types i, ii, and iii contingency tables

hereby some examples drawn from Sokal and Rohlf (1995: 724 et seq.), and edited and expanded a bit by me to (hopefully) clarify the distinction among Models I, II, and III contingency tables:

Type I: neither set of column totals set by investigator:

100 plants are examined, and their soil type and leaf texture is recorded:

	Pubescent Leaves	Smooth Leaves	Total
Serpentine Soil	12	30	42
Non-serpentine Soil	47	11	58
Total	59	41	100

Type II: one set of column totals set by investigator:

100 moths are exposed to bird predation: 50 light morphs and 50 dark morphs (note that the proportion doesn't have to be 50:50, though); investigator records whether moths are eaten or not:

	Prey	Survivor	Total
Light Morph	39	11	50
Dark Morph	30	20	50
Total	69	31	100

Type III: both sets of column totals set by investigator:

one hundred beans are placed in a jar: 50 with thick skins and 50 with thin skins (again, doesn't have to be 50:50). seventy hungry weevil larvae -- each of which will burrow in to one unoccupied bean -- are added to the jar, and some time later the investigator records the numbers of each type of bean and whether or not it was attacked:

	Attacked	Not Attacked	Total
Thick Skin	a	b	50
Thin Skin	c	d	50
Total	70	30	100

at first glance, it seems that having both the row totals and the column totals fixed will automatically fix the cell totals; this is not actually true, as the following values of a, b, c, and d will illustrate:

a = 20, b = 30, c = 50, d = 0;
a = 25, b = 25, c = 45, d = 5;
a = 35, b = 15, c = 35, d = 15;
etc.

Sokal and Rohlf indicate that they have "not yet encounted a [non-hypothetical] example of this model."

ancova

as a (relatively) uncomplicated published example of ancova, i humbly present for my biostats students' consideration the following: http://www.tulane.edu/~guill/Reprints/Guill_and_Heins_2000.pdf

perhaps most useful to them will be the formats it uses for reporting the results of the analyses (which -- looking back over it, i'm embarrassed to say, aren't perfect: one needs 2 values for the degrees of freedom for an F ratio. my bad.)

also, it may serve as a reasonably useful model for what i'll be looking for in their independent projects -- basically something approximating the 'methods' and 'results' section of this paper in length and depth, supported perhaps by a few well-crafted figures and tables, as appropriate. anything beyond that (e.g. intro or discussion) will be lagniappe.

anova by hand

and here i was thinking i was being all progressive and modern by not making my biostats students work through all the calculations for anova by hand, but -- lo and behold! -- busy tosser has opined that the old-skool approach might actually be helpful. she's probably right;) so, let it never be said that i'm not willing to hand out additional work when it's asked for -- here you go:

a quick google search on "anova by hand" turned up the following worksheet:statisticshell.com/anovabyhand.pdf. the 'parent' site that it comes from -- statisticshell.com -- is a hoot. i've worked through the worksheet and it's actually quite good -- he walks you through one example (response to viagra, no less!) and then gives you a second problem to work on your own, followed by the answers to that one as well. i checked his results in R and get the same answers as he did, so -- if you're so inclined -- have at it!

let me know if it helps.