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" @ , @@ , a@@ , a@ , a @ , !@@ , !@ , ! @ , @@ , @ , @ , % Normal_SurveyAnalyzerExample(2d)` YmInstructions & Main MenuFDefinitions#uFind Sample Size (1Sample)#GFind Sample Size (2Sample)'LFind Margin of Error (1Sample)'aFind Margin of Error (2Sample)+
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0LComparing Two Proportions  A margin of error or confidence interval can be Wassociated with each of the observations, the difference between the observations also Xhas uncertainty associated with it. This uncertainty can be described with a margin of [error or confidence interval. For instance, if you observe 40 percent compliance in Round X1 of inspections and 60 percent compliance in Round 2 of inspections, you have observed Udeveloped for a difference in proportions or means, as well. Because uncertainty is ]a difference of 20 percentage points. If you calculated a margin of error of 10 percentage Spoints for this example, you could say that you believe performance improved by 20 Tpercentage points, 10 percentage points, or somewhere between 10 and 30 percentage points. Instructions#Enter your data in the yellow cellsInformation neededInput/
ResultsStatistical terminologyEnter Your InformationConfidence levelResultsReference:
#For Confidence Interval InformationMenu for sample size, 1 sampleZdetermine the proportion of this group of facilities that is in compliance with a certain m0Inspections required with an infinite populationSample size, n1Sample size, n2$ Value of a standard normal, Z(1/2)
Wald interval>Estimate the Sample Size Required for One Round of InspectionsWhen to use this spreadsheet: When you want to find out how many inspections you should conduct in a round of random inspections, based on the margin of error and confidence level you are seeking.#Go Back to Instructions / Main Menu9Estimate the Margin of Error for One Round of InspectionsWhen to use this spreadsheet: When you know the maximum number of inspections you can conduct in a round of random inspections, and you want to find out the margin of error you will have.MHow many facilities is your ERP focusing on?
(Estimate if you do not know.)Confidence level, (1)p(1p)Assumed proportion, pSpreadsheet NameDescription)Calculates the margin of error associated)with a specified number of inspections ina single sample. Vresults, provided in comments in the cells. Cells with comments have a small red flagUin the upper righthand corner. Place the cursor over the cell to see the comment. 4Margin of Error or HalfWidth of Confidence IntervalPopulation or NSample size or n"Sample required for Score intervalWhat margin of error do you want, above and below the estimate of the proportion of facilities that have the characteristic you are measuring (e.g., are in compliance)?UThe Sample Planner is a tool to help you evaluate different approaches for conducting%Quick Guide to the ERP Sample PlannerOther Resources&Calculate Number of Inspections NeededSample required (finite population corrected)Population or N1Population or N23Number of inspections, before continuity adjustment(1)+Halfwidth of the Score confidence interval+What confidence level do you want to have? XHow many facilities is your ERP focusing on in Round 1?
(Estimate if you do not know.)+Number of inspections required for Round 1.+Number of inspections required for Round 2.Sample size or n1Sample size or n2.Factor to achieve level of confidence required>The results are shown in green cells. These cells are locked.1For Advanced Users: Assumptions and CalculationssIf it differs from Round 1, how many facilities is your ERP focusing on in Round 2? (Estimate if you do not know.)TAssumptions and calculations are shown in gray cells. These cells are locked, too. "Value of standard normal, Z(1/2)
SE (p1p2)@this sheet before using the Sample Planner for the first time. 3an overview of the tools within the Sample Planner,,instructions about assumptions and use, and suggestions for other resources.Vthe random inspections in the Environmental Results Program (ERP). Please fully read D%3Overview of Spreadsheet Tools in the Sample PlannerSThe worksheets in the Sample Planner let you evaluate your approach for conducting inspections two different ways:Ryou can evaluate the quality of your estimates based on the number of inspections name to go to that sheet.) Wyou can conduct. Each is described in the following table. (Click on the spreadsheet for a sample, or Uyou can calculate the sample size needed to meet specified data quality requirements %confidence level for a single sample..Calculates the number of inspections needed to(achieve a specified margin of error and <confidence level for the difference between results between /two rounds of inspections. Use this when your )most important evaluation will be of the 3differences between the two rounds of inspections. of inspections. >Calculate Margin of Error for One or Two rounds of Inspections@Calculates the margin of error associated with the difference in&results observed between two rounds of0inspections of given sizes. Use this when your differences between two samples.navigate the sheet:XInstructional comments. Be sure to read the additional information about the inputs and[Protected cells. All the cells in this workbook are protected, except for the yellow ones Qwhere you enter data. Consequently, you do not need to worry about accidentally ^changing the formulas. If you do want to modify protected cells, please do so with caution. RYou can unprotect a cell or worksheet under the Tools menu. There is no password.LPlanning your sample to estimate proportions and means. Note that this tool 8Yassumes you want to estimate a proportion. It does not let you design a sample with the [goal of estimating the mean and standard error of a continuous variable (e.g., the average [quantity of hazardous waste generated by facilities). Typically, ERP planners do not have Zthe necessary information in advance to undertake such designs anyway. You will still be Vable to measure continuous variables in your ERP, and the ERP Results Analyzer allows [you to calculate results for continuous variables. However, you probably will not have an Madvance idea of the uncertainty that will be associated with these estimates.[For more information on the use of statistics in ERP, please refer to the Generic Guide to JXinstance, suppose the true proportion of all facilities in compliance with a particular VNote that if the confidence interval contains zero, you can not be confident that any Rimprovement or change occurred. For instance, if you observed a difference of 20 Zpercentage points 25 percentage points, the confidence interval of the difference would Wbe from  5 to 45 percentage points. This interval includes zero, so you could not be "confident that there was a change.rWhen to use this spreadsheet: When you want to find out how many inspections you should conduct in each round of ERP inspections, based on the margin of error and confidence level you wish to achieve for a difference between proportions observed in two rounds of inspections. Use this when your most important evaluation will be of the differences between two samples.rWhat is your desired margin of error? (+/)
(You may not be able to detect differences smaller than this amount.)IEstimate the Margin of Error for Differences in Proportions (Two Samples)To Definitions of Key TermsEHalfwidth of the confidence interval for a difference in proportions This Quick Guide Sheet Contains:SEase of viewing. Use of this tool is optimized for an average desktop monitor and VMicrosoft Excel setup. Some users, including those with notebook computers, may find Ythe tool easier to use if they change the "zoom" to less than 100%  e.g., to show more \of the comment boxes without scrolling. Choosing the "fullscreen" option will also enable Xseeing more of the tool. Both of these options are accessible u<nder the "View" menu in the Microsoft Excel toolbar.VStatistical Aspects of Developing an Environmental Results Program. Please note that ,Blue cells provide text information for you.
