A confidence interval is the range of values that will include the population parameter based on information from a single sample of the population The population estimate from a sample is only one of the many estimates possible from all samples of the same size drawn from the same population The sampling error or standard error estimates the amount of variation in the sample estimates Random errors follow a normal (bell-shaped) distribution and therefore, the proportion of observations within segments can be calculated For example, 95% of all the values are in a range that is 1 96 standard units on either side of the midpoint A 95% confidence interval indicates that there is a 95% chance that the interval contains the actual population value
A range of values constructed around a point estimate that makes it possible to state that an interval contains the population parameter between its upper and lower confidence limits The most frequently used confidence interval is the 95% confidence interval This can be interpreted as there is only a 5% chance that the sample is so extreme that the 95% confidence interval calculated will not cover the population mean
A range of values within which the true value of a variable is thought to lie, with a specified level of confidence A typical result would be 23 5 (23 1-23 9) The smaller the interval, the more reliable the result If the 95% confidence intervals do not overlap, there is a statistically significant difference Vitalnet uses Poisson distribution to calculate confidence intervals
A confidence interval is an interval used to estimate the likely size of a population parameter It gives an estimated range of values (calculated from a given set of sample data) that has a specified probability of containing the parameter being estimated Most commonly used are the 95% and 99% confidence intervals that have 95 and 99 probabilities respectively of containing the parameter The width of the confidence interval gives some indication about how uncertain we are about the unknown population parameter Confidence intervals are more informative than the simple results of hypothesis tests (where we decide 'reject the null hypothesis' or 'don't reject the null hypothesis') because they provide a range of plausible values for the unknown parameter
A range (M - hw, M + hw) computed such that Pr{M - hw < x <M + hw} =1 - a Where M = the estimate mean, hw = the half width of the interval, 1 - a = the level of the confidence interval hw is computed as t1-a/2,df s/sqrt(n) Here s is the sample standard deviation n is the sample size, df is n -1 and the value of t is selected from a statistical table Note that t has excessivly large values for df < 11 Hence a sample size of at least 12 is recommended
Quantifies the uncertainty in measurement It is usually reported as a 95% CI which is the range of values within which we can be 95% sure that the true value for the whole population lies For example, for an NNT of 10 with a 95% CI of 5 to 15, we would have 95% confidence that the true NNT value lies between 5 and 15
A confidence interval for a parameter is a random interval constructed from data in such a way that the probability that the interval contains the true value of the parameter can be specified before the data are collected
The numerical interval constructed around a point estimate of a population parameter, combined with a probability statement (the confidence coefficient) linking it to the population's true parameter value If the same confidence interval construction technique and assumptions are used to calculate future intervals, they will include the unknown population parameter with the same specified probability
The 95% confidence intervals (CIs) of all estimates were calculated during the preparation of the report As a result, there is a 95% probability that the true value for the population lies somewhere in this range of values If the text reports a difference between two values, the 95% CIs of these estimates do not overlap, and one can be reasonably sure that a true difference exists If the text does not report on a difference found in the values, the reader should assume that none exists
A statistical range with a given probability associated with it The probability represents the chance that a certain value falls within the range For example, for a certain number of CAG repeats, a 95% confidence interval for age of onset means that an individual with that number of CAG repeats has a 95% probability of onset within that age range See Table C-2
The range within which the 'true' value (e g size of effect of an intervention) is expected to lie with a given degree of certainty (e g 95% or 99%) Note: Confidence intervals represent the probability of random errors but not systematic errors (bias) - Note: confidence intervals should only be used to compare independent samples, for example, when comparing severities it is correct to compare the CI for those with 40-69 dBHL impairments with those who have 70-94 dBHL impairments It is not correct to compare those with > 40 dBHL with those with > 70 dBHL
A range of values (a1 < a < a2) determined from a sample of definite rules so chosen that, in repeated random samples from the hypothesized population, an arbitrarily fixed proportion of that range will include the true value, x, of an estimated parameter The limits, a1 and a2, are called confidence limits; the relative frequency with which these limits include a is called the confidence coefficient, and the complementary probability is called the confidence level
A statistic constructed from sample data to provide an interval estimate of a population parameter For example, the average of a sample is generally a good estimate of the population mean However, another sample chosen from the same sample would almost certainly have a different value If the sample size is large enough, both of these estimates should be close to each other and the population mean The confidence interval provides an interval or range of values around the estimate For one parameter, such as the mean, standard deviation, or probability level, the most common intervals are or two sided (i e the statistic is between the lower and upper limit) and one sided (i e the statistic is smaller or larger than the end point) For two or more parameters, a confidence region, the generalization of a confidence interval, can take on arbitrary shapes For sensitivity testing, the smallest confidence regions are oval shapes
Quantifies the uncertainty in measurement It is usually reported as 95% CI, which is the range of values within which we can be 95% sure that the true value for the whole population lies For example, for an NNT of 10 with a 95% CI of 5 to 15, we would have 95% confidence that the true NNT value was between 5 and 15
A range of values for a variable of interest, e g , a rate, constructed so that this range has a specified probability of including the true value of the variable The specified probability is called the confidence level, and the end points of the confidence interval are called the confidence limits
An interval of results that is 95 percent likely to contain the true number; equals reported proportion plus or minus the margin of error (For an alternative explanation)
A range of values for a variable of interest e g , a rate, constructed so that this range has a specified probability of including the true value of the variable e g the reference to Dolk et al mentions "an excess risk of 1 83 (95% CI 1 22 2 74)" This means that the estimated risk is 1 83, and there is a 95% probability that the "true" risk (if that could be ascertained) is within the range 1 22 2 74
(CI): The range of numerical values in which we can be confident (to a computed probability, such as 90 or 95%) that the population value being estimated will be found Confidence intervals indicate the strength of evidence; where confidence intervals are wide, they indicate less precise estimates of effect See Precision
The computed interval with a specified probability (by convention, usually 95%) that the true value of a population parameter is contained within the interval
A statistic constructed from a set of data to provide an interval estimate for a parameter For example, when estimating the mean of a normal distribution, the sample average provides a point estimate or best guess about the value of the mean However, this estimate is almost surely not exactly correct A confidence interval provides a range of values around that estimate to show how precise the estimate is The confidence level associated with the interval, usually 90%, 95%, or 99%, is the percentage of times in repeated sampling that the intervals will contain the true value of the unknown parameter
An interval (range of values) such that there is a specific probability that a parameter (e g the mean) lies within that interval E g , a "95% confidence interval" for the mean is a interval such that the probability of the mean lying with that interval is 0 95 The Upper Confidence Limit (Upper CL) and Lower Confidence Limit (Lower CL) refer to the upper and lower ends of the Confidence Interval