A quick reply. Looks somewhat like the second course ("Intermediate
Statistics and Research Design") I taught for some years at OISE,
Toronto, which was (and is) the Graduate Department of Education for
the University of Toronto. Ask for more later if you want...
On Tue, 20 Feb 2001, Lise DeShea wrote:
> I am looking for a textbook to use in a second-semester stats course in
> a College of Education. ... Material covered in the class includes:
>
> -- Review of kinds of research; kinds of variables; hypothesis testing;
> errors; one- and two-sample stats; and simple regression
> -- one-way and two-way fixed-effects ANOVA
> -- Multiple comparison procedures (usually I provide supplemental
> material instead of relying on the text)
> -- Intro to power
> -- simple repeated measures design
> -- split-plot design
> -- Intro to multiple regression
I'd summarize this as ANOVA, multiple comparisons, and multiple
regression. I could usually find a textbook suitable for ANOVA (more on
that below), which I could supplement with an intro to MR I'd compiled
that was rather heavily based on Bottenberg & Ward; or a textbook good
for MR, which I could supplement with the "Rules of Thumb for Writing the
ANOVA Table" (originally Millman & Glass, J. Educ. Meas. 1967, and
reproduced in Glass & Stanley 1971 and Glass & Hopkins 1984: "Stat'l
Methods in Educ. & Psychology").
Textbooks for ANOVA: Glass & Stanley (later Glass & Hopkins, 2nd ed.),
esp. when I'd used it for the first course ("Elements of Statistics").
Keppel: Design & Analysis: A Researcher's Handbook.
Textbooks for MR: Darlington: Regression & Linear Models.
Judd & McClelland: Data Analysis/A Model-Comparison Approach.
Pedhazur: Multiple Regression in Behavioral Research.
Never did find a text that combined BOTH multiple regression & ANOVA
with enough depth for my purposes. (Good luck!)
> I am looking for a book that is conceptual so that my generally
> math-phobic grad students in Education don't freak out with
> "symbol-shock," yet I want careful coverage of assumptions and
> robustness.
Your "yet" suggests you're aware of the inherent logical contradiction in
that sentence :-). In my view it is not useful to pander to math-phobia;
one must deal with it, but in a strategy that helps the feckless student
to cope with the phobia and, just maybe, eventually overcome it. One of
my stategies was to emphasize at the outset that this is NOT a course in
mathematics (nor, really, a course in statistics, though I didn't usually
say THAT), but a course in several foreign languages (algebra, computing,
statistics, research come to mind) and in a quite foreign (or at least
unaccustomed) style of thinking.
(Just for one example: for students like yours, it's virtually
certain that no one has ever told them that algebra is mostly about using
pronouns instead of proper nouns for talking about numbers; so that
treating the particular forms of algebra used in statistics as a kind of
grammarian's approach to quantitation is wholly new, and might get their
minds off the phobic stuff for a minute or two. Thus "X" is a pronoun
for "a particular value of a variable", where "variable" itself is a
pronoun for "performance on the English test" (or whatever!); the
subscript "i" hung onto the "X" is a pronoun for "the individual who
supplied that particular datum"; so "X_i" is "that particular datum
whose value is 17.5 when the individual referred to is no. 4, who is Mary
Smith". Similarly with symbols for operations: you want to add up X_1
and X_2 and ... and X_n to get the Sum of all the X_i, or perhaps more
simply "Sum(X_i)", but "Sum" is a long word (3 letters!), so we
substitute its initial "S", but spell it in Greek (Sigma producing the
same sound in Greek as S does in English) in ouir ongoing campaign to
help convince the uninitiated that, really, it's all Greek to us...)
Incidentally, on ANOVA: I've never been convinced that all that
agricultural terminology was much help to anyone except agronomists and
the like, so I _never_ used terms like "split plot". By starting off
with a generalizable symbology, one can focus on the _ideas_ of the
details, and the carrying out of the details, without having to know
rather artificial labels just to be able to look up the relevant design.
Using AxB for two crossed factors, C(D) for a factor C nested in
another factor D, superscripts "r" and "f" for "random" and "fixed"
(or just an asterisk * for "random", if you prefer), and subscripts for
the number of levels of a factor, one can represent any complete
balanced design in a single formula like
R*(S*(CxG)xM)
for "Replications" (what someone has called "the ubiquitous nested
factor", which in a design like this one might only have one level, so it
has zero SS and zero df, but its presence helps one see what the proper
denominator mean squares would be if one had them available) nested
within "Subjects", which are in turn nested within explerimental
"Conditions" and "Gender", and crossed with "Measures" (where M is a
repeated-measure factor); R and S are random factors, C, G, and M are
fixed.
Any design where S is crossed with one or more other factors is a
repeated-measures design, and the factor(s) with which it is crossed are
the repeated measure(s). This avoids a LOT of mysticism about repeated-
measures designs in general.
This approach makes ALL specially-named designs mere special
cases of the general complete balanced model, and permits one to focus on
the logic of the analysis (and computations, if one must) rather than the
formal names for them in agriculture or psychology or ... Thus R*(A)
(with r > 1, r = the number of levels of R) is the one-way fixed-factor
design, R*(AxB) it a two-way design, R*(AxB*) with r = 1 is the one-way
randomized-blocks design with B the blocking factor, R*(S*(AxB)xCxD)
with r = 1 is a four-way ANOVA with repeated measures on two factors (C
and D), ...
> Currently I'm using Stevens' "Intermediate Statistics,"
> 2/e, and I am dissatisfied with it.
>
> As I am new to this list, I searched the edstat archives and looked at
> messages dating back as much as four years, and I couldn't find any
> previous notes that apply to my situation.
Right. I certainly don't recall any conversations on this topic.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
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