APDU Webinar User Needs for Calculating Standard Errors in the ACS OR 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 2

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 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 mean 3.Calculate the ratio (the mean itself) 4.Must do the above for Cecil County and the state of Maryland 5.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

The input tables: Denominator – from B11003

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)

Calculating the MOE for the sum of estimates 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:

Calculating the sum of the estimates is easy! For the numerator:

Now we do the same calculations for the denominator

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:

Summary of our results so far:

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 Income Families 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 estimates 2.Calculate the MOE for the sum of the denominator estimates 3.Create the ratio (mean income) 4.Calculate the MOE for the ratio 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. 20 How a web-based SC Tool Might Work

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

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

27 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 to Doug Hillmer. Jane Traynham, Maryland State Data Center, 31 Current Status and Next Steps