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-O =';=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(jMOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65kk$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.65 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.65 * $1,500 = $2,475 90% CI = $30,000 $2,475 = $27,525 to $32,475Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUbPopulation ControlsIntercensal estimates are produced by updating the previous census results using various administrative records data In a multi-stage process, HU, GQ, and population adjustment ratios are applied to the weights GQ population controls applied at the state level by 7 major types.ZcWeighting Areas Controls applied at the weighting area (county or group of counties) level by race/ethnicity and age/sex groups 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@/;/;dWhy Do Place Numbers DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/4s)t*6789:;<=> ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@$?" dd@   " @ ` n?" dd@   @@``PN   @ ` ` p@@ v(    6@ "P@P  T Click to edit Master title style! !$  0C "P@  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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H T 0jB ? 33] 0  d4(  dd d c $NH    d s *w K!    H d 0jB ? 33Z 0 _W t(  tX t C NH   W t S  K!   Will underestimate the SE if two items in a sum are highly positively correlated or if the two items in a difference are highly negatively correlated. Will overestimate the SE if two items in a sum are highly negatively correlated or if the two items in a difference are highly positively correlated. V(X + Y) = V (X) + V(Y) + 2 COV(X,Y) you get COV(X,Y) = 1/2 [V (X + Y) - V(X) - V(Y)] From the collapsed and detailed tables get the appropriate values and compute COV(X,Y). You can get it directly or through an approximation using characteristics thought to have the same degree of correlation. Again, the user will need to use his judgment to make this determination.4-u -tH t 0jB ? 33V 0 pT(  X  C NH     S  K!   VThis information is included in the  Using Data from the 2005 American Community Survey under the  Using the Data tab on the ACS website.$%25H  0jB ? 33d 0 m(  X  C NH     S ܲ K!   o Because ACS does not control to subcounty areas, the estimates for these will differ from the population estimates. 2 possible reasons for differences in cities: 1-person households which tend to be in the city then the suburbs have a lower response rate. Conversion of single-unit structures to multi-unit structures. The MAF may not be picking these up which leads to undercoverage. Lower survey response rate to the ACS in cities than rest of the county could also lead to lower ACS estimate than the pop estimates.( t H  0jB ? 33_b 0 `(  X  C NH     S  K!   In 2006 the Housing estimate will not agree with the pop estimate. GQ controls can be collapsed to Inst/Non-inst if not enough sample to use 7 major types. H  0jB ? 33c 0 p8(  X  C NH     S d K!   :The GQ ACS estimates are subtracted from the population estimates at the weighting area level to obtain the HU population controls. There is collapsing of race/ethnicity and age/sex groups if not enough sample to apply the controls at these levels. $^H  0jB ? 33>xV=LSQ>Ӗ 1` B`h hb"5P$M 1 N9jbA:@b298LLQ[Ϲ>6`^ ѐ{99syo㖏P`A6ʼ1aHFr9{8Wƞ/ s.4|?AHғ H4d[[5ߠ_}?S^ ]vO9 -)f><"?N)Z(\)9~{r f0qfW y|ܛ] TUKTCTKTGTolg2~`tG^qإLr<-H:LޮnJC[c*l}rr*@וZ{H(4y2J 5֨<.֩Hz"&wQ&j 0w#spI|,Fih1<~ư\9{Wg7g ţ32x$O}[!s\K:}x¢M{2Ҳ?;gU~ϻ#mLt@f2d˛UZm5gEWZr5"=P&>xLLl4xz֖p5萶|Les1Sqۧ, _5IGqʀs(>k B1z&(ׂF,(:Dw{9>!kF`]un9!,ߊ tDV- !QQ;'rQf͋nJSxYMlTU>tμcEb,H tDL FtQ6LC ӡtvB1+W.taA"Ţda+mDE* ms=͛)2d=/mhA= ,|R A:[re jTU2˂1AŦPP9ن<,dZ ;XaԻPyeM`9CPQ:/{yMAqX[@Ń=m|b>(i~ddtlAF?QfUE)^睺 z(C}AWY&(XV?