Re: Hybrid Vigor
Sorry, last message was to Marc.
clarion wrote:
> Brian and Cliff;
>
> Great postings from both of you guys! You guys do the math and just tell us
> dummies what the hell will work to do a properly controlled experiment and get
> accurate results!
>
> Marc
>
> -----------------------------------------------------------------------------
> ---
>
> I'm a newbie and don't know a lot about seed genetics but I do know a bit
> about
> statistics. You are pretty close with your estimation on the number of seeds
> you
> need to grow Cliff. Obviously, we're making a couple of assumptions when
> saying
> you only need to grow 15 seeds to obtain a 95 percent confidence interval.
> The
> first and biggest assumption is the percentage of seeds in the pumpkin that
> possess the traits you're after. Without acutally growing every last seed,
> it's
> a shot in the dark. Half of the seeds in the pumpkin could contain the traits
> you're after or as little as 10 percent of the seeds could contain the trait
> you
> want. This assumption greatly effects the number of seeds you need to plant
> in
> order to get an accurate representation of all the seeds. The second
> assumption
> is that the data is accurately represented by a normal curve. I ran the
> numbers
> and used a probability of 0.3 or 30%....meaning that we're assuming 30
> percent
> of the seeds in the pumpkin will exhibit the trait you're after. I'd say
> that's
> a pretty fair and conservative estimate. The higher the probability, the less
> seeds you have to grow.
>
> To figure out the number of seeds you need to plant in order to establish a
> 95
> percent confidence interval, you have to first find the standard deviation.
> Sorry if no one wants to see how the numbers work out, but I think it's
> important.
>
> std. dev. = [np(1-p)]^1/2 where n = the total number of seeds and p is the
> percentage of seeds that posses the trait you want.
>
> = [(300)(0.3)(1-0.3)]^1/2 = 7.94
>
> Using the std. dev. of all the seeds we just found you can calculate the std
> dev. for the based on only 15 samples. This calculation will give us a number
> that represents how confident we are that the 15 seeds we planted accurately
> represent the 300 seeds in the pumpkin.
>
> For 15 seeds.....
>
> std. dev. for the sample = (std. dev. of the 300 seeds)/(n^1/2)
>
> = 7.94/(15^1/2) = 2.05
>
> So, using 15 seeds we've covered a little more than 2 standard deviations.
> This
> means that by planting only 15 seeds of the 300, we're representing the 300
> seeds with an accuracy of 95 percent. By planting only 15 seeds, you're still
> getting a fairly accurate representation of all the seeds (95% accuracy to be
> exact) but you're doing a whole lot less work compared to planting every last
> seed in the pumpkin.
>
> Brian
>
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