A Sequence of Games Useful in Teaching Experimental Design to Agriculture Students

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<ul><li><p>This article was downloaded by: [Northwestern University]On: 20 December 2014, At: 04:24Publisher: Taylor &amp; FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK</p><p>The American StatisticianPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/utas20</p><p>A Sequence of Games Useful in Teaching ExperimentalDesign to Agriculture StudentsK. H. Pollock a , H. M. Ross-Parker b &amp; R. Mead ca Department of Mathematics , University of California , Davis , CA , 95616 , USAb The Postgraduate Institute of Agriculture, University of Sri Lanka , Peradeniya , Sri Lankac Department of Applied Statistics , University of Reading , Reading, EnglandPublished online: 26 Mar 2012.</p><p>To cite this article: K. H. Pollock , H. M. Ross-Parker &amp; R. Mead (1979) A Sequence of Games Useful in Teaching ExperimentalDesign to Agriculture Students, The American Statistician, 33:2, 70-76</p><p>To link to this article: http://dx.doi.org/10.1080/00031305.1979.10482663</p><p>PLEASE SCROLL DOWN FOR ARTICLE</p><p>Taylor &amp; Francis makes every effort to ensure the accuracy of all the information (the Content) contained in thepublications on our platform. However, Taylor &amp; Francis, our agents, and our licensors make no representationsor warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions and views of the authors, and are not theviews of or endorsed by Taylor &amp; Francis. The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor and Francis shall not be liable for any losses,actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoevercaused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.</p><p>This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms &amp; Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions</p><p>http://www.tandfonline.com/loi/utas20http://dx.doi.org/10.1080/00031305.1979.10482663http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditions</p></li><li><p>A Sequence of Games Useful in Teaching ExperimentalDesign to Agriculture Students</p><p>K. H. POLLOCK, H. M. ROSS-PARKER, and R. MEAD*</p><p>In this article a sequence of statistical games is described thatwere found useful for teaching statistics to agriculture students.The ideas of experimental design tend to be neglected in statisticsservice courses for agriculturalists because of the practical diffi-culty of allowing students to learn design by experience. Simulat-ing experiments in the classroom or on the computer console is aviable alternative and should be more widely used. In this article,three games-TOMATO, CHICK, and SELECT-are described.Other games can be invented. The relevance of using games ex-tends to fields other than agriculture.</p><p>KEY WORDS: Games; Teaching; Experimental design; Inter-active computing.</p><p>1. Introduction</p><p>Statistics is a necessary part of the education ofagriculture students. Many of these students, however,have a natural aversion to all things mathematicaland little idea of what statistics is about or why theyshould understand it. Therefore, a first course mustpersuade such students that they need to learn thesubject.</p><p>Some ideal goals of a first course in statistics arethat the students will (a) understand the essential phi-losophy of statistical methods; (b) know how to usebasic statistical techniques, be able to appreciatewhen to use them, and be capable of interpreting theresults; (c) appreciate the principles and practice ofdesigning agricultural experiments; (d) know when toask for statistical advice and be able to discuss theirproblem intelligently with a statistician.</p><p>These goals are difficult to achieve. Many coursesconcentrate solely on the second goal: the analysis ofexperiments using the standard statistical techniques.As a result, the students learn little about the design ofexperiments, the third goal, which is more importantfor them than the method of analysis. Teaching onlyanalysis tends to distort the students' whole view of thesubject and interferes with the realization of the othertwo aims.</p><p>The teaching ofdesign ofexperiments is very difficultbecause it is usually not possible for students todo much designing of their own agricultural experi-ments where they can learn by experience. Whereverfeasible, however, this approach should be used.Another way of providing experience in the design of</p><p>* K.H. Pollock is Lecturer, Department of Mathematics, Uni-versity of California, Davis, CA 95616. H. M. Ross-Parker is SeniorLecturer, The Postgraduate Institute of Agriculture, University of SriLanka, Peradeniya, Sri Lanka. R. Mead is Reader, Department ofApplied Statistics, University of Reading, Reading, England. Thiswork was begun when all the authors were in the Department ofApplied Statistics at Reading. The authors wish to thank their col-leagues at Reading for many helpful discussions.</p><p>experiments is through simulating the experimentalsituation in the classroom.