The following is a description of the methodology employed to obtain the sampling error for the CIS-2008 estimates, presented in this report. The CIS-2008 uses a multi-stage random sample survey method to estimate the incidence and characteristics of cases of reported child abuse and neglect across the country.
The size of this sample ensures that estimates for figures such as the overall rate of reported maltreatment, substantiation rate, and major categories of maltreatment have a reasonable margin of error. Estimates are only representative of the sampling period; therefore, the error estimates do not account for any errors in determining the annual and regional weights.
To assess the precision of the CIS-2008 estimates, sampling errors were calculated taking into account the stratified cluster design of the sample, in which at least one cluster (or site) had been randomly selected from each stratum. As some strata contained only one cluster, the following approach was used (Rust & Kalton, 1987). The following are the variance estimates and confidence intervals for the variables of interest. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. When making inferences about group means, are credible Intervals sensitive to within-subject variance while confidence intervals are not? In the answers there (if I understood correctly) I learned that within-subject variance does not effect inferences made about group means and it is ok to simply take the averages of averages to calculate group mean, then calculate within-group variance and use that to perform significance tests. Here is a plot of the original data along with some simulated data that used the same subject means, but sampled the individual measurements for each subject from a normal distribution using those means and a small within-subject variance (sd=.1). In my answer to your first question, I have suggested you to note that one obtains a classical (fixed effects) Gaussian linear model for the subjects means $\bar y_{ij\bullet}$. And then I claimed that in order to draw inference about the $\mu_i$ you can simply consider the simple classical linear model whose observations are the subjects means $\bar y_{ij\bullet}$. As you see from the boxed formula, the within-variance $\sigma^2_w$ plays a role in the model for the observed group means. That model makes sense, yet the code does not seem to incorporate that information and I guess this is what I would like to understand. I have not tried, but that sounds strange, you remove the fixed intercept but there is a random intercept by subject. I followed this instruction as I could not otherwise figure out how to get an interval estimate.
Though I wonder whether the lsmeans package together with the pbkrtest package could provide good confidence intervals. Not the answer you're looking for?Browse other questions tagged r confidence-interval mixed-model jags error-propagation or ask your own question. What level to use when making inferences on the group mean in a hierarchical Bayesian analysis? What type of under the seat bag is practical, and what should be stored in it for the flight?
The same approach used to calculate a confidence interval for the effect size or statistical power of a t test (see Confidence Intervals for Power and Effect Size of t Tests)  can be employed to create a confidence interval for the noncentrality parameter, and in turn the RMSSE effect size and statistical power, of one-factor ANOVA. Example 1: Find the 95% confidence interval for RMSSE and power of the one-way ANOVA of Example 1 of Power of One-way ANOVA. The analysis is shown in Figure 1 (with references to cells in Figure 1 of Power of One-way ANOVA). We see from Figure 1 that the 95% confidence interval for the noncentrality parameter is (0, 23.68).

This collection highlights important statistical issues that biologists should be aware of and provides practical advice to help them improve the rigor of their work. Nature Methods' Points of Significance column on statistics explains many key statistical and experimental design concepts. 6.  Understand how sample size, level of confidence and standard deviation affect confidence interval length. Other scenarios to think about:  What would happen to the length of our confidence intervals if we increase our sample size from 60 to 100?  Would our intervals decrease or increase in length?  What if the population standard deviation increased? 3.  How large a sample of one-bedroom apartments above would be needed to estimate the population mean within plus or minus $50 with 90% confidence?
Chapter 7 Objectives 5.Determine the minimum sample size for finding a confidence interval for a proportion. 7.1 Confidence Intervals for the Mean When Is Known and Sample Size A point estimate is a specific numerical value estimate of a parameter. Three Properties of a Good Estimator unbiased estimator 1.The estimator should be an unbiased estimator. Three Properties of a Good Estimator consistent estimator 2.The estimator should be consistent.
Confidence Intervals for the Mean When Is Known and Sample Size interval estimate An interval estimate of a parameter is an interval or a range of values used to estimate the parameter.
Confidence Level of an Interval Estimate confidence level The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter is repeated.
Confidence Interval confidence interval A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. Maximum Error of the Estimate Bluman, Chapter 7 14 The maximum error of the estimate is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter.
Rounding Rule When you are computing a confidence interval for a population mean by using raw data, round off to one more decimal place than the number of decimal places in the original data. Example 7-1: Days to Sell an Aveo A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Chevrolet Aveo. 95% Confidence Interval of the Mean Bluman, Chapter 7 22 One can be 95% confident that an interval built around a specific sample mean would cntain the population mean.
Example 2 A study of 40 English composition professors showed that they spent, on average, 12.6 minutes correcting a students term paper. Example 7-3: Credit Union Assets The following data represent a sample of the assets (in millions of dollars) of 30 credit unions in southwestern Pennsylvania.
For example, the estimated number of child maltreatment investigations in Canada during 2008 is 235,842, with a 95% confidence interval ranging from 202,523 to 269,161 investigations.
Nor do they account for any other non-sampling errors that may occur, such as inconsistencies or inadequacies in administrative procedures from site to site. The tables are presented to correspond with the tables in the chapters of the CIS-2008 report. I would like to use a method where the larger the within subject variance the less sure I am about the group means or understand why it does not make sense to desire that.
As can be seen the group level confidence intervals (bottom row) are unaffected by this (at least the way I calculated them). A subset of the confidence intervals are shown in the left panels while the distribution of their widths is shown by the corresponding right panels. It is different than the frequentist model because you assume a different variance for each subject (nested in group).

I don't know what you should do but I claimed that the sampling distribution of your Bayesian model is not the same as the one of the frequentist model. For your model in the particular case of a balanced design there exist some exact least-squares methods, but I don't know whether they are available in some package. This reinforces what we should already know, namely that caution needs to be applied when running statistical tests, especially with small sample sizes.
Other resources include an online plotting tool and links to statistics guides from other publishers.
Which of the assumptions listed above might be problematic in making inference to the population in Question 4? That is, the expected value or the mean of the estimates obtained from samples of a given size is equal to the parameter being estimated.
For a consistent estimator, as sample size increases, the value of the estimator approaches the value of the parameter estimated.
When you are computing a confidence interval for a population mean by using a sample mean and a standard deviation, round off to the same number of decimal places as given for the mean.
Assuming the standard deviation of the population is 0.8 year, find the best point estimate of the population mean and the 99% confidence interval of the population mean. If you are using computer or calculator programs to find the solutions, the answers you get may vary somewhat from the ones given in the textbook. This means that if the study were repeated 20 times, in 19 times the calculated confidence interval (202,523-269,161) would contain the true number of child maltreatment investigations (Table K3-1). In a few sites, an additional sampling stage was performed, in which a shorter collection period was selected or cases were randomly sampled. That is, had different clusters been selected in the sample, different estimates would have been obtained. Each table includes the estimate, its standard error, coefficient of variation (CV), and lower and upper limits of the confidence interval. This meets my intuition of what I would like to occur when making inferences about group means, but I am not sure if this is just some artifact of my model or a property of credible intervals. This is so because computers and calculators do not round the answers in the intermediate steps and can use 12 or more decimal places for computation. The accuracy of these annual estimates depends on the extent to which the sampling period is representative of the whole year. As the stratified random sample’s variability between strata is zero, the variance at the national level is then calculated as the sum of the variance for each stratum.
However, I am still confused by my example above but will follow this up with a new more focused question.
Find the best point estimate of the population mean and the 95% confidence interval of the population mean. A regionalization weight was used to weight the survey data so that data from sites represented regions or strata from which they were selected.

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