ԑkn;2$b݃kJ8980NYԸ3NAzo? a JӀ8-bZL.Hݙ3A=Hc~&m--$ot=1|0گ قv8m;Bul* azOQ{+&r;,?ۇ؟ edv83bE#v(~1Y (\w=gJ;Fw<p AO\kRIRUH}dԊ.kvq96\pBd[#O,Uơ9؞؇FH{ڻC'>jV|K|ߤZsϝjnX>+',XTnQ_ܼni Ֆt4|8l;ɛ/.}[[ t@z1hzƏ_wG+@eQ}XaIoHGuڿ☄N=̿w>ۆ/TT yasڅ ȖۜBI`*Bm47moCjV-+ HǑ IG6!9KDZYN`s?3^dx+2;U?tsWT/u0dx]E%F'qsl`c7VW=hwr\s+ɱO*}?V< |zC%U iZxKLSApv_) 1O4|FFE<@B0S~"M4ēhb(McbT.\ZtJuh ]@5(D,B,F܆X P zvT-g;?V>@ghl,60|#D85ڼ͢32^&mFOq JtjQ9;YgdY+.nRrb]˪0cWgQCY5jhfX pˉ!" &NqL}r]Ο'2~}bae>ZH8?~⼃K]nr)3)-TS pCg;ƌЄƇ9DUЌ>Z]MK[*&M}Į_(o'ķ$e~gS?&j.'*:†~]Wʨ}~_}ox1.wx^oifZKz1;r}L> i*p`lz^tSU2~/Fv~3U/ [Ą0ɱD(3;X@t/R:utjEI^-){O|=R)h1OuIbJr?4BԴГ؃Vt 'S u#;f/?Z+f8/AQkw&2mq~)XE-6  .B3Vm<ZWGV2{IL8j5)c .߇iRN'qMsi<$KVQPtNytNDqb+zo#3ݮM7kvV] ߶0U~ >NNOSV 1=Ǭ.YJGC,/'Tq赏X_qa\VXd闫TnSbMHj4];tQ'dz~Cu hPz \V7v)M|gQH [3m=adw5a۴Jl2ms5ȊR~^;}n謾sKϕFV02c ƣ1xpDxJ2nzikwZgqW19~ͿgpJ|&H(gnϕ [!ŻV'Ú o[2lUJ+XjdZ'G?O(Ob 7grlVdt1`"MН|{x,qJ'S(`An^˾Ad O(4I-\ ! πEn6y_.]SZ-Mk\ Bވ0+0ΟH)6NlOz+^CE@a&;(3$KU}a5@7봵)xKhSApv6/MSmK) -ŐF࡭JXik%A'oEo ~."ę}1I((N웙}K7*8  E4ɘF nBXMPYC4]qm߁S_,@/@z X1-Z*9"of?L񡠭?PUa[ WҊ,YR#+9rdra9SU݀eegL]&GPrgv_,*tow;/7>2Z Np1ł<\|P S_wdZCӐM&/ C/~@(-Ċ|ys>&9?{}(:3eTE1c׮04q섽a|:)'I[\g>?Wħ5WVii Fv1@ y:r+@s06(_f+]2l w+ۓ D!QJM~^|KlWbo<X[MJ6Z9i6^t'$Ib])F*~՞0MB)w a}WvOgn?r.-@I|$@)m`t:d3>%LٿF {Լ(}|AJY]Ӽ|yx<=T lʤzwke.΋k'i4g7inx,,?@:RB)K㌗,C!X'u"GjVFZa"N,bEt#NX<$~nXL8MxI8_[ mǟ'K{uG/hg'[OUW|g7O(II/"BKRK\eX'2t^+ı.t:d,n8_gSi&t͇€gϡ?Z? *k c,>$v˻ d1x|G:I0~1`tJb4&ہ$>ː#UO7#0&8A—_z\I(t֫,/OlETi?Ms|>U51, Eo*i*$:M.yFUr0Vbk p+w;|\s08l~oçwg٠'u{cyɫ\Hl 4[1۸Ǻ s="}e(0   `9Equation Equation.30,Microsoft Equation 3.00-Equation Equation.30,Microsoft Oh+'0tR hpL `l   XGroup Quarters Sampling and Estimation Plans for the 2005 American Community SurveyMark E. Asiala\C:\Documents and Settings\test2000\Application Data\Microsoft\Templates\standardtemp.pot tersi001151Microsoft PowerPoint@74@ h@ËGPg  R('& &&#TNPP`2OMi & TNPP &&TNPP     'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___www#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$L g4=d=da$ 0hpl p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)J @Pictures#$Current User,SummaryInformation(RPowerPoint Document(/DocumentSummaryInformation8Equation 3.007Equation Equation.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00?Equation Equation.30,Microsoft Equation 3.00BEquation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman`t\a$ 0t s 0DArialNew Roman`t\a$ 0t s 0" DCourierw Roman`t\a$ 0t s 00DTahomaw Roman`t\a$ 0t s 0" ` .  @n?" dd@  @@``   25S,$ +B       !" #*  ',,-./023b$&C*x.2$m#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$L g4=d=da$ 0hpl p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =*;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(jMOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65kk$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.65 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.65 * $1,500 = $2,475 90% CI = $30,000 $2,475 = $27,525 to $32,475Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUbPopulation ControlsIntercensal estimates are produced by updating the previous census results using various administrative records data In a multi-stage process, HU, GQ, and population adjustment ratios are applied to the weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/      !"#$%&'()*+,-./0123456789:;<;|/;gHU Population ControlsControls 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  $dWhy Do Place Numbers DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@A = P$(  r  S P@   r  S P@  H  0޽h ? ̙33 ? 0(  x  c $LP@   x  c $0&P@  H  0޽h ? ̙33 A $(  r  S P@P   r  S P@  H  0޽h ? ̙33 >  $(  r  S >P@   r  S >P@  H  0޽h ? ̙33 @ 0(  x  c $t%P@   x  c $(P@  H  0޽h ? ̙33b 0 zr` (  X  C NH   r  S  K!   