the percentage in the formula with the ratio (the total population divided by the subset population) AND change the minus sign under the square root to a plus sign.

Some of these MOE’s look quite high relative to the estimate. If you’d like to quantify this, you can calculate a coefficient of variation for the estimate (not the percentage). This formula is straightforward: divide the MOE by 1.645, divide that result by the estimate, and multiply by 100:

Calculate coefficient of variation

A CV can be used to gauge the reliability of an estimate

Generally speaking, a CV value between 0-15 indicates that as estimate is highly reliable, 12-34 is of medium reliability, and 35 and above is low reliability.

That’s it!. Make sure to copy the columns that have the formulas we created, and do a paste-special values over top of them to replace the formulas with the actual values. Some of the CV values have errors because of division by zero. Select the CV column and do a find and replace, to find #DIV/0! and replace it with nothing. Then save and close the workbook.

For more guidance on working with ACS formulas, take a look at this Census Bureau guidebook, or review Chapter 6 in my book.

Add Data to QGIS and Join

In QGIS, we select the Data Source Manager buttonQGIS Data Source Manager, and in the vector menu add the CBF shapefile. All census shapefiles are in the basic NAD83 system by default, which is not great for making a thematic map.  Go to the Vector Menu – Data Management Tools – Reproject Layer. Hit the little globe beside Target CRS. In the search box type ‘US National’, select the US National Atlas Equal Area option in the results, and hit OK. Lastly, we press the little ellipses button beside the Reprojected box, Save to File, and save the file in a good spot. Hit Run to create the file.

In the layers menu, we remove the original counties file, then select the new one (listed as Reprojected), right click, Set CRS, Set Project CRS From Layer. That resets our window to match the map projection of this layer. Now we have a projected counties layer that looks better for a thematic map. If we right click the layer and open its attribute table, we can see that there are two columns we could use for joining: AFFGEOID is the full census code, and GEOID is the shorter ANSI / FIPS.

Hit the Data Source Manager button again, stay under the vector menu, and browse to add the Excel spreadsheet. If our workbook had multiple sheets we’d be prompted to choose which one. Close the menu and we’ll see the table in the layers panel. Open it up to insure it looks ok.

To do a join, select the counties layer, right click, and choose properties. Go to the Joins tab. Hit the green plus symbol at the bottom. Choose the spreadsheet as the join layer, GEO_ID as the join field in the spreadsheet, and AFFGEOID as the target field in the counties file. Go down and check Custom Field Name, and delete what’s in the box. Hit OK, and OK again in the Join properties. Open the attribute table for the shapefile, scroll over and we should see the fields from the spreadsheet at the end (if you don’t, check and verify that you chose the correct IDs in the join menu).

QGIS Join Menu

QGIS Map

We’re ready to map. Right click the counties and go to the properties. Go to the Symbology tab and flip the dropdown from Single symbol to Graduated. This lets us choose a Column (percentage of children in households with no internet access) and create a thematic map. I’ve chosen Natural Breaks as the Mode and changed the colors to blues. You can artfully manipulate the legend to show the percentages as whole numbers by typing *100 in the Column box beside the column name, and adding a % at the end of the Legend format string. I also prefer to alter the default settings for boundary thickness: click the Change button beside Symbol, select Simple fill, and reduce the width of the boundaries from .26 to .06, and hit OK.

QGIS Symbology Menu

There we have a map! If you right click on the counties in the layers panel and check the Show Feature Count box, you’ll see how many counties fall in each category. Of course, to make a nice finished map with title, legend, and inset maps for AK, HI, and PR, you’d go into the Print Layout Manager. To incorporate information about uncertainty, you can add the county layer to your map a second time, and style it differently – maybe apply crosshatching for all counties that have a CV over 34. Don’t forget to save your project.

QGIS Map

Percentage of Children in Households without Internet Access by County 2014-2018

How About that Web Map?

I used my free ArcGIS Online account to create the web map at the top of the page. I followed all the steps I outlined here, and at the end exported the shapefile that had my data table joined to it out as a new shapefile; in doing so the data became fused to the new shapefile. I uploaded the shapefile to ArcGIS online, chose a base map, and re-applied the styling and classification for the county layer. The free account includes a legend editor and expression builder that allowed me to show my percentages as fractions of 100 and to modify the text of the entries. The free account does not allow you to do joins, so you have to do this prep work in desktop GIS. ArcGIS Online is pretty easy to learn if you’re already familiar with GIS. For a brief run through check out the tutorial Ryan and I wrote as part of my lab’s tutorial series.

