Hong is studying the growth of a particular type of plant. He is testing the effects of three growth factors: lighting, age, and temperature. Here are the levels he's testing for each.

Question

GROWTH FACTOR LEVELS

LIGHTNING Low, Medium, High

AGE 1 months, 2 months, 3 months, 4 months, 5 months

TEMPERATURE 20 ºC, 22 ºC, 24 ºC, 26 ºC

He wants to find the number of ways of combining one level from each of the growth factors. How many ways are there?

Answer 1

Hi Mercy O.,

I think your question is asking how many combinations of the other variable levels is possible for a given setting of (each) of the three properties.

That's going to vary with which property you're fixing, since the # levels is 3, 5, 4 for (light, age, temperature) respectively.

Combinations will just be the #levels for the other variables individually.

So for light, for each one of the light levels, the other 2 variables will have 5*4 = 20 combinations. They are combinations inherently(!) because these are independent variables, and a level MUST be picked for each.

You should note, for future reference, that only an inept researcher would set up each of the 60 possible combinations, to find out everything possible about the plant growth factors. There are much more effective "Experimental Design"s for finding out the same information, with far fewer combinations.

Here, unless he's dealing with a species sensitive to excess light, the plants will do best with the most light, and they will continue to grow over the 5 months (unless they are ephemeral, e.g. Arabidopsis thaliana, perhaps), and most likely they'll do best at 26 C. So he's essentially wasting his time with this experimental variable set, with the levels chosen. That sort of thing does happen, but not oftern to the savvy experimenter (Let's hope not to you!).

I might perhaps leave you with a note regarding the results of just such a trial, for growing beans, with variables of soil type and water supplied (high school biology). The beans sprouted best (most reliably) in a very loose (100% humus) soil mix, but ended up growing most in a slightly more compact (25% clay, 75% humus) soil mix. It doesn't profit a plant to sprout if it can't grow, but it can't be harvested if it doesn't grow well!

-- Cheers, --Mr. d.