Author Topic: A Math/Statistics Question For Anyone Interested  (Read 6957 times)

Al Doggity

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A Math/Statistics Question For Anyone Interested
« on: December 19, 2014, 10:29:43 AM »
So, this is a question another poster and I have had and rather than hijack a thread, was hoping the helpful GetBlerg family could help us out with maths and sciences.

A government poll in crime can be found at this link:
http://www.bjs.gov/index.cfm?ty=dcdetail&iid=245#Methodology

Some of the poll questions have fewer than 10 respondents.
Under a section titled "Standard Error Computations" there is the following line:

(Interpret data with caution. Estimate based on 10 or fewer sample cases, or the coefficient of variation is greater than 50%).

Do you think this means that the data is extremely reliable or that the people who put together the poll feel it might be unreliable?

_aj_

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Re: A Math/Statistics Question For Anyone Interested
« Reply #1 on: December 19, 2014, 10:32:19 AM »
It means that the sample size (number of respondents) compared to the population is not large enough to draw statistically valid conclusions.

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #2 on: December 19, 2014, 10:38:00 AM »
It means that the sample size (number of respondents) compared to the population is not large enough to draw statistically valid conclusions.

Are you sure? Couldn't it also mean that the scientists who conducted the poll weighted the study so that the 10 people who responded could accurately represent the national trend?

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Re: A Math/Statistics Question For Anyone Interested
« Reply #3 on: December 19, 2014, 10:41:10 AM »
Are you sure? Couldn't it also mean that the scientists who conducted the poll weighted the study so that the 10 people who responded could accurately represent the national trend?

That would be statistically impossible. 10 people cannot possibly speak for a nation.

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #4 on: December 19, 2014, 10:43:31 AM »
That would be statistically impossible. 10 people cannot possibly speak for a nation.

What if you interviewed 150,000 people, then took the most relevant 10 from the sample of 150,000. Wouldn't that make the numbers more reliable?

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Re: A Math/Statistics Question For Anyone Interested
« Reply #5 on: December 19, 2014, 10:44:40 AM »
What if you interviewed 150,000 people, then took the most relevant 10 from the sample of 150,000. Wouldn't that make the numbers more reliable?

I now realize that I am being trolled. Well played.

I'm out.

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #6 on: December 19, 2014, 10:47:41 AM »
I now realize that I am being trolled. Well played.

I'm out.

Yes, Archer77 is an idiot. He made these very suggestions in a recent post regarding that study. He's a dishonest man.

OneMoreRep

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Re: A Math/Statistics Question For Anyone Interested
« Reply #7 on: December 19, 2014, 10:50:18 AM »
(Interpret data with caution. Estimate based on 10 or fewer sample cases, or the coefficient of variation is greater than 50%).

Do you think this means that the data is extremely reliable or that the people who put together the poll feel it might be unreliable?

When you calculate the coefficient of variation when looking at things like population-based surveys and/or something like a census, it is employed in order to determine sampling error. The coefficient variation is used to determine the reliability of a sample. You get what this means?

So, for instance, a coefficient variation figure that is low indicates that the sampling error is also low relative to the estimate, this allows for a statistician to assume that the estimate is a pretty solid guess to the population value.

What you need to keep in mind is that the lower the CV value, the more reliable the results of a survey or census are. The higher the CV value, the more inclined that survey is to sampling error (i.e. unreliable results).

"1"

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #8 on: December 19, 2014, 10:52:30 AM »
When you calculate the coefficient of variation when looking at things like population-based surveys and/or something like a census, it is employed in order to determine sampling error. The coefficient variation is used to determine the reliability of a sample. You get what this means?

So, for instance, a coefficient variation figure that is low indicates that the sampling error is also low relative to the estimate, this allows for a statistician to assume that the estimate is a pretty solid guess to the population value.

What you need to keep in mind is that the lower the CV value, the more reliable the results of a survey or census are. The higher the CV value, the more inclined that survey is to sampling error (i.e. unreliable results).