(Yellow cells are where you enter data. Green cells provide results.DGray cells contain assumptions and calculations, for advanced users.
April 25, 2003, version of the Generic Guide.,Find Sample Size (1Sample)Find Sample Size (2Sample)Find Margin of Error (1Sample)Find Margin of Error (2Sample)VTerminology and definitions. Statistics often uses specialized terminology. As much Pas possible, this tool presents plain language along with specialized terms and Kcalculations. There is also a glossary on the second tab of this workbook.Zthe formulas used in this spreadsheet are different than (and improved from) those in the Hcalculate confidence intervals based on the results of your inspections.TThe spreadsheet ResultsAnalyzer2006.xls will help you conduct statistical tests and 'Definitions of Key TermsXPopulation (N)  This is the total set of facilities in your universe. You may want to
Bregulation or makes use of a certain type of treatment technology.PSample Size (n)  The sample size refers to the number of random inspections. A 5Margin of error or
Halfwidth of confidence interval1How many inspections will you conduct in Round 1?MIf it differs from Round 1, how many inspections will you conduct in Round 2?=Maximum margin of error for a difference in proportions (+/)8How many inspections will you conduct in a single round?Margin of error (+/)" Value of standard normal, Z(1/2)VColor scheme. Each sheet has a userfriendly color scheme that allows you to readily
EEstimate Sample Sizes Required for a Specified Margin of Error for a 'Difference in Proportions (Two Samples)_When to use this spreadsheet: When you know the maximum number of inspections you can conduct in each round of ERP, and want to know the maximum margin of error to expect for a difference between proportions observed in two different rounds of inspections. Use this when your most important evaluation will be of the differences between two samples.*What confidence level do you want to have?Kfacilities in the sample that meet your criteria (e.g., are in compliance). PPoint Estimate of the Proportion (p)  This usually refers to the proportion of $HConfidence Interval and Margin of Error (e)  The margin of error and a +Rconfidence interval associated with the random sample are computed to reflect the [interval (used in this tool for singlesample estimations) is not symmetrical except for a `point estimate of 50%, but it is often shorter (i.e., more precise). It is particularly useful mean. Wuncertainty associated with your point estimate of the actual population proportion or WThe confidence interval gives a range of values that is believed to contain the actual WThe standard Wald confidence interval is symmetric about the point estimate. The Score
Q\(see Instructions) and "unhide" hidden rows in the "Results" section of the "Find Margin of ZError (1Sample)" worksheet in the Sample Planner. In the Results Analyzer's "Proportion R(1Sample)" worksheet, the Wald confidence interval is shown in the "For Advanced Users" section.Xsamples of size n whose corresponding confidence intervals contain the actual (unknown) RConfidence Level  The confidence level is the percentage of all possible random Wpopulation proportion or mean. (See the definition of Confidence Interval above.) For _regulation is 62 percent. (In practice, you would only know this if all facilities were in the Ssample.) A 95percent confidence level means that approximately 95% of all random AR]samples of n facilities from the population will produce a confidence interval that includes ^62% (in a confidence interval, the lower limit will be less than 62% and the upper limit will Jbe greater than 62%). Since you are selecting just one random sample, the 36[corresponding confidence interval may or may not contain the true proportion, but the fact Vsaying you have 95% confidence that your particular interval is one of these accurate Bsamples. You do not know for sure that this is the case, however.UTo determine the necessary sample size, the user must specify the desired confidence &level and the desired margin of error.Uoutside the 3070 percent range. For more information on this topic, please see the
Reference:Esample that consists of the entire population is called a census. Tpopulation proportion or mean with the confidence level prescribed by the user (see '7Zbelow). There are several different acceptable ways of constructing confidence intervals. Vfor small sample sizes and for estimating single proportions, especially when they areJEstimation of Binomial Proportions," in The American Statistician, 1998. $%(AWjournal article by Agresti and Coull, "Approximate is Better than 'Exact' for Interval 'WThe length of the Score confidence interval is also twice the margin of error when the Yobserved proportion is 50% (but not for any other observation). When calculating sample Rsizes required for a particular margin of error, the Sample Planner assumes a 50% Yobserved proportion, in order to provide the maximum sample size necessary as well as to Rprovide a symmetrical Score confidence interval that is twice the margin of error.XUsers interested in viewing the Wald confidence interval can unprotect the spreadsheets %Sthat 95% of all possible samples would contain the true proportion is expressed by 1The American Statistician, v. 52, no. 2, 119126.qDerived from: Agresti and Coull. 1998. "Approximate is Better than 'Exact' for Interval Estimation of Binomial *@Proportions." The American Statistician, v. 52, no. 2, 119126.(dDerived from: Kish, Leslie. 1965. Survey Sampling. John Wiley & Sons, Inc. New York, NY. p. 41.$3qAgresti and Coull. 1998. "Approximate is Better than 'Exact' for Interval Estimation of Binomial Proportions." Wadding and subtracting the margin of error to the point estimate. For example, if the ]margin of error of an estimated proportion is 5 percentage points, the confidence interval Xwill range from 5 percentage points less than the observed value to 5 percentage points Zmore than the observed value. In this example, if the observed proportion is 50 percent, Wthe confidence interval would be 45 to 55 percent. Notice that the length of the Wald R2confidence interval is twice the margin of error. Zrequires the user to select a confidence level. The Wald confidence interval is formed by 49XThe margin of error is half the width of the standard confidence interval. It likewise 6I5034468r: ;X=/
