Statistical Significance and Population Controls

Presented to the New Jersey SDC Annual Network Meeting

June 6, 2007

Tony Tersine, U.S. Census Bureau

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Overview of the Session

• Basic Concepts

• Margin of Error

• Confidence Intervals

• Standard Error Formulas

• Statistical Testing

• Population Controls

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Basic Concepts - 1• Sampling error is introduced due to

sampling, selection of a subset of the population to draw inferences about the entire population.

• Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.

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Basic Concepts - 2

• The sampling error is often reported as the estimate “plus or minus” the margin of error, a measure of how precise the estimate is.

• The margin of error describes the precision of the estimate at a given confidence level.

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Basic Concepts - 3

• The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate.

• The Census Bureau statistical standard for published data is to use the 90 percent confidence level.

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Margin of Error• The margin of error is important

because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample.

• It can help prevent you from interpreting small or nonexistent differences as important.

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Margin of Error (MOE)

MOE = 1.65 * Standard Error1.65 is used for the 90 percent confidence level

Standard Error = MOE / 1.65

Starting in 2006 ACS will use 1.645

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Confidence Interval• Confidence Interval

Estimate ± Margin of Error

• 90 percent confidence levelMargin of Error = 1.645 * Std Error

• 95 percent confidence levelMargin of Error = 1.96 * Std Error

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Confidence Interval

• The confidence interval tells you the upper and lower bounds of a range of values that may contain the true value.

• It provides important information about the true value or the population parameter.

• It tells you the limitations on using the estimates.

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MOE / Confidence Interval

Median Family Income – $30,000Standard Error – $1,500

90% MOE = 1.645 * $1,500 = $2,468

90% CI = $30,000 ± $2,468 = $27,532 to $32,468

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Standard Error – Sum/Difference

• Standard Error of X + Y or X – Y

• SE(X+Y) = SE(X-Y)

22 [SE(Y)] [SE(X)]

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Standard Error – Sum

• SE(X1+X2+…+Xn)

2n

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21 )][SE(X ...)][SE(X )][SE(X

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Standard Error – Proportions

• P= X / Y – X is a subset of Y

• SE(P)

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22 [SE(Y)]

Y

X [SE(X)]

Y

1

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Standard Error – Ratios

• X / Y – X is not a subset of Y

• SE(X / Y)

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22 [SE(Y)]

Y

X [SE(X)]

Y

1

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Statistical Testing

• Two estimates are "significantly different" at the 90 percent confidence level if the difference between them is large enough to infer that there was a less than 10 percent chance that the difference was purely random.

• Users may want to compare estimates across years or geographies.

• It is important to note that small differences, which may be statistically significant, may not have any practical significance.

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Statistical Testing - Steps

1. State that two estimates are statistically different if the difference between the two estimates is statistically different from zero.

2. Calculate the standard error of the difference.

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Statistical Testing - Steps

3. Calculate the margin of error of the difference.

4. Compare the original difference between the estimates to the margin of error of the difference.

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Statistical Testing - Steps

5. If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different.

6. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different.

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Statistical Testing - Example

Percent with Bachelor’s Degree or Higher

Geography Percent MOE CIArea 1 20.0 ± 5.0 15.0-25.0Area 2 12.3 ± 4.7 7.6-17.0

Difference = 20.0 – 12.3 = 7.7

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Statistical Testing - Example

MOE of the Difference - Standard Errors for Each EstimateSE = MOE / 1.65

SE(Area 1) = 5.0 / 1.65 = 3.03

SE(Area 2) = 4.7 / 1.65 = 2.85

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Statistical Testing - Example

• Standard Error of the Difference

• Margin of Error of the Difference

MOE(X - Y) = 1.65 * 4.16 = 6.9

16.42.85 3.03 Y)SE(X 22

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Statistical Testing - Example

• Compare the Difference to MOE– Difference = 7.7%– MOE = 6.9%

• Difference > MOE

• Conclude that the two estimates are significantly different with 90 percent confidence

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Census 2000 – Example

• Percent Bachelor’s Degree or Higher – Alexandria, VA• 51,982 / 95,730 = 54.3%• DF = 1.2 – (13.4% in sample)

• 90% MOE =1.65 * 0.4 = 0.7 • 90% CI = 54.3 ± 0.7 = 53.6 to 55.0

4.0)3.54100(*3.54*730,95

5*2.1

SE

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Rules to Remember

• Don’t make a big deal of small differences.

• If the confidence intervals overlap you cannot conclude the difference is not statistically significant.

• Always talk to subject matter experts before making any conclusions.

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Population Controls - Rational

• Correct for coverage– Higher undercoverage in surveys than in

census

• Reduce variance estimates

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2005 ACS Coverage Rates - US

Total Pop

Male Female Hispanic

95.1 93.9 96.2 93.6

Non-HispanicWhite Black AIAN Asian NHOPI

96.3 90.7 97.9 94.5 84.0

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Population Controls

• Intercensal estimates are produced by updating the previous census results using various administrative records data and ACS data on foreign-born

• In a multi-stage process, HU, GQ, and population adjustment ratios are applied to the weights

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GQ Controls

• GQ population controls applied at the STATE level by 7 major types.

• Collapsing across types if not enough sample

• Always control to at least Institutional / Non-Institutional Population

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Housing Unit Controls

• Applied at a weighting area level

• New step to make all 3 agree– Households– Householders– Occupied Housing Units

• Housing Units will not be controlled

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Weighting Areas

• Controls applied at the weighting area (county or group of counties) level

• 1343 weighting areas consist of a single county– All 21 New Jersey counties are weighting

areas

• The other 607 weighting areas are made up of 1798 counties

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HU Population Controls

• Controls applied by race/ethnicity and age/sex groups

• ACS GQ estimates subtracted from population estimates to obtain controls

• Collapsing of race/ethnicity and age/sex groups

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Why Do Place Estimates Differ

• ACS does not control subcounty areas

• 1-person households– Lower response rate

• Multi-Unit Structures– Conversion of single to multi-unit

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Room: 4H477Phone: 301-763-1994Email: Anthony.G.Tersine.Jr@census.gov

U.S. DEPARTMENT OF COMMERCEU.S. Census BureauWashington, DC 20233

Anthony Tersine

Contact Information