[R] Confidence Intervals on Standard Curve

[Ben Ward]

On 20/02/2011 18:52, David Winsemius wrote:
>
> On Feb 20, 2011, at 1:27 PM, Ben Ward wrote:
>
>> However, the
>>
>> Y ~ X + Y^2
>>
>> Produces the best fitting line - it is pretty much on the data points 
>> - I'm trying to make a standard curve, with which to take readings 
>> from a spectrophotometer off of. Rather than what I would normally 
>> use models for - such as hypothesis testing and analysis of data from 
>> experiments.
>
> I thought we were leaving behind the model that had the dependent 
> variable on both sides of hte equation. Can you explain how you would 
> construct a chart or a function that will turn those results into 
> something useful?
>
Sorry for any confusion, I am indeed leaving behind the Y ~ X + Y^2 
model, I was only mentioning that it had a higher R squared than 
anything else I had done.

I'll explain exactly what the chart/function is made from and is for, to 
remove any mystery or highlight anything important: The curve I'm trying 
to produce, is from readings from a spectrophotometer, from series of 
standards called the MacFarland Scale - tubes of solution which were 
made up to simulate different known numbers of bacteria in a liquid 
sample: the standards are of different intensities of coloudy-ness, and 
they represent different numbers of bacteria in a liquid medium. The (X) 
axis is % light transmission as measured by the spectrophotometer, the 
cloudier the standard, the lower this value, and the Bacterial Counts on 
the (Y) axis, are higher, the cloudier a sample (or the standards) are, 
thus it is higher with lower % Light Transmission. This is a negative 
curve, which never goes below 0, because you cant have less than no 
bacteria. This curve/function, which has been made from the standards of 
known numbers, will then be used to estimate the numbers of bacteria 
present in proper samples, rather than known standards. I would take the 
% Light Transmission Readings the spectrophotometer gives me for those 
standards, and then using the curve - or working through the function, 
calculate the (Approximate) number of bacteria present in my samples. I 
took 5, % Light Transmission readings for each standard to make sure the 
machine wasn't giving me wildly different readings (it' wasnt), and used 
them to try and construct a curve.

Hence my comment about  Y ~ X + Y^2 giving me a better fit (R-Squared). 
I need a good fit to make reliable predictions. However, since then, 
I've added an extra standard from the scale (There are about 10/11 
standards to the scale, but I've got 9, because the last few can't be 
made up accurately without introducing error or the lab tech's running 
into difficulty doing it by hand), and the Y ~ X + Y^2 curve is no 
longer sufficient after this.

I followed a suggestion (I think by you) to try a GLM, with the poisson 
distribution, as I mentioned in my last email that went around, which 
wasn't closely fitting as I would like, it's my first experience with 
GLM, but to my understanding, the Residual Deviance, was orders higher 
than the residual degrees of freedom. So under instruction of a 
textbook, I tried with a quasi-poisson, but still got the same result. 
Then (again textbook suggestion) tried with a negative binomial 
distribution, and got a much lower AIC value and a residual deviance 
much much closer to the residual degrees of freedom (the R print outs of 
them are on the previous email I sent around).

I hope this has explained when you asked "Can I explain how I would 
construct a chart or a function that will turn those results into 
something useful?"

Thanks,
Ben.W
>
>> Thanks,
>> Ben.
>>
>> On 20/02/2011 11:53, nzcoops wrote:
>>> model<- lm(Approximate.Counts~X..Light.Transmission +
>>> I(Approximate.Counts^2), data=Standards)
>>>
>>> Might not be addressing the problem, don't you have Y ~ X + Y^2 
>>> here? That's
>>> a violation of the assumptions of an lm isn't it?
>>>
>>> Also for plotting CI on a curve look into ggplot2::geom_ribbon, it's 
>>> much
>>> nicer than just plotting lines and is easy to use. had.co.nz should 
>>> set you
>>> right for setting this up.
>>
>
>
> David Winsemius, MD
> West Hartford, CT
>
>
>