H  0jB ? 33c 0 zrp (  X  C NH   r  S d K!   H  0jB ? 33'e 0 w(  ^  S NH     c $! K!   mYGQ controls can be collapsed to Inst/Non-inst if not enough sample to use 7 major types. H  0jB ? 33g 0 D(  ^  S NH     c $  K!   :The GQ ACS estimates are subtracted from the population estimates at the weighting area level to obtain the HU population controls. There is collapsing of race/ethnicity and age/sex groups if not enough sample to apply the controls at these levels. $^H  0jB ? 33Hf 0  (  X  C NH   J  S  K!   There will be some changes in the relationship distribution. We will be providing a note about this change when the data is released.H  0jB ? 33r8 ^[d?hjw`obGfkmpd"i>sEg(0   ` ՜.+,0     0On-screen ShowBureau Of Census/!# 'Times New RomanArialCourierTahoma standardtempMicrosoft Equation 3.01Statistical Significance and Population ControlsOverview of the SessionBasic Concepts - 1Basic Concepts - 2Basic Concepts - 3Margin of ErrorMargin of Error (MOE)Confidence IntervalConfidence IntervalMOE / Confidence Interval Standard Error Sum/DifferenceStandard Error SumStandard Error ProportionsStandard Error RatiosStatistical TestingStatistical Testing - StepsStatistical Testing - StepsStatistical Testing - StepsStatistical Testing - ExampleStatistical Testing - Example   z !"#$%&'()*+,-./0123456789:;=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{<|}~  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =,;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(jMOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65kk$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.65 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.65 * $1,500 = $2,475 90% CI = $30,000 $2,475 = $27,525 to $32,475Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUhPopulation Controls - Rational^Correct for coverage Higher undercoverage in surveys than in census Reduce variance estimates<00bPopulation ControlsIntercensal 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 weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/;|/;gHU Population ControlsControls 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  $dWhy Do Place Estimates DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@AB B @$(  r  S P@P   r  S 'P@  H  0޽h ? ̙33 = P$(  r  S P@   r  S P@  H  0޽h ? ̙33 < $(  r  S P@   r  S t P@  H  0޽h ? ̙33d 0 K(  X  C NH     S ܲ K!   M Because ACS does not control to subcounty areas, the estimates for these will differ from the population estimates. 2 possible reasons for differences in cities: 1-person households which tend to be in the city than the suburbs have a lower response rate. Conversion of single-unit structures to multi-unit structures. The MAF may not be picking these up which leads to undercoverage. Lower survey response rate to the ACS in cities than rest of the county could also lead to lower ACS estimate than the pop estimates.( H  0jB ? 33#b 0 `s(  X  C NH     S  K!   uaACS Data on Foreign born population are used to approximate the international migration componentH  0jB ? 33h 0 P(  X  C NH     S  K!   !Coverage issues are both frame related and nonresponse related. Missing units on the frame. Lower response rates by characteristics 95.1 for 2005 ACS for total pop 93.9 for males and 95.6 for females>@DD@DDH  0jB ? 33r,s0 h"~s0Eg(0   `9Equation Equation.30,Microsoft Equation 3.00-Equation Equation.30,Microsoft Equation 3.007Equation Equati Slide Titles!on.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00?Equation Equation.30,Microsoft Equation 3.00BEquation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman`t\a$ 0t s 0DArialNew Roman`t\a$ 0t s 0" DCourierw Roman`t\a$ 0t s 00DTahomaw Roman`t\a$ 0t s 0" ` .  @n?" dd@  @@``   45S,$ +B       !" #*  ',,-./02345b$&C*x.2$m#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$L g4=d=da$ 0hpl p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =,;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(jMOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65kk$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.65 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.65 * $1,500 = $2,475 90% CI = $30,000 $2,475 = $27,525 to $32,475Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUhPopulation Controls - Rational^Correct for coverage Higher undercoverage in surveys than in census Reduce variance estimates<00bPopulation ControlsIntercensal 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 weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/;|/;gHU Population ControlsControls 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  $dWhy Do Place Estimates DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@ABh 0 PS(  X  C NH     S  K!   UCoverage issues are both frame related and nonresponse related. Missing units on the frame. Lower response rates by certain populations reduces their coverage Coverage rates for 2005 ACS 95.1 for total pop 93.9 for males and 95.6 for femalesH@_77H  0jB ? 33r]Qh"hT0g(0   `9Equation Equation.30,Microsoft Equation 3.00-Equation Equation.30,Microsoft Equation 3.007Equation Equation.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00?Equation Equation.30,Microsoft Equation 3.00BEquation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman`t\a$ 0t s 0DArialNew Roman`t\a$ 0t s 0" DCourierw Roman`t\a$ 0t s 00DTahomaw Roman`t\a$ 0t s 0" ` .  @n?" dd@  @@``   ,65S,$ +B       !" #*  ',,-./0234568b$&C*x.2$m#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$LStatistical Testing - ExampleStatistical Testing - ExampleCensus 2000 ExampleRules to RememberPopulation Controls - Rational2005 ACS Coverage Rates - USPopulation Controls GQ ControlsHousing Unit ControlsWeighting AreasHU Population ControlsWhy Do Place Estimates DifferContact Information  Fonts UsedDesign TemplateEmbedded OLE Servers_ testtestDi001 g4=d=da$ 0hpl p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =O,;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(jMOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65kk$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.65 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.65 * $1,500 = $2,475 90% CI = $30,000 $2,475 = $27,525 to $32,475Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUhPopulation Controls - Rational^Correct for coverage Higher undercoverage in surveys than in census Reduce variance estimates<00i2005 ACS Coverage Rates - USbPopulation ControlsIntercensal 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 weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/;|/;gHU Population ControlsControls 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  $dWhy Do Place Estimates DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@ABC C `*9(  r  S xǏP@P   n P@  #"&P@ @ <?0? @ L84.0 @` ? <40?  L94.5 @` > <*0?  L97.9 @` = <0?  L90.7 @` < <0?P  L96.3 @` ; <p 0? @  MNHOPI @` : <J?    MAsian @` 9 <J?  LAIAN @` 8 <J?   MBlack @` 7 <J?P   MWhite @` 2 B|J?P& @  V Non-Hispanic    @` 0 <lJ? 3@&  L93.6 @` / <J?3 &  L96.2 @` . <\J?3&  L93.9 @` - <wJ?P3&  L95.1 @` + <bJ? @3 PHispanic   @` * <tm? 3 NFemale @` ) <'?3 LMale @` ( <?P3 Q Total Pop   @``B A 0o ?P`B F 0o ?P`B G 0o ?PP3`B L 0o ?@@3`B  0o ?`B  0o ?P3P& `B  0o ? `B  0o ? @`B  0o ?@3@& `B  0o ?P& P `B  0o ?@& @ `B  0o ?P P `B  0o ?@ @ `B  0o ?P P`B  0o ?@ @`B  0o ?`B  0o ? `B  0o ? `B  0o ?@ZB  s *1 ?P @ H  0޽h ? ̙33Ji 0  (  X  C NH     S X K!   fThese are available on the ACS Quality Measures page. State level available for Total pop and sex. eH  0jB ? 33rT qri"Tg(@   `9Equation Equation.30,Microsoft Equation 3.00-Equation Equation.30,Microsoft Equation 3.007Equation Equation.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00?Equation Equation.30,Microsoft Equation 3.00BEquation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman`t\a$ 0t s 0DArialNew Roman`t\a$ 0t s 0" DCourierw Roman`t\a$ 0t s 00DTahomaw Roman`t\a$ 0t s 0" ` .  @n?" dd@  @@``   ,65S,$ +B       !" #*  ',,-./0234568b$&C*x.2$m#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$L g4=d=da$ 0hpp p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =y,;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(MOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65 Starting in 2006 ACS will use 1.645Z$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.645 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.645 * $1,500 = $2,468 90% CI = $30,000 $2,468 = $27,532 to $32,468Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUhPopulation Controls - Rational^Correct for coverage Higher undercoverage in surveys than in census Reduce variance estimates<00i2005 ACS Coverage Rates - USbPopulation ControlsIntercensal 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 weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/;|/;gHU Population ControlsControls 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  $dWhy Do Place Estimates DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@ABC 0 `(    Nkk z$   n*  K&&KKpp  Nkk  @$  p*  K&&KKppd  c $ ?XL  4  Nkk  M(  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S   Tkk z   n*  K&&KKpp   Tkk  @  p*  K&&KKppH  0.k ? 3380___PPT10.p& p(( {5   NAkk z$   \* K&&KKpp  NMkk  @$  ^* K&&KKpp  TUkk z   \* K&&KKpp  Tl_kk  @  ^* K&&KKppH  0.k ? 3380___PPT10.p&$  ($(  (r ( S     r ( S LP@  H ( 0޽h ? ̙3380___PPT10.   0(  x  c $P@P   x  c $H P@  H  0޽h ? ̙33  0(  x  c $dP@P   x  c $ P@  H  0޽h ? ̙33,; 0 |(  d c $XK    3 ree L)    H  0.k ? ̙33"= 0 Pr(  ^ S YL    # l<gܳgܳ L)    Good morningH  0.k ? ̙33R 0 +(  d  c $XL     s *p9 M(   cH  0.k ? 33[ 0 H+(  Hd H c $XL    H s *R M(   cH H 0.k ? 33\ 0 T4(  Td T c $XL    T s *c M(    H T 0.k ? 33] 0  d4(  dd d c $XL    d s *w M(    H d 0.k ? 33Z 0 kc t(  t^ t S XL   ] t c $ M(   Will underestimate the SE if two items in a sum are highly positively correlated or if the two items in a difference are highly negatively correlated. Will overestimate the SE if two items in a sum are highly negatively correlated or if the two items in a difference are highly positively correlated. V(X + Y) = V (X) + V(Y) + 2 COV(X,Y) you get COV(X,Y) = 1/2 [V (X + Y) - V(X) - V(Y)] From the collapsed and detailed tables get the appropriate values and compute COV(X,Y). You can get it directly or through an approximation using characteristics thought to have the same degree of correlation. Again, the user will need to use his judgment to make this determination.4-u -tH t 0.k ? 33V 0 p`(  ^  S XL     c $      !"#$%&'()*+,-./0123456789:;< M(   VThis information is included in the  Using Data from the 2005 American Community Survey under the  Using the Data tab on the ACS website.$%25H  0.k ? 33d 0 W(  ^  S XL     c $ܲ M(   M Because ACS does not control to subcounty areas, the estimates for these will differ from the population estimates. 2 possible reasons for differences in cities: 1-person households which tend to be in the city than the suburbs have a lower response rate. Conversion of single-unit structures to multi-unit structures. The MAF may not be picking these up which leads to undercoverage. Lower survey response rate to the ACS in cities than rest of the county could also lead to lower ACS estimate than the pop estimates.