Abstract
Statistical inference is the branch of statistics whereby we arrive at conclusions about a population through a sample of the population. We can make inferences concerning several issues related to the data, for example, the parameters of the probability distribution, the parameters of a given model that explains the relationship among variables, goodness of fit to a probability distribution, and differences between groups (e.g., regarding the mean or the variance). In Six Sigma projects, improvement is closely linked to the effect that some parameters of the process (input) have on the features of the process (output). Statistical inference provides the necessary scientific basis to achieve the goals of the project and validate its results. This chapter reviews the main tools and techniques to deal with statistical inference using R.
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- 1.
For sampling distributions, we set the symbol of the statistic a subscript.
- 2.
It in turn uses the ptukey function (see ?ptukey).
- 3.
R provides the sample variance. If you need the population variance, just multiply it by \(\frac{n-1} {n}\).
- 4.
In Bayesian statistics, the credible interval is the counterpart of the confidence interval, which has a probabilistic meaning.
- 5.
A sample size n ≥ 30 is considered large.
- 6.
We will not explain in detail the foundations of hypothesis testing. Some good references can be found in Sect. 10.6.
- 7.
We can choose one of the following methods in the step function: backward, forward, or both.
- 8.
The aov function can also be used. The difference is basically the presentation of the results.
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Cano, E.L., Moguerza, J.M., Redchuk, A. (2012). Statistical Inference with R. In: Six Sigma with R. Use R!, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3652-2_10
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