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{"sheet":"Welcome","index":0,"n_rows":10,"n_cols":2,"rows_kept":10,"cut":false,"hidden":false,"merged":[[9,1,9,18],[7,1,7,14],[4,1,4,18],[6,1,6,18],[8,1,8,18],[5,1,5,18],[7,15,7,18]]}
[]
[]
[null,"  Use this calculator to suggest sample sizes for case reviews and other events that require a sample"]
[]
[null,"Introduction"]
[null,"\nReviewing a sample of cases is a frequently used method in child welfare continuous quality improvement processes to understand the fidelity and quality of practice with children and families. This calculator provides guidance and options for informing decisions about case review sample sizes. "]
[null,"Understanding Sampling"]
[null,"\nIf you need to learn more about a population, like a group of children or families that have something in common, but don't have the resources to interview, survey, or read case notes about every person in the population, you can select a sample from the population. \n\nIf your sample is too small, however, you limit the degree to which you can say the results from your sample match what you would have obtained had you worked with the entire population.\n\nSo how large does your sample need to be to have confidence that it reflects the experience of the entire population? The answer depends mostly on four factors: the size of the population, the variation in the population (e.g., how similar or different each person or case is), how much confidence you want to have, and how much error you are willing to accept. Fortunately, there are some common guidelines you can use to pull samples that meet various levels of confidence and error. The choice you make will likely come down to how many resources you have. Obviously, the larger the sample, the higher your confidence and lower your error. "]
[null,"Stratified Sampling"]
[null,"\nThis Excel tool can suggest various sample sizes with different levels of confidence and error. All you need to do is enter is the size of the population; the tool will do the rest. Many online calculators can also do this. This is called simple random sampling, where each person or case in the population has an equal chance of getting selected. However, this Excel tool can also help suggest stratified samples. \n\nStratified sampling involves dividing your population into smaller sub-groups (called strata), and pulling a sample from each strata. The strata are based on its members having something in common, like people from different counties, from different service providers, etc. Stratified sampling, also called proportional sampling, is recommended when the members from your population can easily be divided into similar groups, the size of those groups vary, and the groups they fall into are of interest to your study. For example, if you wanted to understand the experience of families who receive a service, like in-home parenting services, and there are many different providers that give that service, you might want to get a sample of families from each provider. If you did just a simple random sample, you might end up with a lot of people from the largest providers and few to none from the smaller providers. If that happens, you can't say anything about the experience of families from those small providers, which might be important information to know. Plus, those families are part of the overall population, and you want your sample to reflect the population as much as possible. Stratified sampling will help you achieve this. "]

{"sheet":"1 - Enter data","index":1,"n_rows":43,"n_cols":12,"rows_kept":43,"cut":false,"hidden":false,"merged":[[1,1,1,11],[19,11,20,11],[17,6,18,6],[17,7,18,7],[17,8,18,8],[17,9,18,9],[17,10,18,10],[17,11,18,11],[19,6,20,6],[19,7,20,7],[19,8,20,8],[19,9,20,9],[19,10,20,10]]}
[]
[null,"The example below is designed to inform case review sampling when studying the fidelity and use of Evidenced-Based Practices (EBPs), such as those used by child welfare agencies in the context of the Family First Prevention Services Act (FFPSA). The example uses \"EBP 1,\" \"EBP 2,\" etc. as placeholders for the actual EBPs you might be using and it requires selecting up to five EBPs. In this example, up to 26 strata can be listed. If you would like to customize this calculator for your setting or need a sampling calculator designed for a different need, please reach out to Chapin Hall."]
[]
[null,"  Sample Size Calculator for A Simple Random or Stratified Sample"]
[null,"Step 1","Enter the strata (e.g., counties, regions, providers, etc.) whose members you want to include in your sample."]
[null,null,"If you want a simple random sample instead of a stratified sample, then for strata just enter the population name (e.g., \"All counties,\" \"All providers,\" etc. or whatever population you are sampling))."]
[]
[null,"Step 2","For each strata, select the EBP type(s) and enter the number of cases for that strata for each EBP."]
[null,null,"For example, if your want to select a sample of cases from each EBP provider (your strata), list the providers for your strata, select the EBP type(s), and enter the number of cases each provider"]
[null,null,"served for each EBP. Or, if you want to select a sample of cases from each county (your strata), list the counties for your strata, select the EBP type(s), and enter the number of cases each county had"]
[null,null,"for each EBP. The counts you enter represent the full population from which you will sample. See below for an example of sampling by providers, some of whom provide more than one type of EBP."]
[]
[null,"Step 3","Go to the Results sheet to see your results."]
