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For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
In contrast, it is worth noting that other confidence interval may have coverage levels that are lower than the nominal , i.e., the normal approximation (or "standard") interval, Wilson interval, [8] Agresti–Coull interval, [13] etc., with a nominal coverage of 95% may in fact cover less than 95%, [4] even for large sample sizes.
The confidence interval can be expressed in terms of statistical significance, e.g.: "The 95% confidence interval represents values that are not statistically significantly different from the point estimate at the .05 level." [20] Interpretation of the 95% confidence interval in terms of statistical significance.
Differentiating between two-sided and one-sided intervals on a standard normal distribution curve. Two-sided intervals estimate a parameter of interest, Θ, with a level of confidence, γ, using a lower and upper bound (). Examples may include estimating the average height of males in a geographic region or lengths of a particular desk made by ...
The dependence of the confidence intervals on sample size is further illustrated below. For N = 10, the 95% confidence interval is approximately ±13.5789 standard deviations. For N = 100 the 95% confidence interval is approximately ±4.9595 standard deviations; the 99% confidence interval is approximately ±140.0 standard deviations.
Comparison of the rule of three to the exact binomial one-sided confidence interval with no positive samples. In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/ n is a 95% confidence interval for the rate of occurrences in the population.
Calculating the confidence interval. Let's say we have a sample with size 11, sample mean 10, and sample variance 2. For 90% confidence with 10 degrees of freedom, the one-sided t value from the table is 1.372 . Then with confidence interval calculated from
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.