</p><p>Mead (1974) described an experimental design gameto simulate a poultry experiment. The game, ap-propriately called CHICK, could be played at an on-line computer console. Pike (1976) described a non-computer version of this game called HEN, whichcould be played in the classroom by using slips of papercarrying simulated observations.</p><p>CHICK has been used for several years in a servicecourse for agriculture students at the University ofReading. The class of approximately 150 studentsranged from first year to postgraduate. We found thatCHICK was a little too demanding for the first designgame the students met, partly because it involvedthe use of computer consoles but also because ofsome difficult design concepts inherent in the game.Also, CHICK alone could only illustrate some as-pects of design, and thus we felt a sequence ofgames was necessary. In this article we discuss the se-quence of experimental design games TOMATO,CHICK, and SELECT, which we devised to developthe students' ability to design agricultural experi-ments.</p><p>In the next section we give a description of the games.The description will be followed by a discussion ofthe advantages and disadvantages of using the games onthe computer consoles or in the classroom. Finally, wediscuss the sequence as a whole, including its strengthsand weaknesses.</p><p>2. The Sequence of Games</p><p>2.1. TOMATO</p><p>2.1.1. Introduction. This first game is played early inthe statistics course before the students have beentaught any experimental design. TOMATO introducesthe idea of blocking and encourages the use of an un-balanced design, which students tend to resist at a laterstage in the course. The game also introduces studentsto the concept of a factorial treatment structure,informally laying the groundwork for discussion in laterlectures.</p><p>A brief verbal description of the game is given toaugment the following specification, emphasizing theimportance of the side-of-greenhouse effect, the twostages of the experiment and the treatment structure.</p><p>2.1.2. Specifications given to the students. Twofarmers, Adams and Bloggs, grow glasshouse tomatoesin Guernsey for the English market. After several years,Bloggs clearly gets higher yields than Adams. Unfortu-nately, Bloggs and Adams have difficulty determining</p><p>70 The American Statistician, May 1979, Vol. 33, No.2</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Nor</p><p>thw</p><p>este</p><p>rn U</p><p>nive</p><p>rsity</p><p>] at</p><p> 04:</p><p>24 2</p><p>0 D</p><p>ecem</p><p>ber </p><p>2014</p></li><li><p> The American Statistician. May 1979, Vol. 33. No.2</p><p>1. Treatment Means for TOMATO</p><p>NORTH FACING</p><p>SOUTH FACING</p><p>South</p><p>22.1</p><p>21.9</p><p>29.1</p><p>23.9</p><p>26.1</p><p>25.9</p><p>27.1</p><p>26.9</p><p>71</p><p>Side</p><p>North</p><p>HO</p><p>LO</p><p>C 18.1</p><p>HO</p><p>LO</p><p>D 17.9</p><p>HO L1 C20.1</p><p>HO</p><p>L1</p><p>D 19.9</p><p>HI LO C22.1</p><p>HI LO D21.9</p><p>HI L1 C23.1</p><p>HI L1 D22.9</p><p>Treatment</p><p>A. The Greenhouse Used in the Experiment.</p><p>for the second stage, even though the incorporation ofastage effect would have made the game more realistic.This point is considered further in subsection (2.1.5.).</p><p>When both stages of the experiment were completeand the students had interpreted their observations,we held a class discussion. First, each pair of studentswas asked to give answers for the optimum andeconomic-optimum combinations orally. The answerswere then displayed on the blackboard. The answerswere briefly discussed and the true mean yieldsrevealed. We had to make the point that studentswho received incorrect answers had not necessarilybeen remiss in their design. This point led to a valuablediscussion of uncertainty of inferences in experiments.</p><p>2.lA. The model parameters. In designing the game,we had to decide on both the mean yields of each treat-ment-plot combination and the variability of thesequantities. The standard deviation was chosen asunity for all observations on all treatment-plot com-binations; the chosen values for the means are givenin Table 1. You should note that all plots on each sidehad the same mean for each treatment but distinctenvelopes were used.</p><p>The treatment code is in the order HEAT, LIGHT,and VARIETY, 0 indicating the normal level and Iindicating the supplementary level. C refers to thevariety COWARD, while D refers to DaGER.</p><p>The treatment means were chosen to give a largeside effect and to make the variety effect negligible.</p><p>I 2 3 4 5 6</p><p>ALLEYWAY FOR ACCESS</p><p>I 2 3 4 5 6</p><p>Suppose you are going to grow one greenhouse oftomatoes and that the extra costs of supplementaryheating and lighting are 500and 400 for the whole green-house, respectively, with no difference in the cost ofvarieties. If for a plot mean increase in yield of one unitthe increase in income for your whole greenhouse is200, decide which treatment combination is economi-cally best. Is this the same combination that gives thehighest yield? (Note that all yield slips have to bereturned to the person controlling the game).