Addendum – Excel and CSVs

While csv files can be opened in Excel with one click, csv files are NOT Excel files. Excel interprets the csv data (plain text values separated by commas, with records separated by line breaks) and parses it into rows and columns for us. Excel also makes assumptions about whether values represents text or numbers. In the case of ID codes like GEOIDs or ZIP Codes, Excel guesses wrong and stores these codes as numbers. If the IDs have leading zeros, the zeros are dropped and the codes become incorrect. If they’re incorrect, when you join them to a shapefile the join will fail. Since data.census.gov uses the longer GEOID this doesn’t happen, as the letters ‘US’ are embedded in the code, which forces Excel to recognize it as text. But if you ever deal with files that use the shorter ANSI / FIPS you’ll run into trouble.

Instead of clicking on csvs to open them in Excel: launch Excel to a blank workbook, go to the data ribbon and choose import text files, select your csv file from your folder system, indicate that it’s a delimited text file, and select your ID column and specify that it’s text. This will import the csv and save it correctly in Excel.

Calculate margin of error for ratio (mean income)

Calculating Mean Income for Groups of Geographies with Census ACS Data

When aggregating small census geographies to larger ones (census tracts to neighborhoods for example) when you’re working with American Community Survey (ACS) data, you need to sum estimates and calculate new margins of error. This is straightforward for most estimates; you simply sum them, and take the square root of the sum of squares for the margins of error (MOEs) for each estimate that you’re aggregating. But what if you need to group and summarize derived estimates like means or medians? In this post, I’ll demonstrate how to calculate mean household income by aggregating ZCTAs to United Hospital Fund neighborhoods (UHF), which is a type of public health area in NYC created by aggregating ZIP Codes.

I’m occasionally asked how to summarize median household income from tracts to neighborhood-like areas. You can’t simply add up the medians and divide them, the result would be completely erroneous. Calculating a new median requires us to sort individual household-level records and choose the middle-value, which we cannot do as those records are confidential and not public. There are a few statistical interpolation methods that we can use with interval data (number of households summarized by income brackets) to estimate a new median and MOE, but the calculations are rather complex. The State Data Center in California provides an excellent tutorial that demonstrates the process, and in my new book I’ll walk through these steps in the supplemental material.

While a mean isn’t as desirable as a median (as it can be skewed by outliers), it’s much easier to calculate. The ACS includes tables on aggregate income, including the sum of all income earned by households and other population group (like families or total population). If we sum aggregate household income and number of households for our small geographic areas, we can divide the total income by total households to get mean income for the larger area, and can use the ACS formula for computing the MOE for ratios to generate a new MOE for the mean value. The Census Bureau publishes all the ACS formulas in a detailed guidebook for data users, and I’ll cover many of them in the ACS chapter of my book (to be published by the end of 2019).

Calculating a Derived Mean in Excel

Let’s illustrate this with a simple example. I’ve gathered 5-year 2017 ACS data on number of households (table B11001) and aggregate household income (table B19025) by ZCTA, and constructed a sheet to correlate individual ZCTAs to the UHF neighborhoods they belong to. UHF 101 Kingsbridge-Riverdale in the Bronx is composed of just two ZCTAs, 10463 and 10471. We sum the households and aggregate income to get totals for the neighborhood. To calculate a new MOE, we take the square root of the sum of squares for each of the estimate’s MOEs:

Calculate margin of error for new sum

Calculate margin of error for new sum

To calculate mean income, we simply divide the total aggregate household income by total households. Calculating the MOE is more involved. We use the ACS formula for derived ratios, where aggregate income is the numerator of the ratio and households is the denominator. We multiply the square of the ratio (mean income) by the square of the MOE of the denominator (households MOE), add that product to the square of the MOE of the numerator (aggregate income MOE), take the square root, and divide the result by the denominator (households):

=(SQRT((moe_ratio_numerator^2)+(ratio^2*moe_ratio_denominator^2))/ratio_denominator)
Calculate margin of error for ratio (mean income)

Calculate margin of error for ratio (mean income)

The 2013-2017 mean household income for UHF 101 is $88,040, +/- $4,223. I always check my math using the Cornell Program on Applied Demographic’s ACS Calculator to make sure I didn’t make a mistake.

This is how it works in principle, but life is more complicated. When I downloaded this data I had number of households by ZCTA and aggregate household income by ZCTA in two different sheets, and the relationship between ZCTAs and UHFs in a third sheet. There are 42 UHF neighborhoods and 211 ZCTAs in the city, of which 182 are actually assigned to UHFs; the others have no household population. I won’t go into the difference between ZIP Codes and ZCTAs here, as it isn’t a problem in this particular example.

