introductory statistics: a decision map.by thad r. harshbarger

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Page 1: Introductory Statistics: A Decision Map.by Thad R. Harshbarger

Introductory Statistics: A Decision Map. by Thad R. HarshbargerReview by: Benjamin KingJournal of the American Statistical Association, Vol. 67, No. 339 (Sep., 1972), pp. 713-714Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2284477 .

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Page 2: Introductory Statistics: A Decision Map.by Thad R. Harshbarger

Book Reviews 713

from the U.S. of $.37 billion within three months. Chapter 6 con- tains all of the quarterly results; because of its length, only a few general qualitative results will be mentioned here. Again, both short and long-term portfolio capital were found to be interest sensitive and responsive to trade and GNP movements. The data suggest that errors and omissions in the U.S. balance of pay- ments are movements of short-term funds between New York and Eurodollar deposits in London (a one percentage point increase in the Eurodollar rate is associated with nearly a $1 billion net outflow). Chapter 7 discusses capital flows in economy wide models. Branson's inclusion of the data used in the book in the Data Appendix thoughtfully provides other researchers the op- portunity to test and extend his results.

Critically, I was puzzled by Branson's treatment of interest rates as largely exogenous (there is a brief discussion of the inter- national interdependence of rates in Chapter 4). While it is true that the rate of interest is an exogenous variable in an individual's portfolio decision, this is not true in the aggregate. Branson's results may thus be biased in specifying that interest rates affect capital flows but not vice versa. The size of the bias depends, of course, on the targets and effectiveness of monetary policy in the respective regions. Since capital flows provide the link between national money markets, it would have been appropriate for Branson to provide a closer examination of monetary policy than the theoretical postscript in Chapter 7, and the note above.

A related criticism is that while Branson is careful to integrate well the theories of portfolio and foreign exchange market behav- ior into his empirical work, he largely ignores the relationship between his empirical results (which have important implications for current public policy) and the growing body of theoretical literature on the use of monetary, fiscal and exchange rate policy to correct payments imbalances. Other writers, Willett [3] and Lee [2] to name two, have applied independently portfolio models to international capital flows. Willett does explore this relationship between portfolio-capital flow models and the use of monetary vs. fiscal policy to correct payments deficits.

Three minor points should be made. First, Branson was per- plexed on pages 56-58 that an increase in U.S. imports caused the Canadian exchange rate (in U.S. cents per Canadian dollar) to fall and was further puzzled that simultaneity between U.S. im- ports from Canada and the exchange rate during the flexible rate period did not explain the problem, assuming that the elasticity of demand exceeded unity. However, Houthakker and Magee [2, Table 4] have shown that U.S. Imports from Canada may be price inelastic, which may explain the paradox. Second, there is no author index in the book. Third, there are the usual minor slips: change "and" to "end" on page 75, line 12; change "X" to "AX" in equation 10 on page 92; and change "imports" to "exports" in the title of Table 5 on page 97, to name a few.

On balance, however, Branson's work is an important contri- bution and deserves a serious reading by both international economists and applied econometricians.

STEPHEN P. MAGEE

University of Chicago

REFERENCES

[1] Houthakker, H.S. and Magee, S.P., "Income and Price Elasticities in World Trade," The Reviewv of Economics and Statistics 51 (May 1969), 111-25.

[2] Lee, C.H., "A Stock-Adjustment Analysis of Capital Movements: The United States-Canadian Case," Journal of Political Economy 77 (July/August 1969), 512-23.

[3] Willett, T.D.," A Portfolio Theory of International Short-Term Capital Movements," Abstract of Ph.D. dissertation at the University of Virginia, 1967, in Journal of Finance, 14 (December 1959), 971-2.

Introductory Statistics: A Decision Map,

Thad R. Harshbarger. New York: Macmillan Company, 1971. vii+558 pp. $10.95.

This elementary textbook, aimed at readers in psychology, sociology, and education, is likely to have a certain attraction for both students and instructors because of its use of flowcharts, or "decision maps," in the exposition of statistical techniques. Few of us are not impressed by the tremendous impact of com- puters and programming on the implementation of statistical method. Why should it not be possible to capitalize on the econ-

omy and the cold logic of the flowchart in improving our teaching of the underlying principles and proper application of statistics?

In his preface, the author makes the following claim:

The present approach has several advantages over both traditional and programmed learning materials.

1. One function of the map is to provide a printed representation of relationships among various methods for solving statistical problems. It is hoped that such a visual presentation of interrelationships will (a) provide a stable frame of reference into which new approaches can readily be integrated, so the student will not get lost as easily as with the traditional approach, and (b) encourage the student to learn other techniques that will fill in gaps in his own personal decision map of statistical methods.

2. A second function of the schema is to eliminate from consideration, as efficiently as possible, methods inappropriate for the solution of the given problem. By simulating the classification process an expert might use in deciding on a method for solving a problem, the decision map should give the novice a degree of functional expertise with respect to his own problems that he could not otherwise obtain so quickly. Also, by encouraging the student to learn only that material related to his own problem or area of interest, this method of organization should have a greater potential than the usual text for maintaining a relatively high level of motivation throughout the learning process.