</p><p>2.l.3. The game structure. For each of the 12 plotsthere are 8 possible treatments that can be applied;accordingly, we provide 96 envelopes. Each envelopecontains 50 pieces of paper, each having a simulatedyield written on it for that particular plot-treatmentcombination.</p><p>After the students had considered and chosen theirdesign, they each obtained a set of "yields" from thegame controller. He randomly chose a piece of paperfrom each of the envelopes for the treatment-plotcombinations specified by the students. After consider-ing these yields, but not analyzing them in any for-mal sense, the students designed the second stage oftheir experiment. We used the same set of envelopes</p><p>what causes this discrepancy because several fac-tors-heat, light, and variety-differ in their methodsof growing tomatoes. Farmer Adams is conservative.He uses standard heating and lighting and a variety oftomato called "Coward," while Farmer Bloggs usessupplementary heating and lighting and a varietycalled "Doger."</p><p>The aim of this experimental game is for pairs ofstudents (think of yourselves as Adams and Bloggs) todesign a two-stage experiment and, based on the re-sults, decide which combination of the three factors ofheat, light, and variety gives the highest yield of to-matoes. For simplicity let us consider just two levels ofeach factor (standard heating or supplementary heat-ing, standard lighting or supplementary lighting, and"Coward" or "Doger").</p><p>These are lean times and research money is tight;thus you can have only a small greenhouse to performthis experiment. There are six experimental units (plots)facing north and six plots facing south. We know fromprevious experiments in the greenhouse that there is asubstantial difference in yields between the two sidesof the greenhouse. The second stage is carried out inthe same greenhouse (see Figure A). The procedure isas follows:</p><p>1. Decide which treatments you want to apply to particularplots in the first stage of the experiment.</p><p>2. Obtain simulated yields (written on small labeled slips ofpaper) for your experiment from the person controllingthe game.</p><p>3. Interpret your results.4. Design the second stage, and obtain a set of simulated</p><p>yields for this stage as before.5. Interpret your results.6. Reach a conclusion as to which combination you think</p><p>gives the best yield.</p><p>Dow</p><p>nloa</p><p>ded </p><p>by [</p><p>Nor</p><p>thw</p><p>este</p><p>rn U</p><p>nive</p><p>rsity</p><p>] at</p><p> 04:</p><p>24 2</p><p>0 D</p><p>ecem</p><p>ber </p><p>2014</p></li><li><p>2.2. CHICK</p><p>2.2.1. Introduction. This interactive game is playedon the computer consoles by pairs of students and isintended to encourage them to think critically aboutblocking. The students also have to decide on whichtreatment structure to use in investigating the shape ofresponse curves. In addition, the choice of the num-ber of experiments to carry out to meet the objectivesof the game is left open to the students.</p><p>An interaction between HEAT and LIGHT was builtinto the model, supplementary heat giving an increaseof four units in the absence of supplementary light,supplementary light giving an increase of two units inthe absence of supplementary heat, and supplementaryheat with supplementary light together giving an increaseof only five units more than normal heat and normal light.</p><p>The optimum treatment is supplementary heat andsupplementary light with variety COWARD (HILle),while the economic optimum is supplementary heatand normal light with COWARD (HILoC). The proba-bility of getting the correct heat-light combination isapproximately .88 and .76 for the optimum effect andeconomic optimum, respectively, assuming a reason-able strategy is adopted. The probability of obtainingthe correct variety is obviously much smaller (approxi-mately .6). Thus, the probabilities of complete cor-rect answers are approximately .53 and .46 for theoptimum effect and economic optimum, respectively.</p><p>We think these probabilities are high enough thatthe game is not too difficult but low enough to offer achallenge and illustrate the ideas of uncertainty.</p><p>2.1.5. Comments. The students completed the gamein a little more than an hour and found it extremelyenjoyable. They were absolutely delighted when theyfound that we were not going to tell them how toproceed!</p><p>We think the unbalanced nature of this problem isimportant. Some students were reluctant to use anunbalanced design and did not include all treatmentsat each stage. This approach was successful becausethere was no stage effect; the approach gave them little ad-vantage. In practice a stage effect would be present.This situation made a good discussion point.</p><p>We were interested to see that some of the studentswho had seen experimental designs before tried touse them, even if they did not fit! The studentswho were new to the subject seemed more adventurousin their choices of designs...</p></li></ul>


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