( H  0.k ? 33/b 0 `(  ^  S XL     c $ M(   uaACS Data on Foreign born population are used to approximate the international migration componentH  0.k ? 33c 0 ~p(  ^  S XL   x  c $d M(   H  0.k ? 333e 0 (  d  c $XL     s *! M(   mYGQ controls can be collapsed to Inst/Non-inst if not enough sample to use 7 major types. H  0.k ? 33g 0 P(  d  c $XL     s *  M(   :The GQ ACS estimates are subtracted from the population estimates at the weighting area level to obtain the HU population controls. There is collapsing of race/ethnicity and age/sex groups if not enough sample to apply the controls at these levels. $^H  0.k ? 33Tf 0   (  ^  S XL   J  c $ M(   There will be some changes in the relationship distribution. We will be providing a note about this change when the data is released.H  0.k ? 33h 0 P_(  ^  S XL     c $ M(   UCoverage issues are both frame related and nonresponse related. Missing units on the frame. Lower response rates by certain populations reduces their coverage Coverage rates for 2005 ACS 95.1 for total pop 93.9 for males and 95.6 for femalesH@_77H  0.k ? 33Vi 0 (  ^  S XL     c $X M(   fThese are available on the ACS Quality Measures page. State level available for Total pop and sex. eH  0.k ? 33r ? Gs 7RkT GN?PVLxX[ZG\3^b0e jDl0nMpUsuxh"&{g(@   `9Equation Equation.30,Microsoft Equation 3.00-Equation Equation.30,Microsoft Equation 3.007Equation Equation.30,Microsoft Equation 3.00AEquation Equation.30,Microsoft Equation 3.00?Equation Equation.30,Microsoft Equation 3.00BEquation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman`t\a$ 0t s 0DArialNew Roman`t\a$ 0t s 0" DCourierw Roman`t\a$ 0t s 00DTahomaw Roman`t\a$ 0t s 0" ` .  @n?" dd@  @@``   ,65S,$ +B       !" #*  ',,-./0234568b$&C*x.2$m#XT 2$h3ʰe8s 2$;u[Suw[o  $b$G i蜔MFb$Z!29t贡}5 2$;1 > D"V! 0AA@84)ʚ;Y,ʚ;g4%d%da$ 0hppp@ <42d2d 0$L<4dddd 0$L g4=d=da$ 0hpp p<4BdBd 0$LB'h___PPT2001D<4Xh%___PPTMac11%@f   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography      hnamd` Arial&Monotype Typography   8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  ,   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography   D   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography  D   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography <   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography$ h   hnamd` Arial&Monotype Typography     hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography $   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 8   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography 4   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT10 ___PPT9zWYX? -O =y,;=0Statistical Significance and Population Controls11,ePresented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureaufe$u>Overview of the Session(tBasic Concepts Margin of Error Confidence Intervals Standard Error Formulas Statistical Testing Population Controls uuLBasic Concepts - 1(Sampling error is introduced due to sampling, selection of a subset of the population to draw inferences about the entire population. Standard error is an estimate of the precision of the estimates. It measures the variability of an estimate due to sampling.2ZzoMBasic Concepts - 2(The sampling error is often reported as the estimate  plus or minus the margin of error, a measure of how precise the estimate is. The margin of error describes the precision of the estimate at a given confidence level.DZI/ETBasic Concepts - 3(The confidence level measures the likelihood that the true value is within the margin of error of the sample estimate. The Census Bureau statistical standard for published data is to use the 90 percent confidence level. 