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Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as is parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.
The Mann–Whitney test is a nonparametric statistical test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
Walter Andrew Shewhart was an American physicist, engineer and statistician. He is sometimes also known as the grandfather of statistical quality control and also related to the Shewhart cycle.
Control charts are graphical plots used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line. Control charts are classified into Shewhart individuals control chart and CUSUM(CUsUM)(or cumulative sum control chart)(ISO 7870-4).
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing more specification-conforming products with less waste scrap. SPC can be applied to any process where the "conforming product" output can be measured. Key tools used in SPC include run charts, control charts, a focus on continuous improvement, and the design of experiments. An example of a process where SPC is applied is manufacturing lines.
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In statistical process control (SPC), the and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process. It is often used to monitor the variables data but the performance of the and R chart may suffer when the normality assumption is not valid.
In statistics, a Q–Q plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point (x, y) on the plot corresponds to one of the quantiles of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). This defines a parametric curve where the parameter is the index of the quantile interval.
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Siegel–Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in scale between two groups.
In statistical quality control, the and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. This is connected to traditional statistical quality control (SQC) and statistical process control (SPC). However, Woodall noted that "I believe that the use of control charts and other monitoring methods should be referred to as “statistical process monitoring,” not “statistical process control (SPC).”"
In statistical quality control, an EWMA chart is a type of control chart used to monitor either variables or attributes-type data using the monitored business or industrial process's entire history of output. While other control charts treat rational subgroups of samples individually, the EWMA chart tracks the exponentially-weighted moving average of all prior sample means. EWMA weights samples in geometrically decreasing order so that the most recent samples are weighted most highly while the most distant samples contribute very little.
In statistics, the Cucconi test is a nonparametric test for jointly comparing central tendency and variability in two samples. Many rank tests have been proposed for the two-sample location-scale problem. Nearly all of them are Lepage-type tests, that is a combination of a location test and a scale test. The Cucconi test was first proposed by Odoardo Cucconi in 1968.
In statistics, the Lepage test is an exact distribution-free test for jointly monitoring the location and scale (variability) in two-sample treatment versus control comparisons. It is a rank test for the two-sample location-scale problem. The Lepage test statistic is the squared Euclidean distance of the standardized Wilcoxon rank-sum test for location and the standardized Ansari–Bradley test for scale. The Lepage test was first introduced by Yves Lepage in 1971 in a paper in Biometrika. A large number of Lepage-type tests exists in statistical literature for simultaneously testing location and scale shifts in case-control studies. The details may be found in the book: Nonparametric statistical tests: A computational approach. Wolfgang Kössler in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions. Amitava Mukherjee and Marco Marozzi introduced a class of percentile modified versions of the Lepage test. An alternative to the Lepage-type tests is known as the Cucconi test proposed by Odoardo Cucconi in 1968.
References
- ↑ Bhattacharya, P. K.; Frierson, Dargan (May 1981). "A Nonparametric Control Chart for Detecting Small Disorders". The Annals of Statistics. 9 (3): 544–554. doi: 10.1214/aos/1176345458 . ISSN 0090-5364.
- ↑ Amin, Raid W.; Reynolds, Marion R.; Saad, Bakir (January 1995). "Nonparametric quality control charts based on the sign statistic". Communications in Statistics - Theory and Methods. 24 (6): 1597–1623. doi:10.1080/03610929508831574. ISSN 0361-0926.
- ↑ Balakrishnan, N.; Triantafyllou, I.S.; Koutras, M.V. (September 2009). "Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics". Journal of Statistical Planning and Inference. 139 (9): 3177–3192. doi:10.1016/j.jspi.2009.02.013. ISSN 0378-3758.
- ↑ Mukherjee, A.; Chakraborti, S. (2011-09-26). "A Distribution-free Control Chart for the Joint Monitoring of Location and Scale". Quality and Reliability Engineering International. 28 (3): 335–352. doi:10.1002/qre.1249. ISSN 0748-8017.
- ↑ Chowdhury, S.; Mukherjee, A.; Chakraborti, S. (2013-02-19). "A New Distribution-free Control Chart for Joint Monitoring of Unknown Location and Scale Parameters of Continuous Distributions". Quality and Reliability Engineering International. 30 (2): 191–204. doi:10.1002/qre.1488. ISSN 0748-8017.