Tying them all together would require using the ZCTA in the third sheet in a VLOOKUP formula to carry over the data from the other two sheets. Then I’d have to aggregate the data to UHF using a pivot table. That would easily give me sum of households and aggregate income by UHF, but getting the MOEs would be trickier. I’d have to square them all first, take the sum of these squares when pivoting, and take the square root after the pivot to get the MOEs. Then I could go about calculating the means one neighborhood at a time.

Spreadsheet-wise there might be a better way of doing this, but I figured why do that when I can simply use a database? PostgreSQL to the rescue!

Calculating a Derived Mean in PostgreSQL

In PostgreSQL I created three empty tables for: households, aggregate income, and the ZCTA to UHF relational table, and used pgAdmin to import ZCTA-level data from CSVs into those tables (alternatively you could use SQLite instead of PostgreSQL, but you would need to have the optional math module installed as SQLite doesn’t have the capability to do square roots).

Portion of households table. A separate aggregate household income table is structured the same way, with income stored as bigint type.

Portion of households table. A separate aggregate household income table is structured the same way, with income stored as bigint type.

Portion of the ZCTA to UHF relational table.

Portion of the ZCTA to UHF relational table.

In my first run through I simply tried to join the tables together using the 5-digit ZCTA to get the sum of households and aggregate incomes. I SUM the values for both and use GROUP BY to do the aggregation to UHF. In PostgreSQL pipe-forward slash: |/ is the operator for square root. I sum the squares for each ZCTA MOE and take the root of the total to get the UHF MOEs. I omit ZCTAs that have zero households so they’re not factored into the formulas:

SELECT z.uhf42_code, z.uhf42_name, z.borough,
    SUM(h.households) AS hholds,
    ROUND(|/(SUM(h.households_me^2))) AS hholds_me,
    SUM(a.agg_hhold_income) AS agghholds_inc,
    ROUND(|/(SUM(a.agg_hhold_income_me^2))) AS agghholds_inc_me
FROM zcta_uhf42 z, hsholds h, agg_income a
WHERE z.zcta=h.gid2 AND z.zcta=a.gid2 AND h.households !=0
GROUP BY z.uhf42_code, z.uhf42_name, z.borough
ORDER BY uhf42_code;
Portion of query result, households and income aggregated from ZCTA to UHF district.

Portion of query result, households and income aggregated from ZCTA to UHF district.

Once that was working, I modified the statement to calculate mean income. Calculating the MOE for the mean looks pretty rough, but it’s simply because we have to repeat the calculation for the ratio over again within the formula. This could be avoided if we turned the above query into a temporary table, and then added two columns and populated them with the formulas in an UPDATE – SET statement. Instead I decided to do everything in one go, and just spent time fiddling around to make sure I got all the parentheses in the right place. Once I managed that, I added the ROUND function to each calculation:

SELECT z.uhf42_code, z.uhf42_name, z.borough,
    SUM(h.households) AS hholds,
    ROUND(|/(SUM(h.households_me^2))) AS hholds_me,
    SUM(a.agg_hhold_income) AS agghholds_inc,
    ROUND(|/(SUM(a.agg_hhold_income_me^2))) AS agghholds_inc_me,
    ROUND(SUM(a.agg_hhold_income) / SUM(h.households)) AS hhold_mean_income,
    ROUND((|/ (SUM(a.agg_hhold_income_me^2) + ((SUM(a.agg_hhold_income)/SUM(h.households))^2 * SUM(h.households_me^2)))) / SUM(h.households)) AS hhold_meaninc_me
FROM zcta_uhf42 z, hsholds h, agg_income a
WHERE z.zcta=h.gid2 AND z.zcta=a.gid2 AND h.households !=0
GROUP BY z.uhf42_code, z.uhf42_name, z.borough
ORDER BY uhf42_code;
Query in pgAdmin and portion of result for calculating mean household income

Query in pgAdmin and portion of result for calculating mean household income

I chose a couple examples where a UHF had only one ZCTA, and another that had two, and tested them in the Cornell ACS calculator to insure the results were correct. Once I got it right, I added:

CREATE VIEW household_sums AS

To the top of the statement and executed again to save it as a view. Mission accomplished! To make doubly sure that the values were correct, I connected my db to QGIS and joined this view to a UHF shapefile to visually verify that the results made sense (could also have imported the shapefile into the DB as a spatial table and incorporated it into the query).

