Re: {MEDSTATS} statistical significance (ANOVA?) on a serial dilution

[Peter Flom]

Paul Kaye <paulm...@gmail.com> wrote
>
>I'm afraid this is likely to be a bit wordy as I'm REALLY not a stats
>person:
>
>I have a chemical test that I am performing on biological samples. The
>test is performed on a serial dilution of the sample so as to ensure
>that final reading (colour change) of at least one of the dilutions is
>within the readable limits. Each dilution is performed in triplicate.
>Normally this produces a sigmoid curve and the ideal dilution is read
>from the linear section of the curve - see the following image:
>
>http://dl.getdropbox.com/u/206931/serialdilution.gif
>
>I'm currently performing one-way ANOVA with linkage between
>triplicates. If I were to take only one dilution triplicate (e.g.
>1:1600) I may or may not find statistical significance between
>samples. However, I feel that differences may become more
>statistically significant if I were to take into account other points
>on the curve. My questions are:
>
>1) Is this mathematically/logically allowed?
>2) How would I do it?
>
>My rationale for thinking this might be allowed is that there are
>really two opportunities for the null hypothesis to be proved: 1)
>There might be no statistical significance between the real biological
>data of different groups. 2) The chemical test could be unreliable
>enough to hide any real difference. I really only want to test (1) -
>the other is an artifact. I imagine that by taking into account more
>dilutions on the above chart, the effect of any testing error would be
>minimised whilst keeping the real data intact as all dilutions in a
>single curve are from the same sample.
>
>Any advice would be greatly appreciated, especially if it is worded in
>layman's terms!
>

A few points:
1) I am not sure what null hypothesis you are trying to reject .... Maybe this is because I know nothing about cheistry

2) In any case, what you want to show is almost certainly not an increase in statistical significance, but a change in effect size .... but what effect are you interested in?

3) The null hypothesis is never proved ... You can reject, or fail to reject

4) If the test is unrealiable, then finding differences will be harder. That's always the case. So, again, the key is to formulate a null hypothesis that you want to test.

HTH

Peter

Peter L. Flom, PhD
Statistical Consultant
www DOT peterflom DOT com

[Adrian Sayers]

because they are curves, and each curve is the same sample you need to
take into account any correlation from the original sample.

i bet you need to apply a mixed model of some description... as peter
says ou need tobe clear in what you are trying to achiev.

this webites has some tutorials which might be useful

http://www.cmm.bristol.ac.uk/

good luck adrian

2008/10/28 Peter Flom <peterflom...@mindspring.com>:

[Paul Kaye]

On Oct 28, 12:45 pm, Peter Flom <peterflomconsult...@mindspring.com>
wrote:
>  Paul Kaye <paulmjk...@gmail.com> wrote

Hi,
Thank you both for your replies. Let me try to describe the issue a
little more simply:
I want to prove that each sample is different from the others. Each
sample is represented by one line on the graph and each point is the
mean of a triplicate. I want to know if there's a way to increase the
significance of the differences between each line by saying "The lines
are in order ABCD at dilution X, AND at dilution Y, AND at dilution
Z." My logical (as opposed to mathematical) brain is saying that this
must be relevant and must mean the difference is more significant than
if only one dilution was measured.
Hope that makes things a little clearer. I'd be very grateful for your
re-examination of this.
Thanks again,
Paul

[Adrian Sayers]

multi level mixed model is the way to go. this would be the most
powerful way to analyse this. it preserves each trajectory. and allows
you to commpare curve a with b etc.

this is quite complicated and requires some in depth reading or a
statistician to do it for you.

adrian

2008/10/28 Paul Kaye <paulm...@gmail.com>:

[Bruce Weaver]

On Oct 28, 11:48 am, "Adrian Sayers" <adriansay...@gmail.com> wrote:
> multi level mixed model is the way to go. this would be the most
> powerful way to analyse this. it preserves each trajectory. and allows
> you to commpare curve a with  b etc.
>
> this is quite complicated and requires some in depth reading or a
> statistician to do it for you.
>
> adrian
>

I don't disagree with Adrian's advice. But I wonder if repeated
measures ANOVA would suffice. (It didn't sound like missing data, or
differing numbers of repeated measures was an issue.) I think this
would be much more straightforward for the OP, and would likely
produce similar results.