3. Inappropriate methods of solution are eliminated through explicit consideration of the sequence of decisions made by the user in solving his problem. This approach necessitates more emphasis on the assump- tions necessary for the correct application of any method or general principle. Alternatively, the user will more quickly recognize violations of assumptions when they have been made, and he will therefore be able to interpret the results in the light of the nature and probable effects of those violations.

Although the promise of the first point above is partially ful- filled-flowcharts do make it easier for the student to keep things straight in his mind-I would seriously question an asser- tion that one can learn very much from this book about the meaning of statistics and the things that statisticians do. Harsh- barger has produced a super-cookbook with some nice annotative devices for getting at recipes, but unfortunately (if I may push the metaphor) the student is not likely to end up a Cordon Bleu chef. Some experienced readers will, in fact, find the cuisine sta- tistically indigestible.

The first three chapters present a review of arithmetic and algebra and an introduction to the flowchart. Then, in the fourth chapter, entitled "Graphing," the decision map approach is applied to an exposition of some of the elementary tools of data analysis-frequency distribution, histograms, higher-dimensional plots, etc. This chapter is, in my opinion, the high point of the text because it is in helping the student to choose from among a large number of techniques for graphic display that the flow- chart can be most useful. Branch points such as "Ordinal scale or nominal scale?" make much more sense in describing the decision processes leading to the choice of methods of summariz- ing data than they do in the context of hypothesis testing (Chap- ter 9). If one is at the stage of hypothesis testing, he certainly knows by now whether his data are nominal or ordinal, and to insert the question in a box in the flow diagram for the chapter on hypothesis testing is an embellishment for the sake of embel- lishment. In view of the fact that the use of flowcharts is touted as the great innovative feature of this textbook, it is lamentable to see a steady decline in its value from Chapter 4 to a point where the device becomes excessively "gimmicky"-not neces- sarily due to a lack of trying on the part of the author, but rather because of the limited usefulness of the idea. Some of the students themselves, in Professor Harshbarger's class, must find the boxes in the flowchart that say "select significance level," "draw sample," "compute test statistic," and "accept or reject null hypothesis" somewhat reminiscent of the Dick and Jane books given to the control groups in their experiments.

My remarks, of course, concern a matter of personal taste, and it is entirely possible that many students will be so thrilled by the discovery that someone is trying something different in order to get through to them that sheer motivation will overcome reactions to stylistic imperfections. At any rate, we shall doubtless see someday the results of a carefully controlled experiment de- signed to compare the performance of students exposed to a flowchart text with a sample treated with the conventional approach to the same subject matter. My remarks should not be interpreted as a rejection of the decision map idea for lack of promise.

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Page 3: Introductory Statistics: A Decision Map.by Thad R. Harshbarger

714 Journal of the American Statistical Association, September 1972

Furthermore, I should like to report that this is a very pleasant book to look at. (Not a trivial comment to those who know how beginning students react to multilithed notes as opposed to a nicely designed hard-cover text.) I was quite taken by some of the graphics in Chapter 4 (especially the three-dimensional semantic space on page 53), and I was even willing to attribute to editorial oversight the ambiguity in interval boundaries in the histogram (page 45) and in the cumulative frequency distribution (page 47).

There are, however, some peculiarities of substance that make it impossible for me to recommend this book as the principal text for a first course in statistics. For example,

1. In Chapter 5, entitled "Characteristics of a Distribution," the concept of parameter is defined in terms of a finite population of N members. The distinction between frequency and proba- bility is never made clear, and my guess is that, at best, the brighter students come out of the course thinking of a probability as some sort of ideal relative frequency. (I would not object to this if I could be perfectly sure that the students realize that sample relative frequencies vary from sample to sample about the ideal and that the arithmetic mean is not the same as the so- called population mean. As far as I can see, the concept of ex- pected value has no place in this text.)

With the population variance defined by

a= -i (Xi - A) N

we are told that

^2 E(X-X)2

sZ - N-

is an unbiased estimate of the population variance. Note that the symbol "N" is the same in both formulas. I cannot help but wonder if the author knows that in sampling without replacement, 9 is not an unbiased estimator of U2. Since the precise method of sampling is not specified, I shall give him the benefit of the doubt, but ask at the same time how many behavioral scientists he knows who sample with replacement. My main point here is this: If probability and expectation are not going to be defined (presumably to avoid burdening the student with difficult con- cepts), why, in heaven's name, introduce unbiasedness?

2. On page 78, the following is stated: A sampling process is said to be random if every possible sample of subjects is just as likely to be selected from the population as every other. A sampling method is said to be nonrandom or biased if some possible samples of subjects are less likely to be chosen than others.

