APDU Webinar

User Needs for Calculating Standard Errors in the ACS

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What is a Statistical Calculator?Presented by Doug Hillmer, Independent Consultant

What is a “Statistical Calculator”?

• Data Users need ways to assess statistical quality of estimates and derive statistical information from estimates

• Covers tasks users have been doing on their own for a long time

• An SC tool makes it easier to do these tasks in a consistent manner

• An SC tool relieves the user of the computational burden

• Several SC tools have been developed as spreadsheet applications

• Goal of this webinar is to make the case for an SC tool integrated into a web applications, such as American FactFinder

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A typical problem for data users

• Assignment: Get the most recent estimate of mean family income for families with children for Cecil County, Maryland. Compare this to the mean family income for families with children for the state of Maryland. Need this asap!

• User decides that she must hand over the estimates she derives along with the standard errors for these estimates

After some digging…

• ACS data from the 2009 1-year data release contains the most recent data for this assignment. But, there are some problems and limitations:

• If the aggregated data products are used, we can only create this mean income for families with “own children”

• We can’t use the PUMS data because Cecil County does not coincide with PUMA boundaries.

• After discussing issues with client, they decide to use aggregated ACS data products for families with own children.

As we will see, the assignment has several parts

1. Calculate the numerator for the mean 2. Calculate the denominator for the mean3. Calculate the ratio (the mean itself)4. Must do the above for Cecil County and the

state of Maryland5. Do a statistical comparison between the two

mean incomes

Formula for calculating mean family income for families with own children

Numerator Aggregate family income for families with own children (Source: B19128 from 2009 ACS)

______________________________________________ Denominator Families with own children

(Source: B11003 from 2009 ACS)

The input tables: Numerator – from B19128

Data Set: 2009 American Community Survey 1-Year Estimates

MarylandCecil County, Maryland

Estimate Margin of Error (+/-)Estimate Margin of Error (+/-)Aggregate family income in the past 12 months (in 2009 inflation-adjusted dollars): 148,315,058,800 1,812,998,265 2,256,999,100 177,643,575Married-couple family: 125,717,517,400 1,831,539,827 2,021,664,800 181,465,145With own children under 18 years 56,624,770,000 1,537,445,753 955,444,400 177,481,646No own children under 18 years 69,092,747,400 1,700,298,082 1,066,220,400 167,730,090Other family: 22,597,541,400 865,831,600 235,334,200 66,707,425Male householder, no wife present: 6,347,006,300 560,644,607 108,795,000 38,534,048With own children under 18 years 2,687,180,800 433,509,897 43,854,900 23,297,316No own children under 18 years 3,659,825,400 369,799,745 64,940,100 32,730,520Female householder, no husband present: 16,250,535,100 579,105,419 126,539,200 47,591,581With own children under 18 years 7,424,169,800 344,933,102 40,549,800 21,429,379No own children under 18 years 8,826,365,300 457,928,047 85,989,400 45,072,540

B19128. AGGREGATE FAMILY INCOME IN THE PAST 12 MONTHS (IN 2009 INFLATION-ADJUSTED DOLLARS) BY FAMILY TYPE BY PRESENCE OF OWN CHILDREN UNDER 18 YEARS - Universe: FAMILIES

The input tables: Denominator – from B11003B11003. FAMILY TYPE BY PRESENCE AND AGE OF OWN CHILDREN UNDER 18 YEARS - Universe: FAMILIESData Set: 2009 American Community Survey 1-Year Estimates

MarylandCecil County, Maryland

Estimate Margin of Error (+/-)Estimate Margin of Error (+/-)Total: 1,391,688 11,881 26,207 1,544Married-couple family: 1,012,157 11,510 21,466 1,728With own children under 18 years: 433,179 8,504 9,988 1,239Under 6 years only 104,043 4,965 2,156 682Under 6 years and 6 to 17 years 85,164 4,284 1,471 5956 to 17 years only 243,972 6,770 6,361 1,089No own children under 18 years 578,978 8,914 11,478 1,423Other family: 379,531 9,357 4,741 1,243Male householder, no wife present: 89,905 5,409 1,706 706With own children under 18 years: 42,604 3,932 934 551Under 6 years only 14,273 2,124 648 534Under 6 years and 6 to 17 years 5,932 1,513 0 2856 to 17 years only 22,399 2,599 286 212No own children under 18 years 47,301 3,668 772 381Female householder, no husband present: 289,626 7,554 3,035 880With own children under 18 years: 165,292 5,124 1,763 841Under 6 years only 31,814 3,144 97 139Under 6 years and 6 to 17 years 24,126 2,578 252 2826 to 17 years only 109,352 4,305 1,414 792No own children under 18 years 124,334 5,584 1,272 507

Refresher on Margin of Error (MOE)

• MOE = F * Standard error• where F=1.645 for the 90 pct confidence interval

• Use the MOE to construct the Lower and Upper bounds around the estimate

• Lower Bound = (estimate – MOE)• Upper Bound = (estimate + MOE)

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Calculating the MOE for the sum of estimates

222 )()()(645.1)( ZSEYSEXSEZYXMOE

645.1/)()( XMOEXSE

MOE for Ratio of two Estimates

Formulas we will need

The MOE for the ratio is 1.645*SE(R)

Lots of work for a busy data user!