"1"

Right. So, basically, a sample size of 10 is not going to give you a reliable national statistic. Is that what you're saying?

Hulkotron

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Re: A Math/Statistics Question For Anyone Interested
« Reply #9 on: December 19, 2014, 10:53:29 AM »
I believe it (CoV) can also indicate how likely the results may be to change if you were to have a larger sample since your true "mean" likely lies somewhere within it.  Typically the more samples you collect, the smaller it will be until you have sampled everyone and have the true mean and variance.

For example if it is very big (no homo), then your observed mean could be way off from the true mean, if it is very small then probably will not get a starkly different result with more bodybuilders in your study.

10 is clearly nowhere near big enough to say anything meaningful about the national level.  We call this the "traumatic ocular", i.e. something that is obviously right or wrong without any formal statistical backing.

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #10 on: December 19, 2014, 10:58:06 AM »
I believe it (CoV) can also indicate how likely the results may be to change if you were to have a larger sample since your true "mean" likely lies somewhere within it.  Typically the more samples you collect, the smaller it will be until you have sampled everyone and have the true mean and variance.

For example if it is very big (no homo), then your observed mean could be way off from the true mean, if it is very small then probably will not get a starkly different result with more bodybuilders in your study.

10 is clearly nowhere near big enough to say anything meaningful about the national level.  We call this the "traumatic ocular", i.e. something that is obviously right or wrong without any formal statistical backing.

So, basically, 10 is too small of a sample size to be accurate? And that line from the opening post is saying as much?

Hulkotron

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Re: A Math/Statistics Question For Anyone Interested
« Reply #11 on: December 19, 2014, 11:00:49 AM »
So, basically, 10 is too small of a sample size to be accurate? And that line from the opening post is saying as much?

It looks to me like it is saying potentially two different things, that either N≤10 or the CoV≥50%.  There are cases where these things are okay, but to represent a national sample the former is too small, and the latter is very large, in my opinion.

More N is not always better, this a common misunderstanding of statistics by the unwashed lay population.  For example there is a well-known study on cancer that says taking a multivitamin increases your cancer risk, but it was because they had hundreds of thousands of people in the study and every tiny little observed difference becomes "significant" with a sample that large.  Taking the multivitamin does not meaningfully increase your risk of cancer.

But in this case I agree that N=10 is far too small yes.

OneMoreRep

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Re: A Math/Statistics Question For Anyone Interested
« Reply #12 on: December 19, 2014, 11:01:28 AM »
Right. So, basically, a sample size of 10 is not going to give you a reliable national statistic. Is that what you're saying?

Depends, is that sample group composed of Sheldon Adelson and 9 other of America's richest people?

Another way of looking at it is by asking if the 538 presidential electors that make up the electoral college are a reliable-enough group to chose our president every 4 years (Keeping in mind that there are 316 Million Americans)?

No is the straightforward answer to your question. A sample of 10 people can not give you a reliable national statistic.

"1"

Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #13 on: December 19, 2014, 11:06:15 AM »
Depends, is that sample group composed of Sheldon Adelson and 9 other of America's richest people?

Another way of looking at it is by asking if the 538 presidential electors that make up the electoral college are a reliable-enough group to chose our president every 4 years (Keeping in mind that there are 316 Million Americans)?

No is the straightforward answer to your question. A sample of 10 people can not give you a reliable national statistic.

"1"

Exactly. But more importantly... that's exactly what quoted text from the study is saying, too.

Viking11

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Re: A Math/Statistics Question For Anyone Interested
« Reply #14 on: December 19, 2014, 11:17:52 AM »
It means that the sample size (number of respondents) compared to the population is not large enough to draw statistically valid conclusions.
THIS

Hulkotron

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Re: A Math/Statistics Question For Anyone Interested
« Reply #15 on: December 19, 2014, 11:18:49 AM »
Exactly. But more importantly... that's exactly what quoted text from the study is saying, too.

I only looked at one of the reports but the number of results with the ! looks to be very small and not frequent.  Most of them have samples in the thousands.  So you will need to temper your conclusion if you are wanting to use the presence of the ! anywhere to reject the entirety of the data within this archive.  But for specific results marked with the !, they are very likely not valid yes.