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>@<d"!#%&*7yKConfidence Interval Mean%'Confidence Interval Mean'!HalfWidthClick to go to calculation of confidence interval for estimated meanr&&yK
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2<3This is half the size you would like to have for your confidence interval. E.g., to have an estimate that is within 5 percentage points, enter "0.05."
Assume the estimate of the proportion of facilities in compliance is 50 percent, you chose a confidence level of 95 percent, and the size of the interval is 5 percentage points. In this case, you would have 95 percent confidence that the true proportion of facilities in compliance is 45 to 55 percent.
The smaller the margin of error, the larger the sample size needed.
Note that the Score confidence interval is asymmetrical at proportions other than 50%, so the concept of a margin of error does not readily fit the Score confidence interval in those situations. You are able to use the concept of margin of error in this Sample Planner tool, however, because the Sample Planner assumes a proportion of 50%a conservative approach that will yield the maximum sample size necessary. For more information on the Score confidence interval (and the Wald confidence interval), see the "Definitions" sheet.< 2 N
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<This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result. Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you estimate that 50 percent of facilities are in compliance, with a 95 percent confidence interval of 5 percent, you can state that you are 95 percent confident that the true proportion of facilities in compliance is between 45 and 55 percent.
The higher the level of confidence, the larger the number of inspections needed.
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j<kThis is the sample required to calculate a Score confidence interval, which is considered a more accurate estimate than the standard (Wald) interval, especially with smaller sample sizes and proportions close to 0 percent or 100 percent.
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e<This is the population about which you wish to make inferences. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
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7yK$Go Back to Instructions / Main MenuInstruction^Click to go back to the Instructions pagezyKTo Definitions of Key Terms
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This is the maximum margin of error that will be associated with differences in proportions between the two samples. The smaller the margin of error of the difference, the larger the sample size you will need for a given confidence level.
E.g., say your confidence level is 95% and margin of error is 5 percentage points, and you find 62% compliance in Round 1 and 72% compliance in Round 2. The observed difference between the two samples is 10 percentage points. Since the margin of error of the difference is 5 percentage points, the confidence interval of the difference ranges from 5 to 15 percentage points. Consequently, you would be able to say that you are 95% confident that compliance improved by between 5 and 15 percentage points. In other words, since you observed a change greater than the margin of error for the difference (in our example, 10 percentage points), you can be confident that a change occurred i.e., that there is a significant difference between the results from Round 1 and Round 2.
Suppose, on the other hand, that with a margin of error of 5 percentage points you find 62% compliance in Round 1 and 65% compliance in Round 2. The observed difference is 3 percentage points, and the confidence interval of the difference is 3 5 percentage points. In other words, the confidence interval ranges from or 2 to 8 percentage points. In this case, since the confidence interval of the difference includes zero (because the observed difference is less than the margin of error of the difference), it is possible that there was no change in performance in the overall population. Therefore, you cannot infer that a change in compliance occurred; you can not say that the results from Round 1 and Round 2 are significantly different.
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<This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result (in this case, your result is the difference between the findings from two samples). Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. A 95% confidence level means that you can be 95% confident that the confidence interval includes the true difference between the two populations. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you find that compliance improved 10 percentage points 5 percentage points between the first and second rounds of inspections (with a confidence level of 95%), you can state that you are 95% confident that the actual improvement in compliance is between 5 and 15 percentage points. The higher the level of confidence, the larger the number of inspections needed for a given confidence interval.
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<This is the population about which you wish to make inferences in the first round of inspections. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, you will want to sample from the same population for both rounds of inspections. E.g., if you are looking at drycleaners in compliance in the state, it is important to ensure you have an entire listing of drycleaners before both rounds of sampling.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
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.</This is the total number of inspections you think you can conduct. I.e., it is the sample size.