[null,null,"The calculator will suggest a sample size for each strata, for each type of EBP. It provides three options based on different levels of confidence and error. "]
[]
[null,null,"Strata (e.g., Counties, Providers, etc.) (Step 1)","EBP Type","# of cases served  (Step 2)",null,"Summary of cases served, by EBP"]
[null,null,"Provider Name","EBP Type","Served","GT"]
[null,null,"Provider ABC","EBP_1",100,"Total",{"$f":"'pivot - do not edit'!C3","v":"EBP_1"},{"$f":"'pivot - do not edit'!D3","v":"EBP_2"},{"$f":"'pivot - do not edit'!E3","v":"EBP_3"},{"$f":"'pivot - do not edit'!F3","v":"EBP_4"},{"$f":"'pivot - do not edit'!G3","v":"EBP_5"},{"$f":"'pivot - do not edit'!H3","v":"Total"}]
[null,null,"Provider ABC","EBP_2",50,"Total"]
[null,null,"Provider DEF","EBP_4",50,"Total",{"$f":"'pivot - do not edit'!C4","v":105},{"$f":"'pivot - do not edit'!D4","v":60},{"$f":"'pivot - do not edit'!E4","v":15},{"$f":"'pivot - do not edit'!F4","v":300},{"$f":"'pivot - do not edit'!G4","v":20},{"$f":"'pivot - do not edit'!H4","v":500}]
[null,null,"Provider GHI","EBP_2",10,"Total"]
[null,null,"Provider GHI","EBP_4",200,"Total"]
[null,null,"Provider GHI","EBP_5",20,"Total"]
[null,null,"Provider JKL","EBP_1",5,"Total"]
[null,null,"Provider MNO","EBP_3",15,"Total"]
[null,null,"Provider PQR","EBP_4",50,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]
[null,null,null,null,null,"Total"]

{"sheet":"2 - Results","index":2,"n_rows":48,"n_cols":43,"rows_kept":48,"cut":false,"hidden":false,"merged":[[47,10,77,15],[47,17,77,22],[47,24,77,29],[47,31,77,36],[8,35,8,36],[8,14,8,15],[8,21,8,22],[8,28,8,29],[28,31,28,36],[14,31,27,36]]}
[]
[null,"  Sample Size Calculator for EBP Case Reviews"]
[null,"Sample Size Results",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CI= Confidence Interval",null,null,null,null,null,null,null,null,null,"Sampling parameters",null,null,"Critical values"]
[null,"Below are three sample size options based on the number of cases served during the period which were entered in the previous sheet. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Distribution",0.5,null,0.9,1.645]
[null,"The three options reflect increasing levels of confidence that the sample you review will be representative of the full population of cases that were served.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CI_90",0.9,null,0.95,1.96]
[null,"Generally, the larger the sample size, the more confidence you have that your review findings would match what you would get if you had reviewed every possible case.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CI_95",0.95,null,0.99,2.5750000000000002]
[null,null,null,null,null,null,null,null,null,null,"Less confidence",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"More confidence",null,null,null,null,null,null,null,null,"MOE_10",0.1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"MOE_5",0.05]
[null,null,"Number of cases served, by provider and EBP",null,null,null,null,null,null,null,"Option 1",null,null,null,"see notes",null,null,"Option 2",null,null,null,"see notes",null,null,"Option 3",null,null,null,"see notes",null,null,"Option 4",null,null,null,60,null,"  <---  Enter maximum number of\n           cases agency can review"]
[null,null,"from the previous sheet",null,null,null,null,null,null,null,"90% CI, 10% Margin of error",null,null,null,null,null,null,"95% CI, 10% Margin of error",null,null,null,null,null,null,"95% CI, 5% Margin of error",null,null,null,null,null,null,{"$f":"AJ9/P13","v":0.38709677419354838},"of the total suggested sample size from Option 1"]
[]
[null,null,null,{"$f":"'pivot - do not edit'!C3","v":"EBP_1"},{"$f":"'pivot - do not edit'!D3","v":"EBP_2"},{"$f":"'pivot - do not edit'!E3","v":"EBP_3"},{"$f":"'pivot - do not edit'!F3","v":"EBP_4"},{"$f":"'pivot - do not edit'!G3","v":"EBP_5"},{"$f":"'pivot - do not edit'!H3","v":"Total"},null,{"$f":"D12","v":"EBP_1"},"EBP_2","EBP_3","EBP_4","EBP_5","Total",null,{"$f":"K12","v":"EBP_1"},"EBP_2","EBP_3","EBP_4","EBP_5","Total",null,{"$f":"R12","v":"EBP_1"},"EBP_2","EBP_3","EBP_4","EBP_5","Total",null,{"$f":"Y12","v":"EBP_1"},{"$f":"Z12","v":"EBP_2"},{"$f":"AA12","v":"EBP_3"},{"$f":"AB12","v":"EBP_4"},{"$f":"AC12","v":"EBP_5"},{"$f":"AD12","v":"Total"}]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,"Option 1 Explanation",null,null,null,null,null,null,"Option 2 Explanation",null,null,null,null,null,null,"Option 3 Explanation",null,null,null,null,null,null,"Option 4 Explanation"]
[]
[null,null,null,null,null,null,null,null,"Assumptions",null,"50% response distribution",null,null,null,null,null,null,"50% response distribution",null,null,null,null,null,null,"50% response distribution",null,null,null,null,null,null,"NA response distribution"]
[null,null,null,null,null,null,null,null,"The suggested sample size is based on three paramaters (response distribution,  ",null,"90% confidence interval",null,null,null,null,null,null,"95% confidence interval",null,null,null,null,null,null,"95% confidence interval",null,null,null,null,null,null,"NA confidence interval"]
[null,null,null,null,null,null,null,null,"confidence internal, and margin of error), plus the population size estimated earlier.",null,"10% margin of error",null,null,null,null,null,null,"10% margin of error",null,null,null,null,null,null,"5% margin of error",null,null,null,null,null,null,"NA margin of error"]
[]