Archer77

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Re: A Math/Statistics Question For Anyone Interested
« Reply #16 on: December 19, 2014, 11:20:42 AM »
That would be statistically impossible. 10 people cannot possibly speak for a nation.
 



This is the methodology.

In 2013, 90,630 households and 160,040 persons age 12 or older were interviewed for the NCVS. Each household was interviewed twice during the year. The response rate was 84% for households and 88% for eligible persons. Victimizations that occurred outside of the United States are excluded. In 2013, less than 1% of the unweighted victimizations occurred outside of the United States and are excluded from analyses of NCVS data.

Estimates in NCVS reports typically use data from the 1993 to 2013 NCVS data files, weighted to produce annual estimates of victimization for persons age 12 or older living in U.S. households. Since the NCVS relies on a sample rather than a census of the entire U.S. population, weights are designed to inflate sample point estimates to known population totals and to compensate for survey nonresponse and other aspects of the sample design.
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Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #17 on: December 19, 2014, 11:20:55 AM »
I only looked at one of the reports but the number of results with the ! looks to be very small and not frequent.  Most of them have samples in the thousands.  So you will need to temper your conclusion if you are wanting to use the presence of the ! anywhere to reject the entirety of the data within this archive.  But for specific results marked with the !, they are very likely not valid yes.

My point is specifically for cases containing 10 or less sample studies.

Archer77

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Re: A Math/Statistics Question For Anyone Interested
« Reply #18 on: December 19, 2014, 11:25:59 AM »
My point is specifically for cases containing 10 or less sample studies.

You said they don't use weighing adjustments.


https://www2.fbi.gov/ucr/cius_04/appendices/appendix_04.html

In addition, some differences in the data from the two programs may result from sampling variation in the NCVS and from estimating for nonresponse in the UCR. The BJS derives the NCVS estimates from interviewing a sample and are, therefore, subject to a margin of error. The BJS uses rigorous statistical methods to calculate confidence intervals around all survey estimates. The BJS describes trend data in the NCVS reports as genuine only if there is at least a 90-percent certainty that the measured changes are not the result of sampling variation. The UCR Program bases its data on the actual counts of offenses reported by law enforcement agencies. In some circumstances, the UCR Program estimates its data for nonparticipating agencies or those reporting partial data.

Apparent discrepancies between statistics from the two programs can usually be accounted for by their definitional and procedural differences or resolved by comparing NCVS sampling variations (confidence intervals) of those crimes said to have been reported to police with UCR statistics.
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_aj_

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Re: A Math/Statistics Question For Anyone Interested
« Reply #19 on: December 19, 2014, 11:26:07 AM »
 



This is the methodology.

In 2013, 90,630 households and 160,040 persons age 12 or older were interviewed for the NCVS. Each household was interviewed twice during the year. The response rate was 84% for households and 88% for eligible persons. Victimizations that occurred outside of the United States are excluded. In 2013, less than 1% of the unweighted victimizations occurred outside of the United States and are excluded from analyses of NCVS data.

Estimates in NCVS reports typically use data from the 1993 to 2013 NCVS data files, weighted to produce annual estimates of victimization for persons age 12 or older living in U.S. households. Since the NCVS relies on a sample rather than a census of the entire U.S. population, weights are designed to inflate sample point estimates to known population totals and to compensate for survey nonresponse and other aspects of the sample design.


OK, that methodology computes to me, at least. The sample size is 160K, which is more than significant for the US population.

El Diablo Blanco

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Re: A Math/Statistics Question For Anyone Interested
« Reply #20 on: December 19, 2014, 11:31:14 AM »
I asked Tito's mom and she said

"GRRBRBDAGLLLL"

Then I pulled my cock out of her mouth.

Archer77

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Re: A Math/Statistics Question For Anyone Interested
« Reply #21 on: December 19, 2014, 11:33:02 AM »
OK, that methodology computes to me, at least. The sample size is 160K, which is more than significant for the US population.

