Resampling Stats(ID:6903/)

Resmaplong capability Omnitab 


Monte Corlo etc stats package based on Omnitab


Related languages
OMNITAB => Resampling Stats   Influence

References:
  • Simon, Julian L. and Peter Bruce, "Resampling: A tool for everyday statistical work." Chance 4(1) 1991 pp22-32 view details
  • Simon, Julian L. and Bruce, Peter C. "Resampling Stats: User Guide (with software)" Resampling Stats, Arlington, VA 1993 view details
  • Simon, Julian L. "Resampling: The New Statistics (text to accompany Resampling Stats software)" Resampling Stats, Arlington, VA 1993 view details Abstract: This text grew out of chapters in the 1969 edition of Basic Research Methods in Social Science by the same author, and contains the first published example of what was later called the bootstrap. Simon is best known for his research in demography, population and the economics of natural resources, and gained fame when the noted biologist Paul Ehrlich selected five commodities and bet Simon that scarcity would drive their prices up over the period of the bet (in fact, their prices all dropped). Resampling: The New Statistics contains a number of examples in Resampling Stats, a computer program originated by Simon, but can be read on its own without the program. External link: Online copy
  • Simon, Julian L., Resampling Stats User's Guide 1995 view details
  • Simon, Julian L. "Resampling: A Better Way to Teach (and Do) Statistics" Robert H. Smith School of Business University of Maryland, College Park July 13-19, 1997 view details External link: Online copy Extract: INTRODUCTION
    INTRODUCTION
    The aim of this book is to present to statisticians, and to statistics instructors, ideas and data relevant to teaching  statistical inference - especially at the introductory level -  using resampling methods in addition to, or in place of,  conventional methods.
    Before proceeding further, here are a problem in  probability, and one in statistics, to show you what we mean by  simulation (in probability) and resampling simulation (in  statistics):
         P:  INSERT ? Three girls  from statbook?
         P:  INSERT ? Bush-Dukakis  from statbook?
    Part I introduces resampling and its teaching to that large part of humanity, and even of the statistics profession, that is  still unaware of resampling.  We begin in Chapter I-1 with the  results of studies of resampling in the classroom (and a bit of  data for afterwards, too) from the early 1970s to the present; if  there were no demonstrated successes or proven superiority over  the conventional method, there would be no reason to read  further.  Chapter I-2 then describes the resampling method  itself.  And Chapter I-3 tells some of the history of the  development of resampling method.
    Part II discusses methods of teaching statistical inference with resampling.  Resampling is best understood by seeing it  being learned.  Hence Chapter II-1 transcribes an edited taped  class, to give the sense of the class atmosphere.  Chapter II-2  discusses the teaching of resampling in a fashion complementary  with the conventional method and books.  And Chapter II-3  discusses some of the benefits and costs of teaching the  resampling method - the spontaneity of the give-and-take between  students and teachers being both a benefit to students and a cost  to the teacher because it demands more effort than does a  standard structured class hour.
    Part III analyses the resampling method from the point of view of its effectiveness for users and students, and the nature  of the cognitive processes involved in carrying out statistical  inference with resampling and with the conventional method.   Chapter III-1 looks into the nature of statistical inference to  ascertain why it is such a difficult subject, and discusses how  resampling allows the student to focus on the true inherent  difficulties without getting distracted by unnecessary  mathematical difficulty and obscurity using the formulaic  approach.  Chapter III-2 discusses why simulation can sensibly  attack some problems that the formal sample-space approach cannot  address.  Chapter III-3 analyses several famous problems and  shows how the simulation approach that solves them also eases  problems in statistics.  An afternote shows - half seriously,  half in jest - how a "try it" simulation approach can hugely  raise students' IQ (as defined by a newspaper IQ test) in a  matter of minutes; this typifies the effect of resampling on  one's intellectual capabilities.
    Part IV takes up some special topics.  Chapter IV-1 discusses the relationship between mathematicians and the  teaching of statistics; their love of the esthetics of  mathematics is a major barrier against teaching the simulation  approach, which (to mathematicians) lacks the beauty of formal  equations and proofs.  Chapter IV-2 describes a computer-based  tutor that uses artificial intelligence to detect whether a  student's program is correct, and if not, to tell the student  where errors in logic have been made; the nature of the  resampling approach uniquely enables the operation of such a  tutor that works understandably, rather than a mere dumb device  that finds deviations from the formula that is demanded.  Chapter  IV-3 discusses the nature of the Resampling Stats program that  emobdies the resampling approach; it and other parallel languages  such as Mathematica and APL work in an entirely different fashion  from Basic and Pascal because they closely mimic the operations  in simulation.  (Resampling Stats has the additional advantage  over Mathematica and APL that it is designed only for statistics  and probability, and therefore is much less difficult to master.)  
    Part V discusses the future of resampling, and the barriers it must overcome before it is adopted widely or universally for  instruction and everyday use - as it surely will be.  Chapter V-1  discusses students' reactions to conventional statistics teaching  in the general context of the teaching of mathematics.  And  Chapter V-II discusses the short-run prospects for resampling  instruction.  
    These chapters may seem as if they are an argument for the use and teaching of resampling methods.  But if that is so, we  believe, the reason is the characteristics of the resampling and  the conventional parametric methods, rather than our partiality  to resampling.  And we do our very best to present all the  relevant material, pro and con, in as unbiased a manner as  possible, though we are certainly are adherents of resampling -  because of its characteristics, we believe.
    The reader who is interested in learning more about the practical procedures of resampling methods may consult  Resampling:  The New Statistics by Julian L. Simon.  And the same  author's The Philosophy and Practice of Statistics and Resampling  discusses the philosophical foundations of the subject.