Mean household income by UHF neighborhood in QGIS

Mean household income by UHF neighborhood in QGIS

Conclusion

While it would be preferable to have a median, calculating a new mean for an aggregated area is a fair alternative, if you simply need some summary value for the variable and don’t have the time to spend doing statistical interpolation. Besides income, the Census Bureau also publishes aggregate tables for other variables like: travel time to work, hours worked, number of vehicles, rooms, rent, home value, and various subsets of income (earnings, wages or salary, interest and dividends, social security, public assistance, etc) that makes it possible to calculate new means for aggregated areas. Just make sure you use the appropriate denominator, whether it’s total population, households, owner or renter occupied housing units, etc.

The Map Reliability Calculator for Classifying ACS Data

The staff at the Population Division at NYC City Planning take the limitations of the American Community Survey (ACS) data seriously. Census estimates for tract-level data tend to be unreliable; to counter this, they aggregate tracts into larger Neighborhood Tabulation Areas (NTAs) to produce estimates that have better precision. In their Census Factfinder tool, they display but grey-out variables where the margin of error (MOE) is unacceptably large. If users want to aggregate geographies, the Factfinder does the work of re-computing the margins of error.

Now they’ve released a new tool for census mappers. The Map Reliability Calculator is an Excel spreadsheet for measuring the reliability of classification schemes for making choropleth maps. Because each ACS estimate is published with a MOE, it’s possible that certain estimates may fall outside their designated classification range.

For example, we’re 90% confident that 60.5% plus or minus 1.5% of resident workers 16 years and older in Forest Hills, Queens took public transit to work during 2011-2015. The actual value could be as low as 59% or as high as 62%. Now let’s say we have a classification scheme that has a class with a range from 60% to 80%. Forest Hills would be placed in this class since its estimate is 60.5%, but it’s possible that it could fall into the class below it given the range of the margin of error (as the value could be as low as 59%).

The tool determines how good your classification scheme is by calculating the percent of estimates that could fall outside their assigned class, based on each MOE and the break point of the class. On the left of the sheet you paste your estimates and MOEs, and then type the number of classes you want. On the right, the reliability of classifying that data is calculated for equal intervals (equal range of values in each class) and quantiles (equal number of data points in each class). You can see the reliability of each class and the overall reliability of the scheme. The scheme is classified as reliable if: no individual class has more than 20% of its values identified as possibly falling outside the class, and less than 10% of all the scheme’s values possibly fall outside their classes.

I pasted some 5-year ACS data for NYC PUMAs below (the percentage of workers 16 years and older who take public transit to work in 2011-2015) under STEP 1. In STEP 2 I entered 5 for the number of classes. In the classification schemes on the right, equal intervals is reliable; only 6.6% of the values may fall outside their class. Quantiles was not reliable; 11.9% fell outside. If I reduce the number of classes to 4, reliability improves and both schemes fall under 10%; although unreliability for one of the classes for quantiles is high at 18%, but still below the 20% threshold. Equal intervals should usually perform better than quantiles, as the latter scheme can make rather arbitrary breaks that result in small differences in value ranges between classes (in order to insure that each class has the same number of data points).

Map reliability calculator with 5 classes

Map reliability calculator with 4 classes

You can also enter custom-defined schemes. For example let’s say you use natural breaks (classes determined by gaps in value ranges). There’s a 2-step process here; first you classify the data in GIS and determine what the breaks are, and then you enter them in the spreadsheet. If you’re using QGIS there’s a snag in doing this; QGIS doesn’t show you the “true” breaks of your data based on the actual values, and when you classify data it displays clean breaks that overlap. For example, natural breaks of this data with 5 classes appears like this:

24.4 – 29.0
29.0 – 45.9
45.9 – 55.8
55.8 – 65.1
65.1 – 73.3

So, does the value for 29.0 fall in the first class or the second? The answer is, the first (test it by selecting that record in the attribute table and see where it is on the map, and what color it is). So you need to adjust the values appropriately, paying attention to the precision and scale of your numbers. In this case I bump the first value of each class up by .1, except for the bottom class which you leave alone:

24.4 – 29.0
29.1 – 45.9
46.0 – 55.8
55.9 – 65.1
65.2 – 73.3

In the calculator you have to enter the top class value first, and just the first value in the range:

65.2
55.9
46.0
29.1
29.4

Map reliability calculator with user defined classes

In this case only 7.1% of the total values may fall outside their class so things look good – but my bottom class barely makes the minimum class threshold at 19.4%. I can try dropping the classes down to 4 or I can manually adjust this class to see if I can improve reliability.