--
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/
"When all else fails, RTFM."

[Adrian Sayers]

if you cant stomach the mixed models the rm anova is definately easier.

if rm anova relies on ml the your se's me be a little off. with these
small sample sizes i tend to go for reml based estimates..

it depends how crucial it is to be spot on with everything. you may
find no one understands your more complex method either. most
definately horses for courses..

bw adrian

2008/10/28 Bruce Weaver <bwe...@lakeheadu.ca>:

[BXC (Bendix Carstensen)]

Maybe it should be pointed out that repated measures ANOVA (rm anova) actually IS a mixed model, but one where there is but a single random effect for each person to account for dependency between observations on the same person. Wheter a model, that assumes the same correlation between observations from the same person regardless of their distance, is preferable solely on the grounds of understandability for the lay audience is however secondary to the scientifice relevance of the model to the problem at hand.

Just my usual fundamentalism...

b.r. Bendix
______________________________________________

Bendix Carstensen
Senior Statistician
Steno Diabetes Center
Niels Steensens Vej 2-4
DK-2820 Gentofte
Denmark
+45 44 43 87 38 (direct)
+45 30 75 87 38 (mobile)
b...@steno.dk http://www.biostat.ku.dk/~bxc

[Adrian Sayers]

bendix is completely cright about rm anova being equivalent to a
random intercept model. i usually make the distinction because a loot
of statistical ackags can do rm anova but not fully blown multilevel
models with the flexiility of something like mlwin.

apologies about the bad typing, i attack my finger with a stanley
knife, diy is dangerous statistics is much safer.

adrian

2008/10/29 BXC (Bendix Carstensen) <b...@steno.dk>:

[Paul Kaye]

Hi all,

Apologies for taking so long to get back to this. I really do regret
not doing stats at school; I think it should have been made compulsory
as none of the science means anything without it.

I think I understand the conversation and I would certainly prefer to
stick with rm anova, especially as I am using GraphPad Prism and have
finally begun to understand how to use it! If anyone is familiar with
this package, it might help to understand this part of my question:

The data table in GraphPad Prism is normally a 2D plot of columns
(A,B,C...) and rows. When doing grouped analysis such as rm ANOVA it
provides a virtual third dimension whereby repeated measures can be
inserted. Until now, I have used this feature by arranging individual
experiments on separate rows, the test groups in separate columns and
the three individual measurements of each test in the virtual third
dimension. All of this data is effectively from one X-value on my
original graph (see above). If you can picture what I mean, you will
see that if I wanted to now consider the other X-values as repeated
measures, I would run out of dimensions to lay out the data. I'm
thinking of using only the mean of the triplicate values which are
currently my 'repeated measures' in order to 'make room' for the new
repeated measures which are the different dilutions (the X-values on
the original graph).

1) If anyone understands what I've said, what do they think?
2) Will rm ANOVA really examine the pattern between groups across
different absolute values (i.e. dilutions) if they are plotted as
'repeated measures'?

Many thanks for your time,

Paul

> >> 2008/10/28 Bruce Weaver <bwea...@lakeheadu.ca>:

>
> >> > On Oct 28, 11:48 am, "Adrian Sayers" <adriansay...@gmail.com> wrote:
> >> >> multi level mixed model is the way to go. this would be the most
> >> >> powerful way to analyse this. it preserves each trajectory. and
> >> >> allows you to commpare curve a with  b etc.
>
> >> >> this is quite complicated and requires some in depth reading or a
> >> >> statistician to do it for you.
>
> >> >> adrian
>
> >> > I don't disagree with Adrian's advice.  But I wonder if repeated
> >> > measures ANOVA would suffice.  (It didn't sound like
> >> missing data, or
> >> > differing numbers of repeated measures was an issue.)  I think this
> >> > would be much more straightforward for the OP, and would likely
> >> > produce similar results.
>
> >> > --
> >> > Bruce Weaver

> >> > bwea...@lakeheadu.ca