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g<hThis is half the size of your confidence interval. E.g., assume the estimate of the proportion of facilities in compliance is 50
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95% confidence that the true proportion of facilities in compliance is 45 to 55 percent.
The confidence interval calculated here is the Score confidence interval, which is considered a more accurate estimate than the standard (Wald) interval, especially with smaller sample sizes and proportions close to 0% or 100%.
Also note that the Score confidence interval is asymmetrical at proportions other than 50%, so the concept of a margin of error does not readily fit the Score confidence interval in those situations. You are able to use the concept of margin of error in this Sample Planner tool, however, because the Sample Planner assumes a proportion of 50%  a conservative approach that will yield the maximum sample size necessary. For more information on the Score confidence interval (and the Wald confidence interval), see the "Definitions" sheet. <gtmiZR
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<This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result. Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you estimate that 50 percent of facilities is in compliance, with a 95 percent confidence interval of 5 percent, you can state that you are 95 percent confident that the true proportion of facilities in compliance is between 45 and 55 percent.
The higher the level of confidence, the larger the number of inspections needed.
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Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
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If there is a maximum number of inspections you can carry out in the first round due to budget constraints or other reasons, enter that number here. You can vary this sample size and see how it affects the margin of error.
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<{ This is the maximum margin of error associated with the difference in proportions observed in the two samples. The margin of error is half the width of the confidence interval of the difference.
E.g., if your margin of error is 10 percentage points, then you can be confident (at a 90% or 95% confidence level) that the actual difference is within 10 percentage points of the observed value. If you were to observe a 15 percentage points difference between Round 1 and Round 2 results, you can be confident that the actual difference was between 5 and 25 percentage points. If you were to instead observe a 7 percentage points difference between Round 1 and Round 2, the confidence interval of the difference would be 3 to 17 percentage points. In this case, because the confidence interval of the difference includes zero, you can not be confident that a change occurred in the population as a whole i.e., the results from Round 1 and Round 2 are not significantly different. On the other hand, if you were to observe a change greater than the margin of error (in our example, 10 percentage points), you can be confident that a change occurred i.e., that there is a significant difference.
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<This is the sample size for Round 2 of inspections  i.e., the number of inspections you expect to conduct in the second round.
If there is a maximum number of inspections you can carry out in the second round due to budget constraints or other reasons, enter that number here. You can vary this sample size and see how it affects the margin of error.
Since many ERPs will have the same number of inspections in both rounds, this cell defaults to the Round 1 value.<@@@
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Typically, you will want to sample from the same population for both rounds of inspections. E.g., if you are looking at drycleaners in compliance in the state, it is important to ensure you have an entire listing of drycleaners before both rounds of sampling.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
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E.g., if you find that compliance improved 10 percentage points 5 percentage points between the first and second rounds of inspections (with a confidence level of 95%), you can state that you are 95% confident that the actual improvement in compliance is between 5 and 15 percentage points. The higher the level of confidence, the larger the number of inspections needed for a given confidence interval.
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; @@@@@@@@ @7E%Quick Guide to the ERP Sample PlannerE89455562].UThe Sample Planner is a tool to help you evaluate different approaches for conducting../2a.Vthe random inspections in the Environmental Results Program (ERP). Please fully read D../2H@this sheet before using the Sample Planner for the first time. ../2.../2(D This Quick Guide Sheet Contains:../2 ?;.3an overview of the tools within the Sample Planner,
./ 2 ?4 .,instructions about assumptions and use, and
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. suggestions for other resources.
./2.../2;D3Overview of Spreadsheet Tools in the Sample Planner../
2D../2[.SThe worksheets in the Sample Planner let you evaluate your approach for conducting ../2'.inspections two different ways:../2 ?].Uyou can calculate the sample size needed to meet specified data quality requirements
./
2.for a sample, or
./2 ?Z.Ryou can evaluate the quality of your estimates based on the number of inspections
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2._.Wyou can conduct. Each is described in the following table. (Click on the spreadsheet
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./2.../
2.sSpreadsheet NametDescription/
2..{&Calculate Number of Inspections Needed/
2.#Find Sample Size (1Sample)6~.Calculates the number of inspections needed to/2.0}(achieve a specified margin of error and /2.v%confidence level for a single sample./
2.#Find Sample Size (2Sample)6}.Calculates the number of inspections needed to/2.0}(achieve a specified margin of error and /2.Dy<confidence level for the difference between results between /2.7y/two rounds of inspections. Use this when your /2.1y)most important evaluation will be of the / 2.; y3differences between the two rounds of inspections. /DlK{fFd]QYyE9CKZ\KyNbUO!@"#@$@%@&@'@(@)@*@ +,;@./0123456789:;<=>?@!2.!wof inspections. !/
"2.F">Calculate Margin of Error for One or Two rounds of Inspections
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#2.'#Find Margin of Error (1Sample)1#x)Calculates the margin of error associated#/$2.1$y)with a specified number of inspections in$/%2.%wa single sample. %/
&2.'&Find Margin of Error (2Sample)H&x@Calculates the margin of error associated with the difference in&/'2..'&results observed between two rounds of'/(2.8(0inspections of given sizes. Use this when your (/)2.1))most important evaluation will be of the )/*2. (*z differences between two samples.*/+2=uu/,2,DInstructions,uu/2Duu/.2a.VColor scheme. Each sheet has a userfriendly color scheme that allows you to readily
.uu//2/navigate the sheet:/uu/02 0?70,Blue cells provide text information for you.