Surely the author does not mean that the Bureau of the Census sample of households used in the Current Population Survey and based upon sampling with probabilities proportional to size is a biased sample. (It is biased, but nonresponse and frame im- perfections are not the issues here.) And what about dispropor- tionate stratified sampling? Later on (pages 79-80) a definition of stratified random sampling is presented which is really that of proportionate stratified sampling. How many behavioral scientists wanting to compare disadvantaged and non-disadvantaged school children, for example, would sample proportionately from a population with a 90-10 distribution for the two strata?

3. In Chapter 7, "Theoretical Distributions" (page 127), we are told that:

The normal distribution is the most important single distribution in statistical analysis, because it is the theoretical distribution of random error when the scale is continuous.

Somewhat taken aback by the sweeping generality of this state- ment, we read further (page 128) and find that the formula for the normal distribution (i.e., the p.d.f.) is described as "messy," and we observe that the expression shown is incorrect (doubtless a typographical error). There are many of us who do not think that the formula (correctly printed) is "messy" at all, but really quite beautiful. My point here is that we have another example of the kind of destructive pedantry (albeit unintentional) that can cause a withering of whatever curiosity a student might have about the mathematics underlying statistical method. In saying, "Look at this messy formula that I know how to write down but that you will never have to worry about if you follow my surefire procedures for looking up areas under the normal

curve," the author is merely encouraging a yahooistic attitude toward advanced study in statistics. It is easy to slip into this stance in in the classroom-we all have done it at one time or another-"buddying-up" to the students, sympathizing with their pain and suffering, in order to be more pedagogically effec- tive, but when it is carried over to the printed textbook, it be- comes a bit too cute for my taste.

4. Chapter 9 is entitled "Hypothesis Testing," and it is ad- mitted by the author to be oversimplified:

It is presented in simplified form primarily to ease the learning process; however, Chapters 9 through 14 do represent rather closely the hy- pothesis-testing procedures of behavioral scientists up until the very recent past. Some important considerations, such as power of a test, sample size needed to carry out an analysis, and magnitude of treat- ment effect have received widespread recognition only recently. An introduction to these topics will be deferred to Chapter 19.

My immediate reaction upon reading the foregoing was to remark that the fact that inadequate procedures have been followed in the past is no excuse for perpetuating them in a mod- ern textbook. There is, however, on page 179, a statement that causes the reader expecting a tired treatment of one- and two- tailed tests to do a double-take. The author has just presented the following example to illustrate the logic of hypothesis testing:

(1) If [a] sample is drawn from a population with a mean of 40, the probability is .95 that the sample mean will fall between 30 and 50. (2) The sample has a mean of 58.23. (3) Therefore, the probability that the sample came from a population with a mean of 40 is .05 or less.

Then he says:

The statement that you want to disprove is called the null hypothesis and labeled Ho. The twist amounts to the fact that you usually don't even mention the hypothesis that you are interested in testing, here to be called the motivated hypothesis, Hm. It is often not necessary to mention Hm, because you arrange your hypotheses so that Ho and H,, are mutually exclusive and exhaustive.... Then in disproving Ho you automatically demonstrate Hm with the same degree of certainty.

[Last italics mine]

If this were a Bayesian treatment of statistics, the preceding remark, although correct only in restricted circumstances, would not be so surprising; but the word "Bayes" does not appear in the book. I should like to know just how Harshbarger leaps from a conditional probability statement of significance to what I take to be an unconditional probability statement about the truth of the motivated hypothesis.

5. The rest of the textbook from Chapter 10 to the final pages is basically an enumeration of the favorite recipes-analysis of variance, regression, the Mann-Whitney U test, etc.-with the aforementioned closing chapter on power. As a compendium, this book is rather more complete than many, and I must admit that when a student came to me the other day asking for an explana- tion of the Wilcoxon test for paired data (something I have not thought about in years), I found the appropriate section in this book to be a useful reminder of how the test statistic is com- puted. The discussion of Wilcoxon's T, however, is presented totally without theoretical justification or motivation, except that it is another available instrument in the statistical tool box, there for the asking if your path in Harshbarger's decision map hap- pens to bring you to it.

It is certainly easier to take potshots at someone else's efforts than it is to write a good introductory textbook in statistics. Few of us, I daresay, are totally satisfied with the book that we are currently using in class, and attempts at innovation should be encouraged and applauded. But at a time when behavioral scientists are subjecting their own statistical practices to serious criticism and reappraisal, the subject matter of this text can only be called archaic, and, in some respects, just plain wrong. There is not even a discussion of confidence interval estimation-yet, a number of prominent writers in the behavioral field see interval estimation as a way out of some of the problems caused by tradi- tional practices.' A word about Bayes (even with the usual ad- mission of the difficulty in assessing subjective probabilities and losses) would be, I suppose, simply too much to hope for.

BENJAMIN KING University of Chicago

1 See, for example, B. Lieberman (ed.), Contemporary Problems in Statistics: A Book of Readings for the Behavioral Sciences. New York: Oxford University Press, 1970.

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