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Re: Basic normal and t table questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110054] Re: Basic normal and t table questions
  • From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
  • Date: Sun, 30 May 2010 23:46:56 -0400 (EDT)

Hi Kurt

In[46]:= Off[ Solve::"ifun" ]
sol = Solve[ (1 - CDF[NormalDistribution[0, 1], z]) == 0.025, z ][[1]]

Out[47]= {z -> 1.95996}

In[48]:= z95 = z /. sol

Out[48]= 1.95996

Thus:

In[49]:= pValue2Sided = 2*(1 - CDF[NormalDistribution[0, 1], z95])

Out[49]= 0.05

And:

In[50]:= zScore = Quantile[ NormalDistribution[ 0, 1 ], pValue2Sided/2 ]
{zScore, -zScore}

Out[50]= -1.95996

Out[51]= {-1.95996, 1.95996}

In[52]:= Off[ Solve::"ifun" ]
sol = Solve[ (1 - CDF[NormalDistribution[0, 1], z]) == 0.05, z ][[1]]

Out[53]= {z -> 1.64485}

In[54]:= z90 = z /. sol

Out[54]= 1.64485

Thus

In[55]:= pValue2Sided = 2*(1 - CDF[NormalDistribution[0, 1], z90])

Out[55]= 0.1

In[56]:= zScore = Quantile[ NormalDistribution[ 0, 1 ], pValue2Sided/2 ]
{zScore, -zScore}

Out[56]= -1.64485

Out[57]= {-1.64485, 1.64485}

 Cheers

Barrie

>>> On 30/05/2010 at 8:48 pm, in message <201005301048.GAA29139 at smc.vnet.net>,
Canopus56 <canopus56 at yahoo.com> wrote:
> I am taking an intro to stats class and am trying to learn some Mathematica 
> functions related to basic statistics. 
> 
> I would like to use Mathematica to calculate exact values and inverse values 
> from the standard normal table and Student's t distribution table.
> 
> For example, the following returns the cdf equvialent to standard normal 
> distribution table for a known mu, sigma (STD) and target x-bar: 
> 
> (1 - CDF[NormalDistribution[187000, 2181.9716], 190000])
> 
> The following returns the two-sided t-distribution value for a known 
> z-statistic: 
> 
> StudentTPValue[-0.1373, 6, TwoSided -> True] 
> 
> Q1) How do I get the inverse of these, which the equivalent of reading a cdf 
> table and a t-distribution table backwards, i.e. - 
> 
> a) Given a cdf, how do I return the z-statistic from a standard normal 
> distribution? 
> 
> b) Given a P-Value and sampling distribution size, how did I return the z-star 
> critical test value? 
> 
> Thanks - Kurt 



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