0u/12 1?31(Yellow cells are where you enter data.
1u/22 2?'2Green cells provide results.
2u/32 3?O3DGray cells contain assumptions and calculations, for advanced users.
3u/42uu/52a5VTerminology and definitions. Statistics often uses specialized terminology. As much 5u/62X6gPas possible, this tool presents plain language along with specialized terms and 6u/72S7gKcalculations. There is also a glossary on the second tab of this workbook.7u/7>82guu/92c9XInstructional comments. Be sure to read the additional information about the inputs and9u/:2^:gVresults, provided in comments in the cells. Cells with comments have a small red flag:u/;2];gUin the upper righthand corner. Place the cursor over the cell to see the comment. ;uu/<2guu/=2f=[Protected cells. All the cells in this workbook are protected, except for the yellow ones =uu/>2Y>gQwhere you enter data. Consequently, you do not need to worry about accidentally >uu/?2f?g^changing the formulas. If you do want to modify protected cells, please do so with caution. ?uu/@2Z@gRYou can unprotect a cell or worksheet under the Tools menu. There is no password.@uu/D
l6fxO8LVOF29`\Pxv{{wABCDEFGHIJKLMNOPQR;S;TUVWXYZ[ A2uu/B2WBLPlanning your sample to estimate proportions and means. Note that this tool 8Buu/C2aCgYassumes you want to estimate a proportion. It does not let you design a sample with the Cuu/D2cDg[goal of estimating the mean and standard error of a continuous variable (e.g., the average Duu/E2cEg[quantity of hazardous waste generated by facilities). Typically, ERP planners do not have Euu/F2bFgZthe necessary information in advance to undertake such designs anyway. You will still be Fuu/G2^GgVable to measure continuous variables in your ERP, and the ERP Results Analyzer allows Guu/H2cHg[you to calculate results for continuous variables. However, you probably will not have an Huu/I2UIgMadvance idea of the uncertainty that will be associated with these estimates.Iuu/J2===/K2^KSEase of viewing. Use of this tool is optimized for an average desktop monitor and K==/L2^LVMicrosoft Excel setup. Some users, including those with notebook computers, may find L==/M2aMYthe tool easier to use if they change the "zoom" to less than 100%  e.g., to show more M==/N2dNg\of the comment boxes without scrolling. Choosing the "fullscreen" option will also enable N==/O2`OgXseeing more of the tool. Both of these options are accessible under the "View" menu in O==/P2$Pgthe Microsoft Excel toolbar.P==/Q2=../R2RDOther ResourcesR../SdDeefT2fTg[For more information on the use of statistics in ERP, please refer to the Generic Guide to JT../U2^UgVStatistical Aspects of Developing an Environmental Results Program. Please note that U../V2bVgZthe formulas used in this spreadsheet are different than (and improved from) those in the V../W2:WgApril 25, 2003, version of the Generic Guide.,W../X2g../Y2aYgTThe spreadsheet ResultsAnalyzer2006.xls will help you conduct statistical tests and 'Y../Z2PZgHcalculate confidence intervals based on the results of your inspections.Z../[:us~B5Xn=818X>
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; 7 EDefinitions of Key TermsE89455564gCXPopulation (N)  This is the total set of facilities in your universe. You may want to
C564b5Zdetermine the proportion of this group of facilities that is in compliance with a certain 5564J5Bregulation or makes use of a certain type of treatment technology.556455564[CPSample Size (n)  The sample size refers to the number of random inspections. A 5564M5Esample that consists of the entire population is called a census. 556 45556
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5564S5Kfacilities in the sample that meet your criteria (e.g., are in compliance).55645556
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HConfidence Interval and Margin of Error (e)  The margin of error and a +
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>4Z5Rconfidence interval associated with the random sample are computed to reflect the 5564_5Wuncertainty associated with your point estimate of the actual population proportion or 55645mean. 556455564bWThe confidence interval gives a range of values that is believed to contain the actual 5564a5Tpopulation proportion or mean with the confidence level prescribed by the user (see '75564b5Zbelow). There are several different acceptable ways of constructing confidence intervals. 5564f5WThe standard Wald confidence interval is symmetric about the point estimate. The Score
Q5564c5[interval (used in this tool for singlesample estimations) is not symmetrical except for a 5564h5`point estimate of 50%, but it is often shorter (i.e., more precise). It is particularly useful 5564^5Vfor small sample sizes and for estimating single proportions, especially when they are5564]5Uoutside the 3070 percent range. For more information on this topic, please see the 5564b5Wjournal article by Agresti and Coull, "Approximate is Better than 'Exact' for Interval '5564[JEstimation of Binomial Proportions," in The American Statistician, 1998. $%(A556455564gXThe margin of error is half the width of the standard confidence interval. It likewise 6I5564g5Zrequires the user to select a confidence level. The Wald confidence interval is formed by 495564_5Wadding and subtracting the margin of error to the point estimate. For example, if the 556 4e 5]margin of error of an estimated proportion is 5 percentage points, the confidence interval 556Dl>hykyq{x},{y}!"#$%&'()*+,./012;3456789:;<=>?