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For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are approximately ± one standard deviation σ from the central value x, which means that the region x ± σ will cover the true value in roughly 68% of cases. If the uncertainties are correlated then covariance must be taken into account ...
If the sampling distribution is normally distributed, the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean.
Data cleansing may also involve harmonization (or normalization) of data, which is the process of bringing together data of "varying file formats, naming conventions, and columns", [2] and transforming it into one cohesive data set; a simple example is the expansion of abbreviations ("st, rd, etc." to "street, road, etcetera").
For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement, then one might weight the first measurement twice that of the second.
Diagram showing the cumulative distribution function for the normal distribution with mean (μ) 0 and variance (σ 2) 1. These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φ μ,σ 2 (z)) · 2).
Image credits: GerbilFeces #11. Did this by accident the other day. Outside having a smoke and made eye contact with a girl who lives in my apartment block. Start chatting about normal stuff.
In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment.