Re: two questions - Mathematica's statistical capacities

*To*: mathgroup at smc.vnet.net*Subject*: [mg116387] Re: two questions - Mathematica's statistical capacities*From*: Andy <andyr at wolfram.com>*Date*: Sat, 12 Feb 2011 05:22:00 -0500 (EST)*References*: <201102110919.EAA08095@smc.vnet.net>

On 2/11/2011 3:19 AM, Francisco Gutierrez wrote: > Dear Group: > Mathematica's statistical capacities have been enhanced in the last versions. However, I have two questions: > > a. Has anybody developed code for doing multi-level regressions in Mathematica? If yes, where can it be found? > > b. A simple but important command, MeanDifferenceTest was made obsolete. However, it was quite nice. It still works, but Mathematica informs it has been "superseded". Furthermore, the commands that are supposed to replace it, like LocationEquivalenceTest, seem inferior, and produce different results. How to interpret such differences? Anyway I hope MeanDifferenceTest is not wiped from the surface of the earth! > > Best, > Francisco > > > > MeanDifferenceTest has been replaced by a collection of tests including LocationEquivalenceTest, LocationTest, and a number of individual named tests such as SignTest, SignedRankTest, TTest, and ZTest. LocationEquivalenceTest is designed primarily to test for equivalence in means for 3 or more populations and so isn't likely to give the results you are wanting compared to MeanDifferenceTest. LocationTest contains many more tests (both nonparametric and parametric) and automates choosing an appropriate one. If you are really wanting to perform what MeanDifferenceTest does you should use either TTest, or ZTest. Some of the examples in MeanDifferenceTest are a bit difficult to replicate because of the underlying assumptions of the test. For the first basic example we have to force TTest to use Satterthwaite degrees of freedom. Also, the p-value is one-sided by default in MeanDifferenceTest. We now return a two-sided value by default and allow control over the direction. The first example in MeanDifferenceTest is one of the hardest to replicate... In[2]:= MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0] Out[2]= OneSidedPValue -> 0.00879997 Notice that the degrees of freedom default to 9 (not the Satterthwaite degrees of freedom..) In[46]:= TTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}, 0, "DegreesOfFreedom"] Out[46]= 9 This is because the variances of the two populations were not detected to be significantly different from one another at the default significance level... In[40]:= VarianceEquivalenceTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}] Out[40]= 0.7641 We can force the Satterthwaite degrees of freedom by setting the significance level above this value. In[48]:= TTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}, 0, "DegreesOfFreedom", SignificanceLevel -> .8] Out[48]= 8.9724 With the proper alternative hypothesis setting we reproduce MeanDifferenceTest. In[49]:= TTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}, 0, "PValue", AlternativeHypothesis -> "Less", SignificanceLevel -> .8] Out[49]= 0.00879997 We have to work far less hard to get the example under "EqualVariances" since these are detected by default. In[2]:= MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, EqualVariances -> True] Out[2]= OneSidedPValue -> 0.00940084 In[51]:= TTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}, 0, "PValue", AlternativeHypothesis -> "Less"] Out[51]= 0.00940084 To assume known variances as in the "KnownVariance" example use ZTest. In[2]:= MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, KnownVariance -> {1, 3}] Out[2]= OneSidedPValue -> 7.03827*10^-6 In[54]:= ZTest[{{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}}, {1, 3}, 0, AlternativeHypothesis -> "Less"] Out[54]= 7.03827*10^-6 The reporting features offered by MeanDifferenceTest have not been completely replicated by design. You can still automatically generate nice test summary tables and all of the information for constructing the old table is readily available by extracting properties from the "HypothesisTestData" object. You can also still get test conclusions as strings. Hope this helps. Any suggestions on improvements are most welcome. Andy Ross Wolfram Research

**References**:**two questions - Mathematica's statistical capacities***From:*Francisco Gutierrez <fgutiers2002@yahoo.com>