@!4`!5Xwill range from 5 percentage points less than the observed value to 5 percentage points !556"4b"5Zmore than the observed value. In this example, if the observed proportion is 50 percent, "556#4b#Wthe confidence interval would be 45 to 55 percent. Notice that the length of the Wald R#556$4:$2confidence interval is twice the margin of error. $556%4556&4d&WThe length of the Score confidence interval is also twice the margin of error when the &556'4a'Yobserved proportion is 50% (but not for any other observation). When calculating sample '556(4Z(Rsizes required for a particular margin of error, the Sample Planner assumes a 50% (556)4a)Yobserved proportion, in order to provide the maximum sample size necessary as well as to )556*4_*Rprovide a symmetrical Score confidence interval that is twice the margin of error.*556+4556,4e,XUsers interested in viewing the Wald confidence interval can unprotect the spreadsheets %,5564d\(see Instructions) and "unhide" hidden rows in the "Results" section of the "Find Margin of 556.4b.5ZError (1Sample)" worksheet in the Sample Planner. In the Results Analyzer's "Proportion .556/4_/5R(1Sample)" worksheet, the Wald confidence interval is shown in the "For Advanced /5560405Users" section.055614555624]2CRConfidence Level  The confidence level is the percentage of all possible random 255634`35Xsamples of size n whose corresponding confidence intervals contain the actual (unknown) 355644_45Wpopulation proportion or mean. (See the definition of Confidence Interval above.) For 455654`55Xinstance, suppose the true proportion of all facilities in compliance with a particular 555664g65_regulation is 62 percent. (In practice, you would only know this if all facilities were in the 655674`75Ssample.) A 95percent confidence level means that approximately 95% of all random AR755684h8]samples of n facilities from the population will produce a confidence interval that includes 855694f95^62% (in a confidence interval, the lower limit will be less than 62% and the upper limit will 9556:4W:5Jbe greater than 62%). Since you are selecting just one random sample, the 36:556;4c;5[corresponding confidence interval may or may not contain the true proportion, but the fact ;556<4[<5Sthat 95% of all possible samples would contain the true proportion is expressed by <556=4c=Vsaying you have 95% confidence that your particular interval is one of these accurate =556>4J>Bsamples. You do not know for sure that this is the case, however.>556?4556@4]@UTo determine the necessary sample size, the user must specify the desired confidence @556D&l~Xx}}5{~}~~uyhABC;DEFGHIJKLMNOPQRS TA4.A&level and the desired margin of error.A5 A5 A6B4556C4WCLComparing Two Proportions  A margin of error or confidence interval can be C556D4bDUdeveloped for a difference in proportions or means, as well. Because uncertainty is D556E4_E5Wassociated with each of the observations, the difference between the observations also E556F4`F5Xhas uncertainty associated with it. This uncertainty can be described with a margin of F556G4cG5[error or confidence interval. For instance, if you observe 40 percent compliance in Round G556H4`H5X1 of inspections and 60 percent compliance in Round 2 of inspections, you have observed H556I4eI]a difference of 20 percentage points. If you calculated a margin of error of 10 percentage I556J4[JSpoints for this example, you could say that you believe performance improved by 20 J556K4\K5Tpercentage points, 10 percentage points, or somewhere between 10 and 30 percentage K556L4L5 points. L556M4 M5 M5
M56N4^N5VNote that if the confidence interval contains zero, you can not be confident that any N556O4ZO5Rimprovement or change occurred. For instance, if you observed a difference of 20 O556P4bP5Zpercentage points 25 percentage points, the confidence interval of the difference would P556Q4_Q5Wbe from  5 to 45 percentage points. This interval includes zero, so you could not be Q556R4*R5"confident that there was a change.R556S30001+T#Go Back to Instructions / Main Menu,C ]u}~~yz/2x}H=818X>
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DefinitionsFind Sample Size (2Sample)!Find Margin of Error (1Sample)!Find Margin of Error (2Sample)
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When to use this spreadsheet: When you want to find out how many inspections you should conduct in a round of random inspections, based on the margin of error and confidence level you are seeking.ooooo+h#Enter your data in the yellow cellsiiijF>The results are shown in green cells. These cells are locked.\TAssumptions and calculations are shown in gray cells. These cells are locked, too. Information needed Input/
Results Statistical terminologyEnter Your Information3
M+What confidence level do you want to have?
Confidence levelUMHow many facilities is your ERP focusing on?
(Estimate if you do not know.)~
@@Population or N What margin of error do you want, above and below the estimate of the proportion of facilities that have the characteristic you are measuring (e.g., are in compliance)?~
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Halfwidth of confidence intervalResults7+H!Number of inspections required !Number of inspections required 1Pq@DDDA5+Sample required (finite population corrected)91For Advanced Users: Assumptions and Calculations80Inspections required with an infinite populationkFsw@UDDDDDDDDA*"Sample required for Score intervalAssumed proportion, p~
?,Assumed proportion, p,p(1p)$?DDp(1p),Confidence level^Effffff?/;ZBNConfidence level, (1?)6.Factor to achieve level of confidence required+1\?DA(/ $Value of a standard normal, Z(1?/2)!"""#$
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This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result. Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you estimate that 50 percent of facilities are in compliance, with a 95 percent confidence interval of 5 percent, you can state that you are 95 percent confident that the true proportion of facilities in compliance is between 45 and 55 percent.
