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Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
The longer the lines, the wider the confidence interval, and the less reliable the data. The shorter the lines, the narrower the confidence interval and the more reliable the data. If either the box or the confidence interval whiskers pass through the y-axis of no effect, the study data is said to be statistically insignificant.
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.
The "chart" actually consists of a pair of charts: one, the individuals chart, displays the individual measured values; the other, the moving range chart, displays the difference from one point to the next.
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.
The confidence interval summarizes a range of likely values of the underlying population effect. Proponents of estimation see reporting a P value as an unhelpful distraction from the important business of reporting an effect size with its confidence intervals, [7] and believe that estimation should replace significance testing for data analysis ...
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".