The least significant difference (LSD) test is used in the context of the analysis of variance, when the F-ratio suggests rejection of the null hypothesis H 0, that is, when the difference between the population means is significant.
This test helps to identify the populations whose means are statistically different. The basic idea of the test is to compare the populations taken in pairs. It is then used to proceed in a one-way or two-way analysis of variance, given that the null hypothesis has already been rejected.
HISTORY
The LSD test was developed by Fisher, Ronald Aylmer (1935), who wanted to know which treatments had a significant effect in an analysis of variance.
MATHEMATICAL ASPECTS
If in an analysis of variance the F-ratio leads to rejection of the null hypothesis H 0, we can perform the LSD test in order to detect which means have led H 0 to be rejected.
The test consists in a pairwise comparison of the means. In general terms, the standard deviationof the difference...
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REFERENCES
Dodge, Y., Thomas, D.R.: On the performance of non-parametric and normal theory multiple comparison procedures. Sankhya B42, 11–27 (1980)
Fisher, R.A.: The Design of Experiments. Oliver & Boyd, Edinburgh (1935)
Miller, R.G., Jr.: Simultaneous Statistical Inference, 2nd edn. Springer, Berlin Heidelberg New York (1981)
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(2008). Least Significant Difference Test. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_226
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