The higher the level of confidence, the larger the number of inspections needed.
keThis is the population about which you wish to make inferences. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
82This is half the size you would like to have for your confidence interval. E.g., to have an estimate that is within 5 percentage points, enter "0.05."
Assume the estimate of the proportion of facilities in compliance is 50 percent, you chose a confidence level of 95 percent, and the size of the interval is 5 percentage points. In this case, you would have 95 percent confidence that the true proportion of facilities in compliance is 45 to 55 percent.
The smaller the margin of error, the larger the sample size needed.
Note that the Score confidence interval is asymmetrical at proportions other than 50%, so the concept of a margin of error does not readily fit the Score confidence interval in those situations. You are able to use the concept of margin of error in this Sample Planner tool, however, because the Sample Planner assumes a proportion of 50%a conservative approach that will yield the maximum sample size necessary. For more information on the Score confidence interval (and the Wald confidence interval), see the "Definitions" sheet.pjThis is the sample required to calculate a Score confidence interval, which is considered a more accurate estimate than the standard (Wald) interval, especially with smaller sample sizes and proportions close to 0 percent or 100 percent.
For more information on the Score confidence interval (and the Wald confidence interval), see the "Definitions" sheet. =818X>
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DefinitionsFind Sample Size (1Sample)!Find Margin of Error (1Sample)!Find Margin of Error (2Sample)
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When to use this spreadsheet: When you want to find out how many inspections you should conduct in each round of ERP inspections, based on the margin of error and confidence level you wish to achieve for a difference between proportions observed in two rqFFFG+k#Enter your data in the yellow cellslllmF>The results are shown in green cells. These cells are locked.\TAssumptions and calculations are shown in gray cells. These cells are locked, too.
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JStatistical terminologyEnter Your Information3M+What confidence level do you want to have? ;Confidence levelO`XHow many facilities is your ERP focusing on in Round 1?
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\;];\\]]P]8: @l$$(:(;r] 8: @$$):);rThis is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result (in this case, your result is the difference between the findings from two samples). Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. A 95% confidence level means that you can be 95% confident that the confidence interval includes the true difference between the two populations. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you find that compliance improved 10 percentage points 5 percentage points between the first and second rounds of inspections (with a confidence level of 95%), you can state that you are 95% confident that the actual improvement in compliance is between 5 and 15 percentage points. The higher the level of confidence, the larger the number of inspections needed for a given confidence interval.
This is the population about which you wish to make inferences in the first round of inspections. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, you will want to sample from the same population for both rounds of inspections. E.g., if you are looking at drycleaners in compliance in the state, it is important to ensure you have an entire listing of drycleaners before both rounds of sampling.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
This is the population about which you wish to make inferences in the second round of inspections. For more information, see the comment above (regarding population, Round 1). This population size will typically be the same as for the first round of inspections. If the population size is expected to change substantially between rounds, then insert the expected population for Round 2 here. By default, this cell is set to equal the population for the first round of inspections.This is the maximum margin of error that will be associated with differences in proportions between the two samples. The smaller the margin of error of the difference, the larger the sample size you will need for a given confidence level.
E.g., say your confidence level is 95% and margin of error is 5 percentage points, and you find 62% compliance in Round 1 and 72% compliance in Round 2. The observed difference between the two samples is 10 percentage points. Since the margin of error of the difference is 5 percentage points, the confidence interval of the difference ranges from 5 to 15 percentage points. Consequently, you would be able to say that you are 95% confident that compliance improved by between 5 and 15 percentage points. In other words, since you observed a change greater than the margin of error for the difference (in our example, 10 percentage points), you can be confident that a change occurred i.e., that there is a significant difference between the results from Round 1 and Round 2.
Suppose, on the other hand, that with a margin of error of 5 percentage points you find 62% compliance in Round 1 and 65% compliance in Round 2. The observed difference is 3 percentage points, and the confidence interval of the difference is 3 5 percentage points. In other words, the confidence interval ranges from or 2 to 8 percentage points. In this case, since the confidence interval of the difference includes zero (because the observed difference is less than the margin of error of the difference), it is possible that there was no change in performance in the overall population. Therefore, you cannot infer that a change in compliance occurred; you can not say that the results from Round 1 and Round 2 are significantly different.
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+#Go Back to Instructions / Main Menu# To Definitions of Key Terms
When to use this spreadsheet: When you know the maximum number of inspections you can conduct in a round of random inspections, and you want to find out the margin of error you will have.
+h#Enter your data in the yellow cellsiiiiiiij F>The results are shown in green cells. These cells are locked. \TAssumptions and calculations are shown in gray cells. These cells are locked, too. Information needed Input/
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*What confidence level do you want to have?
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(Estimate if you do not know.)~
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This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result. Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you estimate that 50 percent of facilities is in compliance, with a 95 percent confidence interval of 5 percent, you can state that you are 95 percent confident that the true proportion of facilities in compliance is between 45 and 55 percent.
The higher the level of confidence, the larger the number of inspections needed.
keThis is the population about which you wish to make inferences. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
4.This is the total number of inspections you think you can conduct. I.e., it is the sample size.