If you’re unsure if you made the right adjustments to the classes in translating them from QGIS to the calculator, in QGIS turn on the Show Feature Count option for the layer to see how many data points are in each class, and compare that to the class counts in the calculator. If they don’t match, you need to re-adjust.

QGIS natural breaks and feature count

This is a great tool for census mappers who want or need to account for issues with ACS reliability. It’s an Excel spreadsheet but I used it in LibreOffice Calc with no problem. In addition to the calculator sheet there’s a second sheet with instructions and background info. Download the Map Reliability Calculator here. You can try it out with this test data,  workers who commute with mass transit, 2011-2015 ACS for NYC PUMAs.

Formulas for Working With Census ACS Data in Excel / Calc

After downloading US census data, you often need to reformat it before using it. It’s quite common that you download files where the population is broken down by gender and age, and you need to aggregate the data to get a total or divide a particular characteristic to get a percent total. This is pretty straightforward if you’re working with decennial census data, but data from the American Community Survey (ACS) is a little trickier to deal with since you’re working with estimates that have a margin of error. When creating new data, you also have to calculate what the margin of error is for your derived numbers. I’ll walk through some examples of how you would do this in a spreadsheet (the formulas below will work in either Excel or Calc).

Creating an Aggregate

We’ll use the following data in our example:

screenshot1

We have the total population of people three years and older who are enrolled in school, and a breakdown of this population enrolled in grades 1 through 4 and grades 5 through 8 in a few counties in New York, with margins of error for each data point. Our data is from the 3 year averaged 2005-2007 American Community Survey.

Let’s say we want to create a total for students who are enrolled in grades 1 through 8 for each county. We create a new column and sum the estimates for each county with the formula e3+g3, or sum(e3:g3).

To calculate a margin or error (MOE) for our grade 1 to 8 data, first we have to use the find and replace command to get rid of the “+/-” signs in the MOE column, so our spreadsheet will treat our values as numbers and not text (this is an issue if you downloaded the data as an Excel file – if you download a txt file the +/- is not included). Depending on the dataset you’re working with, you may also need to replace dashes, which represent data that was null or not estimated.

Once the data is cleaned up, we can insert a new column with this formula:

=SQRT((F3^2)+(H3^2))

This calculates our new margin of error by squaring the moes for each of our data points, summing the results together, and taking the square root of that sum. In other words,

=SQRT((MOE1^2)+(MOE2^2))

Once that’s done, you may want to round the new MOE to a whole number.

Creating a Percent Total

Let’s calculate the percentage of the population 3 years and older enrolled in school that are in grades 1 through 8. Based on what we have thus far (I hid the columns E,F,G, and H for grades 1-4 and 5-8 in this screenshot, as we don’t need them):

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We insert a new column where we divide our subgroup by the total, as you would expect – I3/C3. In the next column we insert the following formula to create a MOE for our new percent total:

=(SQRT((J3^2)-((K3^2)*(D3^2))))/C3

This one’s a little weightier than our last formula. We’re taking the square of our percent total (K3) and the square of the MOE of the total population (D3), multiplying them together, then subtracting that number from the square of the MOE of our subgroup (J3). Then we take the square root of the whole thing, then divide it by our total population (C3). If you’re saying – HUH? Maybe this is clearer:

=(SQRT((MOEsubset^2)-((PercentTotal^2)*(MOEtotalpop^2))))/TotalPop

Finally, we have something like this:

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Based on our data, we can say things like “There were approximately 30,556 students enrolled in 1st through 8th grade per year in Dutchess County, NY between 2005 and 2007, plus or minus 1,184 students. An estimated 37% of the population enrolled in school in the county was in the 1st through 8th grade, plus or minus 1%.” The ACS estimates have a 90% confidence interval.

Wrap Up

In this example we worked with aggregating and calculating percentages based on characteristics. We could also use these same formulas to aggregate data by geography, if we wanted to add the characteristics for all the counties together.

For the full documentation on working with ACS data, take a look at the appendix in the Census’ ACS Compass Guide, What General Data Users Need to Know. It provides you with the formulas in their proper statistical notation (for those of you more mathematically inclined than I) and includes formulas for calculating other kinds of numbers, such as ratios and percent change. It does provide you with worked-through examples, but not with spreadsheet formulas. I used their examples when I created formulas the first time around, so I could compare my formula results to their examples to insure that I was getting it right. I’d strongly recommend doing that before you start plugging away with your own data – one misplaced parentheses and you could end up with a different (and incorrect) result.