2ZNMargin of Error(The margin of error is important because relying on statistical inference can save you from drawing incorrect conclusions from data based on a sample. It can help prevent you from interpreting small or nonexistent differences as important. PUMargin of Error (MOE)(MOE = 1.65 * Standard Error 1.65 is used for the 90 percent confidence level Standard Error = MOE / 1.65 Starting in 2006 ACS will use 1.645Z$OConfidence Interval(Confidence Interval Estimate Margin of Error 90 percent confidence level Margin of Error = 1.645 * Std Error 95 percent confidence level Margin of Error = 1.96 * Std Error8Z  QConfidence 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.ZPMOE / Confidence Interval(Median Family Income  $30,000 Standard Error  $1,500 90% MOE = 1.645 * $1,500 = $2,468 90% CI = $30,000 $2,468 = $27,532 to $32,468Z Z>Standard Error  Sum/DifferencejStandard Error of X + Y or X  Y SE(X+Y) = SE(X-Y)66 ^(Standard Error  SumSE(X1+X2+& +Xn) b        _8Standard Error  ProportionsHP= X / Y  X is a subset of Y SE(P)%% `.Standard Error  RatiosRX / Y  X is not a subset of Y SE(X / Y)** VStatistical 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. PWStatistical Testing - Steps(State that two estimates are statistically different if the difference between the two estimates is statistically different from zero. Calculate the standard error of the difference." YStatistical Testing - Steps(Calculate the margin of error of the difference. Compare the original difference between the estimates to the margin of error of the difference." XStatistical Testing - Steps(If the difference is greater than the margin of error, then you conclude that the two estimates are significantly different. If the difference is less than the margin of error, you conclude that the two estimates are not significantly different." RStatistical Testing - ExampleRPercent with Bachelor s Degree or Higher Geography Percent MOE CI Area 1 20.0 5.0 15.0-25.0 Area 2 12.3 4.7 7.6-17.0 Difference = 20.0  12.3 = 7.7@ZT " 2[Statistical Testing - ExampleMOE of the Difference - Standard Errors for Each Estimate SE = MOE / 1.65 SE(Area 1) = 5.0 / 1.65 = 3.03 SE(Area 2) = 4.7 / 1.65 = 2.85Z\Statistical Testing - ExampleeStandard Error of the Difference Margin of Error of the Difference MOE(X - Y) = 1.65 * 4.16 = 6.96!"!f ]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@h h a*Census 2000  Example(f 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>pC SRules to RememberDon 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. .ZUhPopulation Controls - Rational^Correct for coverage Higher undercoverage in surveys than in census Reduce variance estimates<00i2005 ACS Coverage Rates - USbPopulation ControlsIntercensal 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 weightse GQ ControlsGQ 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 PopulationZfHousing Unit ControlsApplied at a weighting area level New step to make all 3 agree Households Householders Occupied Housing Units Housing Units will not be controlled<?/%?/%cWeighting AreasControls 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:|/;|/;gHU Population ControlsControls 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  $dWhy Do Place Estimates DifferACS does not control subcounty areas 1-person households Lower response rate Multi-Unit Structures Conversion of single to multi-unit P:$:$\;Contact Information(/s)t*6789:;<=>?@ABC= 0 P^(  ^ S YL    # l<gܳgܳ L)   H  0.k ? ̙33r{t="{0Root EntrydO)@T8 @Pictures#$Current User/SummaryInformation(R      !"#$%&'()*+,-./0123456789:;<<