Do I have sufficient statistical power to test the effect of potato chitting, in my back-yard garden? Or is it laughable to think I might be able to learn anything whatsoever about the effect of chitting, from a single small-scale potato planting?
The upshot is in red below. Chitting has to make quite a bit of difference, in order for it to show up in this small sample.
Each 5-pound bag had about ~18 to 19 potatoes, so two such bags determines the total sample size for the full experiment.
And, to be clear, in the light of day, I may not want to plant that many in my small garden. It looks like almost all potatoes will yield two plantable pieces, call it 40 pieces at best. That’s 40 to 60 feet of row at a 1′ to 1.5′ spacing, per five-pound bag. Divide by 3 for a three rows across in a 4′ bed, and that’s a lot of 8′ long beds, for two bags. So I may want to go half-sized on this, closer to the area I usually plant to potatoes.
Can you tell anything from the yield you get from these 18 potatoes, versus those 18 potatoes? That depends on a number of things, and ultimately boils down to how how much typical variation there is in yield, from spud to spud, and year to year, all things considered, including both genetics and exact field conditions.
If they all grow like robots, and each piece of seed potato typically yields near-identical weight in harvested potatoes, then plausibly 18 potatoes in each group would be enough to reveal the subtle effects of chitting.
By contrast, if there’s a lot of plant-to-plant variation — and that’s my observation, for potatoes — then I’m not going to be able to say much, from 18 vs. 18 potatoes, randomly chosen and inter-planted.
But I’m not going to know that variation until the experiment is done. Realistically.
Hmmm.
In the meantime, can I at least get my expectations in the right space, by modeling the statistical test as a coin flip. The let me define a yes/no result for the yield of each plant or each seed tuber: Is that yield above the median, yes/no, heads/tails.
Then if I didn’t screw up the math, and ignoring that the all-sample median itself depends on each potato’s yield (but only a tiny bit!), a crude calculation from an on-line coin flip calculator says I need to see 13 out of 18 potatoes in the chit group exceed the median yield, before I could say I was unlikely to achieve that result merely by chance.
That is, quick cut, the 5% confidence level for this experiment, assuming I do everything else right, is that I’d need to see that 13 (or more) above-average plants in the 18-plant treatment (chit) group. (And since average is median yield for all the plants, then at the same time, I’d by definition be observing 5 or fewer in the control (fridge) group.
I think this vaguely seems realistic. I have so few potatoes that I’ll only be able to say chitting has an effect, if it has a fairly overwhelming effect. Based on this above/below median yes/no outcome attached to each plant.
So I think that the short answer is that if chitting has a strong and consistent effect, I should be able to see that in this small a sample. This tiny experiment ought to have enough statistical power to detect whether chitting turns a group of 70% losers into a group of 70% winners.
Where winner and loser plants are defined as having above and below all-sample median yield, respectively.
All other things equal. Which they seldom are, but which I will do my best to impose via randomization and inter-planting.
Whether or not I have more statistical power if I give up this simple-minded yes/no outcome, and deal with total yield, cannot be known until I get the plant-level yields at the end of the experiment. (At which point, I shall jackknife the results. Bet that promise puts you right on the edge of your seats, eh?)
Bottom line, yeah, arguably, it’s worth doing this as an experiment, even with this few potatoes. Particularly as long as it costs me more-or-less nothing to do so.
Unscientifically, think of it as mainly being able to rule out that chitting has some profound effect. That’s as much information as this small test can provide.
Note on pictures: These bag of store-bought spuds is picture of a real object. The rest are all from gencraft.com, prompt “potato statistics”, styles from top to bottom: cartoon, anime, and watercolor.