• The calculations required are tedious

•It’s easy to make a mistake

•Especially when you’re under time pressure

Back to our assignment:

MarylandCecil County, Maryland

Estimate Margin of Error (+/-)Estimate Margin of Error (+/-)Aggregate family income in the past 12 months (in 2009 inflation-adjusted dollars):Married-couple family:With own children under 18 years 56,624,770,000 1,537,445,753 955,444,400 177,481,646

Male householder, no wife present:With own children under 18 years 2,687,180,800 433,509,897 43,854,900 23,297,316

Female householder, no husband present:With own children under 18 years 7,424,169,800 344,933,102 40,549,800 21,429,379

Numbers we will need for the numerator calculations

Calculating the sum of the estimates is easy!

For the numerator:

MarylandCecil County, Maryland

Estimate EstimateAggregate family income in the past 12 months (in 2009 inflation-adjusted dollars):Married-couple family:With own children under 18 years 56,624,770,000 955,444,400

Male householder, no wife present:With own children under 18 years 2,687,180,800 43,854,900

Female householder, no husband present:With own children under 18 years 7,424,169,800 40,549,800Total Aggregate Income for Families with Own Children = 66,736,120,600 1,039,849,100

Now we do the same calculations for the denominator

Married-couple family:With own children under 18 years: 433,179 9,988

Male householder, no wife present:With own children under 18 years: 42,604 934

Female householder, no husband present:With own children under 18 years: 165,292 1,763Total Families with Own Children = 641,075 12,685

Go to Statistical Calculations Excel File (SC Tool) to do the necessary

calculations!

Thank you Dr. Lenny Gaines, New York State Data Center

One location for this tool:www.mdp.state.md.us/msdc/ACS.shtml

Summary of our results so far:

Margin of Error (+/-)

Margin of Error (+/-)

Total Aggregate Income for Families with Own Children = $66,736,120,600 $1,634,212,079 $1,039,849,100 $179,004,189

Total Families with Own Children = 641,075 10,679 12,685 1,596

Mean income for families with own children $104,100 $81,975

Maryland Estimate

Cecil County, Maryland Estimate

Back to our SC Tool to calculate MOE of the Ratio !

Summary of Results (and what we had to do to get them)

Mean Family IncomeFamilies with Own Children

90% Margin of Error

Maryland $104,100 $3,083

Cecil County, Maryland $81,975 $17,559

What we had to do:1.Calculate the MOE for the sum of the numerator estimates2.Calculate the MOE for the sum of the denominator estimates3.Create the ratio (mean income)4.Calculate the MOE for the ratio

< We have not yet done the statistical comparison between the mean incomes!>

The SC Tool made the work much easier!

A Web-based SC Tool

• We can make the work even easier

• We can easily expand the capabilities of the tool over time

• We can help the user avoid simple mistakes

A few screen shots of a hypothetical web-based SC tool will illustrate these points

Sequence of web pages for two scenarios

– Repeat the mean family income example– Do a statistical comparison of median income for several NJ counties

NOTE: The screen shots that follow are not meant to suggest any specific user interface design.

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How a web-based SC Tool Might Work

Numerator:

Table: B19128 AGGREGATE FAMILY INCOME IN THE PAST 12 MONTHS (IN 2009 INFLATION-ADJUSTED DOLLARS) BY FAMILY TYPE BY PRESENCE OF OWN CHILDREN UNDER 18 YEARS Universe : FAMILIES

Check the cell(s) needed

Aggregate family income in the past 12 months (in 2009 inflation-adjusted dollars):

Married-couple family: With own children under 18 years X No own children under 18 years

Other family: Male householder, no wife present: With own children under 18 years X No own children under 18 years

Female householder, no husband present: With own children under 18 years X No own children under 18 years

The user is presented with a table shell for the numerator data source, B19128 and checks the 3 cells needed to create the numerator

Denominator

Table: B11003 FAMILY TYPE BY PRESENCE AND AGE OF OWN CHILDREN UNDER 18 YEARS Universe : FAMILIES

Example:

Check the cell(s) needed

Total: Married-couple family: With own children under 18 years: X Under 6 years only Under 6 years and 6 to 17 years 6 to 17 years only

No own children under 18 years Other family: Male householder, no wife present: With own children under 18 years: X Under 6 years only Under 6 years and 6 to 17 years 6 to 17 years only

No own children under 18 years Female householder, no husband present: With own children under 18 years: X Under 6 years only Under 6 years and 6 to 17 years 6 to 17 years only

No own children under 18 years

Then the user is prompted to select the cell(s) needed from the denominator data source, B11003. The user checks the 3 cells needed to create the denominator.

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Scenario 2: Comparing a single estimate for multiple geographic areas

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• Next Steps for developing requirements for an SC Tool– Want to include other reviewers– Finalize requirements before end of November– Hand document over to Census Bureau by Nov 30, 2010

• How to contact us and get a copy of the requirements if you want to participate in developing these requirements:

Send email to Doug Hillmer. dhillmer1@yahoo.com or Jane Traynham, Maryland State Data Center, JTraynham@mdp.state.md.us

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Current Status and Next Steps