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Cautionary Tales in Designed Experiments

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Cautionary Tales in Designed Experiments The correct bibliographic citation for this manual is as follows: Salsburg, David S. 2020. Cautionary Tales in Designed Experiments. Cary, NC: SAS Institute Inc. Cautionary Tales in Designed Experiments Copyright © 2020, SAS Institute Inc., Cary, NC, USA ISBN 978-1-952363-24-5 (Paperback) ISBN 978-1-952363-23-8 (Web PDF) All Rights Reserved. Produced in the United States of America. For a hard copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. 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If FAR 52.227-19 is applicable, this provision serves as notice under clause (c) thereof and no other notice is required to be affixed to the Software or documentation. The Government’s rights in Software and documentation shall be only those set forth in this Agreement. SAS Institute Inc., SAS Campus Drive, Cary, NC 27513-2414 September 2020 SAS® and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies. SAS software may be provided with certain third-party software, including but not limited to open-source software, which is licensed under its applicable third-party software license agreement. For license information about third- party software distributed with SAS software, refer to http://support.sas.com/thirdpartylicenses. Contents Preface .............................................................................................................. vii Chapter 1: Experimental Design from Harvey to Fisher ..................................... 1 1.1 The Circulation of the Blood ....................................................................................................... 1 1.2 The Statistical Model of Experimental Design ............................................................................ 3 1.3 Summary .................................................................................................................................... 6 References ....................................................................................................................................... 7 Chapter 2: Measuring the “Good” in Milk ........................................................... 9 2.1 Pasteurization and the “Good” in Milk......................................................................................... 9 2.2 Experiments on Mice ................................................................................................................ 10 2.3 Summary .................................................................................................................................. 12 Reference ....................................................................................................................................... 12 Chapter 3: Designing the Lanarkshire Milk Experiment ................................... 13 3.1 “Man Is Not a Big Mouse” ......................................................................................................... 13 3.2 Measuring the “Good” in Milk ................................................................................................... 14 3.3 Adjusting for Differences among the Children .......................................................................... 15 3.4 Summary .................................................................................................................................. 16 Reference ....................................................................................................................................... 16 Chapter 4: The Execution of the Lanarkshire Experiment ................................ 17 4.1 Matching the Children............................................................................................................... 17 4.2 Fisher’s Model .......................................................................................................................... 18 4.3 Randomization ......................................................................................................................... 19 4.4 The Lanarkshire Experiment Begins ........................................................................................ 20 4.5 Summary .................................................................................................................................. 21 Chapter 5: The Results of the Lanarkshire Experiment.................................... 23 5.1 Gossett’s Criticism .................................................................................................................... 23 5.2 What Went Wrong .................................................................................................................... 25 5.3 Mismanaged Experiments ........................................................................................................ 25 5.4 Summary .................................................................................................................................. 26 References ..................................................................................................................................... 26 iv Cautionary Tales in Designed Experiments Chapter 6: How to Randomize Experimental Units ........................................... 27 6.1 Random versus Haphazard Treatment Assignment .................................................................. 27 6.2 Using Random Numbers to Assign Treatments ........................................................................ 29 6.3 Pseudo Random Numbers on the Computer ............................................................................ 31 6.4 How a Pseudo Random Number Generator Works ................................................................... 32 6.5 Summary ................................................................................................................................... 32 References ...................................................................................................................................... 32 Chapter 7: When Randomization Cannot Be Done ........................................... 33 7.1 Observational Studies ............................................................................................................... 33 7.2 The Development of “Evidence-Based Medicine” ..................................................................... 35 7.3 The DES Debacle ...................................................................................................................... 36 7.4 Deickmann’s Study .................................................................................................................... 36 7.5 The Misuse of Observational Studies ........................................................................................ 37 7.6 Summary ................................................................................................................................... 37 References ...................................................................................................................................... 38 Chapter 8: Different Designs for Experiments ................................................. 39 8.1 Crossover Designs .................................................................................................................... 39 8.2 Carry-over Effects ..................................................................................................................... 41 8.3 Latent Response Models ........................................................................................................... 42 8.4 Summary ................................................................................................................................... 43 Reference ........................................................................................................................................ 43 Chapter 9: Analysis of Variance ....................................................................... 45 9.1 Fisher’s Model ........................................................................................................................... 45 9.2 “Errors” to “Residual” ................................................................................................................
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