[null,null,null,null,null,null,null,null,"Interpretation",null,"The review is designed to tell us the extent to which the EBP is being implemented with fidelty. Let's call this the \"fidelity amount.\" We don't know the true fidelity amount because we can't review every single case, so we will make a conservative guess that for any given EBP about 50% of the cases are being implemented with fidelity. This is the most conservative assumption. \n\nThe bigger our sample, the more likely our case review will produce a fidelity amount that's close to the true one. How often we get a fidelity amount that's close to the true one (90% of the time? 95% of the time?) is our confidence, and how close we get to the true value (within 5% of the true value? 10%?) is our margin of error. \n\nA sample size based on a 90% confidence interval and 10% margin of error means that, if we were to repeat the case review many times (with a new sample each time), 90% of the time our case review will produce a fidelity amount that's within 10% of the true fidelity amount. In other words, if we assume that 50% of EBPs are implemented with fidelity (our best guess), and we went with the suggested sample size, about 90% of the time our review would find that between 40% to 60% of the cases were implemented with fidelity. This means that 10% of the time our review would suggest fidelity is much lower  (< 40%) or much higher (> 60%) than it truly is.",null,null,null,null,null,null,"The review is designed to tell us the extent to which the EBP is being implemented with fidelty. Let's call this the \"fidelity amount.\" We don't know the true fidelity amount because we can't review every single case, so we will make a conservative guess that for any given EBP about 50% of the cases are being implemented with fidelity. This is the most conservative assumption. \n\nThe bigger our sample, the more likely our case review will produce a fidelity amount that's close to the true one. How often we get a fidelity amount that's close to the true one (90% of the time? 95% of the time?) is our confidence, and how close we get to the true value (within 5% of the true value? 10%?) is our margin of error. \n\nA sample size based on a 95% confidence interval and 10% margin of error means that, if we were to repeat the case review many times (with a new sample each time), 95% of the time our case review will produce a fidelity amount that's within 10% of the true fidelity amount. In other words, if we assume that 50% of EBPs are implemented with fidelity (our best guess), and we went with the suggested sample size, about 95% of the time our review would find that between 40% to 60% of the cases were implemented with fidelity. This means that 5% of the time our review would suggest fidelity is much lower  (< 40%) or much higher (> 60%) than it truly is.",null,null,null,null,null,null,"The review is designed to tell us the extent to which the EBP is being implemented with fidelty. Let's call this the \"fidelity amount.\" We don't know the true fidelity amount because we can't review every single case, so we will make a conservative guess that for any given EBP about 50% of the cases are being implemented with fidelity. This is the most conservative assumption. \n\nThe bigger our sample, the more likely our case review will produce a fidelity amount that's close to the true one. How often we get a fidelity amount that's close to the true one (90% of the time? 95% of the time?) is our confidence, and how close we get to the true value (within 5% of the true value? 10%?) is our margin of error. \n\nA sample size based on a 95% confidence interval and 5% margin of error means that, if we were to repeat the case review many times (with a new sample each time), 95% of the time our case review will produce a fidelity amount that's within 5% of the true fidelity amount. In other words, if we assume that 50% of EBPs are implemented with fidelity (our best guess), and we went with the suggested sample size, about 95% of the time our review would find that between 45% to 55% of the cases were implemented with fidelity. This means that 5% of the time our review would suggest fidelity is lower (< 45%) or higher (> 55%) than it truly is.",null,null,null,null,null,null,"This option takes the number of cases the agency has the capacity to review (entered in the yellow box) and determines what percentage that number represents of the total suggested sample from Option 1. For example, if Option 1 suggested a total sample (across all EBPS) of 100, but the agency can only review 60 cases, the agency can review 60% (60 / 100) of what was recommended (for Option 1). The calculator then takes 60% (using this example) of the samples Option 1 recommended for each EBP to calculate the suggested samples.\n\n"]

{"sheet":"pivot - do not edit","index":3,"n_rows":10,"n_cols":10,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[null,"Provider Pivot Table (populates the population table in 2 - Results)"]
[null,"Sum of Served","Column Labels",null,null,null,null,null,null,"EBPs"]
[null,"Row Labels","EBP_1","EBP_2","EBP_3","EBP_4","EBP_5","Total",null,"EBP_1"]
[null,"Total",105,60,15,300,20,500,null,"EBP_2"]
[null,"Provider ABC",100,50,null,null,null,150,null,"EBP_3"]
[null,"Provider DEF",null,null,null,50,null,50,null,"EBP_4"]
[null,"Provider GHI",null,10,null,200,20,230,null,"EBP_5"]
[null,"Provider JKL",5,null,null,null,null,5]
[null,"Provider MNO",null,null,15,null,null,15]
[null,"Provider PQR",null,null,null,50,null,50]