Date:         Tue, 8 Apr 2003 19:03:58 -0700
Reply-To:     Paul Tan <pault@INTRA.NIDDK.NIH.GOV>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Paul Tan <pault@INTRA.NIDDK.NIH.GOV>
Organization: http://groups.google.com/
Subject:      Re: Nested ANOVA & Estimable Functions
Content-Type: text/plain; charset=ISO-8859-1

The third dish was measured three times to determine
the level of variability attributable only to the technical
process of measurement, not due to any dish to dish biological
variability.  These measurements were made using microarrys
so the measurement process required numerous steps, thus
the technical variability could have been high.  The experiment
was also very expensive, thus the low number of replicates.
We've modeled the data with a nested ANOVA to maximize
our sample size; so that all 5 data points for each phenotype
were used.

With the model I've specified, is the test simply
a test of a difference in the mean value of the 5
data points in state C vs the mean of the 5 data points in state D?
Where nesting allows a better estimate of the standard error of
the difference?

Would it be preferable to first average the three measurements
from 1 dish, then run a 2 sample t test with n=3 in each group?

Regards,

Paul Tan


Mark.Lamias@GRIZZARD.COM (Mark Lamias) wrote in message news:<16484F90DE05BB478A0CA3336AE307B1025BCAA5@atl_mail.griz-main.com>...
> Paul,
>
> Why was one dish measured three times?  Using three measurements from the
> same dish within a state, without making any adjustments, would violate the
> independence assumption of your model's error terms.
>
> Sincerely yours,
>
> Mark J. Lamias,
> Statistical Consultant
>
> -----Original Message-----
> From: Paul Tan [mailto:pault@INTRA.NIDDK.NIH.GOV]
> Sent: Saturday, April 05, 2003 10:36 AM
> To: SAS-L@LISTSERV.UGA.EDU
> Subject: Nested ANOVA & Estimable Functions
>
>
> I'm trying to model some biological data using a nested ANOVA.
>
> My data is structured as follows:
>
>  Observation      state    DISH        Signal (measured quantity)
>   1                 C      DISHC1
>   2                 C      DISHC2
>   3                 C      DISHC3
>   4                 C      DISHC3
>   5                 C      DISHC3
>   6                 D      DISHD1
>   7                 D      DISHD2
>   8                 D      DISHD3
>   9                 D      DISHD3
>   10                D      DISHD3
>
> Using SAS I ran a nested anova model of signal with 2 factors: a fixed
> effect called state (aka phenotypic state) and a random effect for
> dish.  There were 3 dishes for each state.  1 of the dishes was
> measured 3 times.  I'm interested wether the measured signal is
> different across states.  I also specified the type III SS option.
>
>
>
> SAS returns listing with "Type III estimable functions."  Can anyone
> help me interpret this?  Is this equivalent to orthogonal linear
> contrasts?
>
>                  Type III Estimable Functions
>
>                                ------Coefficients-------
>       Effect                   state         dish(state)
>
>       Intercept                0             0
>
>       state       C            L2            0
>       state       D            -L2           0
>
>       dish(state) DISHC1 C     0.3333*L2     L4
>       dish(state) DISHC2 C     0.3333*L2     L5
>       dish(state) DISHC3 C     0.3333*L2     -L4-L5
>       dish(state) DISHD1 D     -0.3333*L2    L7
>       dish(state) DISHD2 D     -0.3333*L2    L8
>       dish(state) DISHD3 D     -0.3333*L2    -L7-L8
>
>
> Thanks,
>
> Paul Tan