National Crime Victimization Survey
The Bureau of Justice Statistics’ (BJS) NCVS, which began in 1973, provides a detailed picture of crime incidents, victims, and trends. After a substantial period of research, the BJS completed an intensive methodological redesign of the survey in 1993. The BJS conducted the redesign to improve the questions used to uncover crime, update the survey methods, and broaden the scope of crimes measured. The redesigned survey collects detailed information on the frequency and nature of the crimes of rape, sexual assault, personal robbery, aggravated and simple assault, household burglary, theft, and motor vehicle theft. It does not measure homicide or commercial crimes (such as burglaries of stores).

Two times a year, U.S. Bureau of the Census personnel interview household members in a nationally representative sample of approximately 43,000 households (about 76,000 people). Approximately 150,000 interviews of persons age 12 or older are conducted annually. Households stay in the sample for 3 years. New households rotate into the sample on an ongoing basis.

The NCVS collects information on crimes suffered by individuals and households, whether or not those crimes were reported to law enforcement. It estimates the proportion of each crime type reported to law enforcement, and it summarizes the reasons that victims give for reporting or not reporting.

The survey provides information about victims (age, sex, race, ethnicity, marital status, income, and educational level), offenders (sex, race, approximate age, and victim-offender relationship), and the crimes (time and place of occurrence, use of weapons, nature of injury, and economic consequences). Questions also cover the experiences of victims with the criminal justice system, self-protective measures used by victims, and possible substance abuse by offenders. Supplements are added periodically to the survey to obtain detailed information on topics like school crime.

https://www2.fbi.gov/ucr/cius_04/appendices/appendix_04.html
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Archer77

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Re: A Math/Statistics Question For Anyone Interested
« Reply #22 on: December 19, 2014, 11:36:03 AM »

http://www.bjs.gov/index.cfm?ty=dcdetail&iid=245#Methodology


Survey coverage

The National Crime Victimization Survey (NCVS) is an annual data collection conducted by the U.S. Census Bureau for the Bureau of Justice Statistics (BJS). The NCVS is a self-report survey in which interviewed persons are asked about the number and characteristics of victimizations experienced during the prior 6 months. The NCVS collects information on nonfatal personal crimes (rape or sexual assault, robbery, aggravated and simple assault, and personal larceny) and household property crimes (burglary, motor vehicle theft, and other theft) both reported and not reported to police. In addition to providing annual level and change estimates on criminal victimization, the NCVS is the primary source of information on the nature of criminal victimization incidents.

Survey respondents provide information about themselves (e.g., age, sex, race and Hispanic origin, marital status, education level, and income) and whether they experienced a victimization. Information is collected for each victimization incident, about the offender (e.g., age, race and Hispanic origin, sex, and victim-offender relationship), characteristics of the crime (including time and place of occurrence, use of weapons, nature of injury, and economic consequences), whether the crime was reported to police, reasons the crime was or was not reported, and experiences with the criminal justice system.

The NCVS is administered to persons age 12 or older from a nationally representative sample of households in the United States. The NCVS defines a household as a group of members who all reside at a sampled address. Persons are considered household members when the sampled address is their usual place of residence at the time of the interview and when they have no usual place of residence elsewhere. Once selected, households remain in the sample for 3 years, and eligible persons in these households are interviewed every 6 months either in person or over the phone for a total of seven interviews.
Generally, all first interviews are conducted in-person. New households rotate into the sample on an ongoing basis to replace outgoing households that have been in sample for the 3-year period. The sample includes persons living in group quarters, such as dormitories, rooming houses, and religious group dwellings, and excludes persons living in military barracks and institutional settings, such as correctional or hospital facilities, and the homeless.

Nonresponse and weighting adjustments

In 2013, 90,630 households and 160,040 persons age 12 or older were interviewed for the NCVS. Each household was interviewed twice during the year. The response rate was 84% for households and 88% for eligible persons. Victimizations that occurred outside of the United States are excluded. In 2013, less than 1% of the unweighted victimizations occurred outside of the United States and are excluded from analyses of NCVS data.