If there is a maximum number of inspections you can carry out due to budget constraints or other reasons, enter that number here. You can vary this sample size and see how it affects the margin of error.mgThis is half the size of your confidence interval. E.g., assume the estimate of the proportion of facilities in compliance is 50
percent, you chose a confidence level of 95%, and the size of the interval is 5 percentage points. In this case, you would have
95% confidence that the true proportion of facilities in compliance is 45 to 55 percent.
The confidence interval calculated here is the Score confidence interval, which is considered a more accurate estimate than the standard (Wald) interval, especially with smaller sample sizes and proportions close to 0% or 100%.
Also note that the Score confidence interval is asymmetrical at proportions other than 50%, so the concept of a margin of error does not readily fit the Score confidence interval in those situations. You are able to use the concept of margin of error in this Sample Planner tool, however, because the Sample Planner assumes a proportion of 50%  a conservative approach that will yield the maximum sample size necessary. For more information on the Score confidence interval (and the Wald confidence interval), see the "Definitions" sheet. =818X>
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When to use this spreadsheet: When you know the maximum number of inspections you can conduct in each round of ERP, and want to know the maximum margin of error to expect for a difference between proportions observed in two different rounds of inspectionqFFFG+k#Enter your data in the yellow cellslllmF>The results are shown in green cells. These cells are locked.\TAssumptions and calculations are shown in gray cells. These cells are locked, too. JInformation needed K LInput/
Results K JStatistical terminologyEnter Your Information2
*What confidence level do you want to have?
;Confidence level
O`XHow many facilities is your ERP focusing on in Round 1?
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{sIf it differs from Round 1, how many facilities is your ERP focusing on in Round 2? (Estimate if you do not know.)@@DPopulation or N2
9n1How many inspections will you conduct in Round 1?~
Y@Sample size or n1UPMIf it differs from Round 1, how many inspections will you conduct in Round 2?cY@D<Sample size or n2ResultsQE=Maximum margin of error for a difference in proportions (+/)w?8 DDMEHalfwidth of the confidence interval for a difference in proportions
IQI91For Advanced Users: Assumptions and CalculationsSQSMConfidence levelEffffff?/;ZB
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This is the confidence level, an estimate of the certainty associated with the margin of error or confidence interval for your result (in this case, your result is the difference between the findings from two samples). Conclusions based on sampling, rather than inspecting every facility, will always involve some amount of uncertainty.
You can choose either 90% or 95%, which are two standard levels of confidence. A 95% confidence level means that you can be 95% confident that the confidence interval includes the true difference between the two populations. Most, if not all, ERPs to date have used a 95% confidence level.
E.g., if you find that compliance improved 10 percentage points 5 percentage points between the first and second rounds of inspections (with a confidence level of 95%), you can state that you are 95% confident that the actual improvement in compliance is between 5 and 15 percentage points. The higher the level of confidence, the larger the number of inspections needed for a given confidence interval.
This is the population about which you wish to make inferences in the first round of inspections. E.g., if you want to know what proportion of 500 dry cleaners is in compliance with proposed standards, enter 500. If you're not sure how many there are, put the largest likely number to be sure you inspect enough facilities to achieve the confidence level and confidence interval you are seeking.
Typically, you will want to sample from the same population for both rounds of inspections. E.g., if you are looking at drycleaners in compliance in the state, it is important to ensure you have an entire listing of drycleaners before both rounds of sampling.
Typically, the characteristic you intend to measure applies to all facilities in the population. If the characteristic applies to a subset of facilities, you should enter the number to which it applies rather than the total number of facilities.
This is the population about which you wish to make inferences in the second round of inspections. For more information, see the comment above (regarding population, Round 1). This population size will typically be the same as for the first round of inspections. If the population size is expected to change substantially between rounds, then insert the expected population for Round 2 here. By default, this cell is set to equal the population for the first round of inspections.gaThis is the sample size for Round 1 of inspections  i.e., the number of inspections you expect to conduct in the first round.
If there is a maximum number of inspections you can carry out in the first round due to budget constraints or other reasons, enter that number here. You can vary this sample size and see how it affects the margin of error.
This is the sample size for Round 2 of inspections  i.e., the number of inspections you expect to conduct in the second round.
If there is a maximum number of inspections you can carry out in the second round due to budget constraints or other reasons, enter that number here. You can vary this sample size and see how it affects the margin of error.
Since many ERPs will have the same number of inspections in both rounds, this cell defaults to the Round 1 value.This is the maximum margin of error associated with the difference in proportions observed in the two samples. The margin of error is half the width of the confidence interval of the difference.
E.g., if your margin of error is 10 percentage points, then you can be confident (at a 90% or 95% confidence level) that the actual difference is within 10 percentage points of the observed value. If you were to observe a 15 percentage points difference between Round 1 and Round 2 results, you can be confident that the actual difference was between 5 and 25 percentage points. If you were to instead observe a 7 percentage points difference between Round 1 and Round 2, the confidence interval of the difference would be 3 to 17 percentage points. In this case, because the confidence interval of the difference includes zero, you can not be confident that a change occurred in the population as a whole i.e., the results from Round 1 and Round 2 are not significantly different. On the other hand, if you were to observe a change greater than the margin of error (in our example, 10 percentage points), you can be confident that a change occurred i.e., that there is a significant difference.
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