Can confidence interval be used for population?

If you know the standard deviation for a population, then you can calculate a confidence interval (CI) for the mean, or average, of that population. You estimate the population mean, μ, by using a sample mean, x̄, plus or minus a margin of error. The result is called a confidence interval for the population mean, μ.

What is population confidence interval?

A confidence interval for the mean is a way of estimating the true population mean. Instead of a single number for the mean, a confidence interval gives you a lower estimate and an upper estimate. For example, instead of “6” as the mean you might get {5,7}, where 5 is the lower estimate and 7 is the upper.

What is profile likelihood confidence interval?

Profile likelihood confidence intervals are based on the log-likelihood function. For a single parameter, likelihood theory shows that the 2 points 1.92 units down from the maximum of the log-likelihood function provide a 95% confidence interval when there is no extrabinomial variation (i.e. c = 1)..

What are the 95% confidence intervals estimating?

Strictly speaking a 95% confidence interval means that if we were to take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).

Which is the 95% confidence interval in likelihood theory?

  For a single parameter, likelihood theory shows that the 2 points 1.92 units down from the maximum of the log-likelihood function provide a 95% confidence interval when there is no extrabinomial variation (i.e. c= 1)..   The value 1.92 is half of the chi-square value of 3.84 with 1 degree of freedom.

When to use log likelihood for Likelihood intervals?

  However, problems are encountered with this approach when the parameter estimate is on the boundary, e.g., when a survival rate is estimated as 1, and/or the standard error is estimated as zero. Profile likelihood confidence intervals are based on the log-likelihood function.

How to calculate the same confidence interval with the deviance?

  Thus, the same confidence interval can be computed with the deviance by adding 3.84 to the minimum of the deviance function, where the devianceis the log-likelihood multiplied by -2 minus the -2 log likelihood value of the saturated model. MARK will compute profile likelihood confidence intervals with extrabinomial variationassumed, i.e., c> 1.

How to calculate the confidence interval of a saturated model?

  The value 1.92 is half of the chi-square value of 3.84 with 1 degree of freedom.   Thus, the same confidence interval can be computed with the deviance by adding 3.84 to the minimum of the deviance function, where the devianceis the log-likelihood multiplied by -2 minus the -2 log likelihood value of the saturated model.