Estimates in NCVS reports typically use data from the 1993 to 2013 NCVS data files, weighted to produce annual estimates of victimization for persons age 12 or older living in U.S. households. Since the NCVS relies on a sample rather than a census of the entire U.S. population, weights are designed to inflate sample point estimates to known population totals and to compensate for survey nonresponse and other aspects of the sample design.

The NCVS data files include both person and household weights. Person weights provide an estimate of the population represented by each person in the sample. Household weights provide an estimate of the U.S. household population represented by each household in the sample. After proper adjustment, both household and person weights are also typically used to form the denominator in calculations of crime rates.

Victimization weights used in analysis of NCVS data account for the number of persons present during an incident and for high-frequency repeat victimizations (or series victimizations). Series victimizations are similar in type but occur with such frequency that a victim is unable to recall each individual event or describe each event in detail. Survey procedures allow NCVS interviewers to identify and classify these similar victimizations as series victimizations and to collect detailed information on only the most recent incident in the series.

The weight counts series incidents as the actual number of incidents reported by the victim, up to a maximum of 10 incidents. Including series victimizations in national rates results in rather large increases in the level of violent victimization; however, trends in violence are generally similar regardless of whether series victimizations are included.

In 2013, series incidents accounted for about 1% of all victimizations and 4% of all violent victimizations. Weighting series incidents as the number of incidents up to a maximum of 10 incidents produces more reliable estimates of crime levels, while the cap at 10 minimizes the effect of extreme outliers on the rates. Additional information on the series enumeration is detailed in the report Methods for Counting High Frequency Repeat Victimizations in the National Crime Victimization Survey, NCJ 237308, BJS web, April 2012.

Standard error computations

When national estimates are derived from a sample, as with the NCVS, caution must be taken when comparing one estimate to another estimate or when comparing estimates over time. Although one estimate may be larger than another, estimates based on a sample have some degree of sampling error. The sampling error of an estimate depends on several factors, including the amount of variation in the responses, and the size of the sample. When the sampling error around an estimate is taken into account, the estimates that appear different may not be statistically different.

One measure of the sampling error associated with an estimate is the standard error. The standard error can vary from one estimate to the next. Generally, an estimate with a small standard error provides a more reliable approximation of the true value than an estimate with a large standard error. Estimates with relatively large standard errors are associated with less precision and reliability and should be interpreted with caution.

In order to generate standard errors around numbers and estimates from the NCVS, the Census Bureau produced generalized variance function (GVF) parameters for BJS. The GVFs take into account aspects of the NCVS complex sample design and represent the curve fitted to a selection of individual standard errors based on the Jackknife Repeated Replication technique. The GVF parameters are used to generate standard errors for each point estimate (such as counts, percentages, and rates) in reports using NCVS data.

BJS conducts tests to determine whether differences in estimated numbers and percentages in  reports using NCVS data are statistically significant once sampling error is taken into account. Using statistical programs developed specifically for the NCVS, all comparisons in the text of reports are tested for significance. The Student’s t-statistic is the primary test procedure, which tests the difference between two sample estimates.

Data users can use the estimates and the standard errors of the estimates provided in  reports to generate a confidence interval around the estimate as a measure of the margin of error. The following example illustrates how standard errors can be used to generate confidence intervals:
According to the NCVS, in 2013, the violent victimization rate among persons age 12 or older was 23.2 per 1,000 persons (see table 1 in Criminal Victimization, 2013, NCJ 247648, September 2014). Using the GVFs, it was determined that the estimated victimization rate estimate has a standard error of 1.6 (see appendix table 2 in Criminal Victimization, 2013, NCJ 247648, September 2014). A confidence interval around the estimate was generated by multiplying the standard errors by ±1.96 (the t-score of a normal, two- tailed distribution that excludes 2.5% at either end of the distribution). Therefore, the 95% confidence interval around the 23.2 estimate from 2013 is 23.2 ± (1.6 X 1.96) or (20.0 to 26.3). In others words, if different samples using the same procedures were taken from the U.S. population in 2013, 95% of the time the violent victimization rate would fall between 20.0 and 26.3 per 1,000 persons.

