Re: Hybrid Vigor
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
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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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