M-Distribution

[Max Jasper-2]

Hi all,

Any link to, or information about M-Distribution probability function mathematical formulas and tables is appreciated with thanks.

Sample:
Z for M(p=0.05, c1=1.5, k=11)= {(a)19.20, (b)18.67}

Max.

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[Art Kendall]

Please give us more detail about the context of your question?

MaxJasper wrote:

> Hi all,
>
> Any link to, or information about M-Distribution probability function mathematical formulas and tables is appreciated with thanks.
>
> Sample:
> Z for M(p=0.05, c1=1.5, k=11)= {(a)19.20, (b)18.67}
>
> Max.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> LISTSERV@... (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
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>
>

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[Art Kendall]

No single picture comes immediately to mind.  I suggest you re-post
these details to the list with more detail.
Different disciplines use different symbols for the same ideas, and the
same symbols for different ideas. So give more details. Where did you
come across this?
What discipline are you working in?
Can you put words with each symbol?
What entities constitute  "observations"? Are they grouped in any way?
What are the means and SDs taken of: repeated measures of the same
variable, e.g., patient temperature on different visits?  Sub-entities
that are a simple random sample within an"observation", e.g., students
within classes? etc.

These days most software produces a p-value without users needing to
resort to tables etc.
Do you have the raw data?

When you say "variation among the observations" are you asking if "at
least one pair of observations "is statistically significant different"?


Art Kendall
Social Research Consultants

MaxJasper wrote:

> I wish I had more info. It appears to be a probability distribution function that best fits variances of a series of observations with {mean, sd, df=n-1} while df of each series might different from others. For example:
>
>               mean            sd              n       df=n-1
> Obs 1         120.1           3.4             6       5
> Obs 2         127.6           2.7             11      10
> .....
> ......
> Obs k         ....            .....           ...     ...
>
> >From these data one computes arguments {M, phi, c1, k} that has an M-distribution and resulting value is a Z(M,phi, c1, k) and  then Z can be compared with M-distribution critical values at specific significance to accept or reject hypothesis:
>       H0:Variation among Obs1 to k is NOT sig.
>       H1:Variation among Obs1 to k is     sig.
>
> I am looking for mathematical formula of M-Distribution as f(phi, c1, k)
>
> Phi(f) = sum(f(i))    i=1...k
> C1 = sum(1/f(i) - 1/phi)
> M = phi*ln(sum(f(i)*sd(i)**2)/phi - sum(f(i)*ln(sd(i)**2)
>
>
> |-----Original Message-----
> |From: SPSSX(r) Discussion [mailto:SPSSX-L@...] On
> |Behalf Of Art Kendall
> |Sent: Thursday, November 12, 2009 15:02
> |To: SPSSX-L@...
> |Subject: Re: M-Distribution
> |
> |
> |Please give us more detail about the context of your question?
> |
> |MaxJasper wrote:
> |> Hi all,
> |>
> |> Any link to, or information about M-Distribution probability
> |function
> |> mathematical formulas and tables is appreciated with thanks.
> |>
> |> Sample:
> |> Z for M(p=0.05, c1=1.5, k=11)= {(a)19.20, (b)18.67}
> |>
> |> Max.
> |>
> |> =====================
> |> To manage your subscription to SPSSX-L, send a message to
> |> LISTSERV@... (not to SPSSX-L), with no body text except
> |> the command. To leave the list, send the command SIGNOFF SPSSX-L
> |> For a list of commands to manage subscriptions, send the command
> |> INFO REFCARD
> |>
> |>
> |
> |=====================
> |To manage your subscription to SPSSX-L, send a message to
> |LISTSERV@... (not to SPSSX-L), with no body text
> |except the command. To leave the list, send the command
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> |subscriptions, send the command INFO REFCARD
> |
>
>
>

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[García-Granero]

Hi:

It looks a lot like Bartlett test (*). Since you want to test for
homogeneity of variation across groups ("Obs"), it fits. Why do you need
to use to M distribution istead of Levene, or Bartlett test?

HTH,
Marta GG

(*) http://www.itl.nist.gov/div898/handbook/eda/section3/eda357.htm

>
>
> MaxJasper wrote:
>> I wish I had more info. It appears to be a probability distribution
>> function that best fits variances of a series of observations with
>> {mean, sd, df=n-1} while df of each series might different from
>> others. For example:
>>
>>               mean            sd              n       df=n-1
>> Obs 1         120.1           3.4             6       5
>> Obs 2         127.6           2.7             11      10
>> .....
>> ......
>> Obs k         ....            .....           ...     ...
>>
>> >From these data one computes arguments {M, phi, c1, k} that has an
>> M-distribution and resulting value is a Z(M,phi, c1, k) and  then Z
>> can be compared with M-distribution critical values at specific
>> significance to accept or reject hypothesis:
>>       H0:Variation among Obs1 to k is NOT sig.
>>       H1:Variation among Obs1 to k is     sig.
>>
>> I am looking for mathematical formula of M-Distribution as f(phi, c1, k)
>>
>> Phi(f) = sum(f(i))    i=1...k
>> C1 = sum(1/f(i) - 1/phi)
>> M = phi*ln(sum(f(i)*sd(i)**2)/phi - sum(f(i)*ln(sd(i)**2)
>>
>>
>> |-----Original Message-----
>> |From: SPSSX(r) Discussion [mailto:SPSSX-L@...] On
>> |Behalf Of Art Kendall
>> |Sent: Thursday, November 12, 2009 15:02
>> |To: SPSSX-L@...
>> |Subject: Re: M-Distribution
>> |
>> |
>> |Please give us more detail about the context of your question?
>> |
>> |MaxJasper wrote:
>> |> Hi all,
>> |>
>> |> Any link to, or information about M-Distribution probability
>> |function
>> |> mathematical formulas and tables is appreciated with thanks.
>> |>
>> |> Sample:
>> |> Z for M(p=0.05, c1=1.5, k=11)= {(a)19.20, (b)18.67}
>> |>
>> |> Max.
>> |>
>> |> =====================
>> |> To manage your subscription to SPSSX-L, send a message to
>> |> LISTSERV@... (not to SPSSX-L), with no body text except
>> |> the command. To leave the list, send the command SIGNOFF SPSSX-L
>> |> For a list of commands to manage subscriptions, send the command
>> |> INFO REFCARD
>> |>
>> |>
>> |
>> |=====================
>> |To manage your subscription to SPSSX-L, send a message to
>> |LISTSERV@... (not to SPSSX-L), with no body text
>> |except the command. To leave the list, send the command
>> |SIGNOFF SPSSX-L For a list of commands to manage
>> |subscriptions, send the command INFO REFCARD
>> |
>>
>>
>>
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
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>

--
For miscellaneous SPSS related statistical stuff, visit:
http://gjyp.nl/marta/

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