BJS also calculates a coefficient of variation (CV) for all estimates, representing the ratio of the standard error to the estimate. CVs provide a measure of reliability and a means to compare the precision of estimates across measures with differing levels or metrics. In cases where the CV is greater than 50%, or the unweighted sample had 10 or fewer cases, the estimate is noted with a “!” symbol (Interpret data with caution. Estimate based on 10 or fewer sample cases, or the coefficient of variation is greater than 50%).

National Crime Victimization Survey (NCVS) restoration and redesign

In 1972, the Bureau of Justice Statistics (BJS) instituted the National Crime Victimization Survey (NCVS), formerly known as the National Crime Survey (NCS), to produce national estimates of the levels and characteristics of criminal victimization in the United States, including crime not reported to police departments. Along with the FBI’s Uniform Crime Reporting (UCR) Program, the NCVS constitutes a key component of our nation’s system to measure the extent and nature of crime in the United States.

In 2008, BJS sponsored an expert panel study carried out by the National Research Council of the National Academies to review the survey’s methodology and provide guidelines for options to redesign the NCVS. The panel’s recommendations are contained in Surveying Victims: Options for Conducting the National Crime Victimization Survey (National Research Council, 2008). In response to these recommendations, BJS initiated a two-prong approach to redesign and restore the NCVS with the ultimate goals to improve the survey’s methodology, contain costs, assure sustainability, increase value to national and local stakeholders, and better meet the challenges of measuring the extent, characteristics, and consequences of criminal victimization.

To restore the quality of the NCVS data, BJS and the U.S. Census Bureau implemented two large-scale interventions. First, the number of sample cases was increased to improve the stability and precision of national and subgroup estimates of victimization. Second, in late 2011, refresher training and performance monitoring of field representatives (FR) were initiated to improve the quality and costs associated with data collection. The effects of these interventions have been monitored in an effort to maintain consistent year-to-year comparisons. BJS continues to evaluate the impact of each on-going intervention on criminal victimization estimates and other estimates of data quality, including response rates and measures of interview quality.

Methodological changes to the NCVS in 2006

Methodological changes implemented in 2006 may have affected the crime estimates for that year to such an extent that they are not comparable to estimates from other years. Evaluation of 2007 and later data from the NCVS conducted by BJS and the Census Bureau found a high degree of confidence that estimates for 2007, 2008, 2009, 2010, 2011, 2012, and 2013 are consistent with and comparable to estimates for 2005 and previous years. The reports, Criminal Victimization, 2006, NCJ 219413, December 2007; Criminal Victimization, 2007, NCJ 224390, December 2008; Criminal Victimization, 2008, NCJ 227777, September 2009; Criminal Victimization, 2009, NCJ 231327, October 2010; Criminal Victimization, 2010, NCJ 235508, September 2011; Criminal Victimization, 2011, NCJ 239437, October 2012, and Criminal Victimization, 2012, NCJ 243389, October 2013 are available on the BJS website.
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Al Doggity

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Re: A Math/Statistics Question For Anyone Interested
« Reply #23 on: December 19, 2014, 11:37:25 AM »
You said they don't use weighing adjustments.



Where did I say this?

Archer77

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Re: A Math/Statistics Question For Anyone Interested
« Reply #24 on: December 19, 2014, 11:39:47 AM »

Where did I say this?


In several of the categories, there are less than 10 sample cases. You made the claim that you could make an accurate assessment on race based on these sample cases. Within the very study, it says that you cannot make an accurate assessment because the sample sizes are too small. You have stated over and over that the BOJ created some kin d of weight that corrects for this. That's simply not true. You are clinging to that point because you feel like it makes a point about race and crime, when no logical point can be inferred from such a small sample size. The authors of the study admit that.

Please peddle some more idiotic mumbo jumbo to stay the course.
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