    Resources
    • The RESAMPLING STATS Language at Exeter Software

      The
      RESAMPLING STATS Language


      color=#663333>BASIC COMMANDS:


      ADD {adds the elements of two vectors together}

      CONCAT {combines two vectors into one long one}

      COPY {records data or copies vectors}

      COUNT {determines the frequency of a particular number or range of numbers}

      DEDUP {eliminates duplicate values}

      DIVIDE {divides the contents of one vector by another}

      END {ends a loop, sends you back to a "REPEAT" statement}

      GENERATE {produces the desired quantity of random numbers within the desired
      range}

      HISTOGRAM {produces a histogram of trial results}

      IF {succeeding commands execute only when IF condition holds}

      MEAN {calculates the mean of a vector}

      MULTIPLES {determines the frequency of multiplicates of a number}

      MULTIPLY {multiplies the elements in one vector by those in another}

      PERCENTILE {calculates the xth percentile of a frequency distribution}

      PRINT {specifies output to be shown on screen}

      REMARK {precede remarks with an apostrophe '}

      REPEAT {allows user to repeat simulation up to 15,000 times}

      RUNS {calculates the number of runs of a given length}

      SAMPLE {samples with replacement}

      SCORE {allows user to keep track of the result of each simulation}

      SHUFFLE {randomizes the elements in a vector}

      SORT {sorts the elements in a vector}

      SUBTRACT {subtracts the elements in one vector from those in another}

      SUM {adds together the elements of a vector}

      TAGSORT {creates a vector of sorted positions, allowing you to sort multiple
      vectors according to the order of a "key" vector}

      TAKE {takes a specified number of elements from a vector and creates a new
      vector}

      WEED {removes specified numbers or a specified range}

      color=#663333>ADDITIONAL MATHEMATICAL AND STATISTICAL
      COMMANDS:


      ABS {finds absolute value of each element in a vector}

      BOXPLOT {produces a boxplot}

      CORR {calculates correlation coefficient}

      EXP {raises "e" to the power of each vector element}

      EXPONENTIAL {generates numbers from an exponential distribution}

      LOG {takes the log of elements in a vector}

      MAX {identifies the maximum value in a vector}

      MEDIAN {calculates the median of a vector}

      MIN {identifies the minimum value in a vector}

      MODE {identifies the most frequent value in a vector}

      NORMAL {generates numbers from a normal distribution}

      POWER {raises each element in first vector to the power of the corresponding
      element in the second}

      REGRESS {does multiple linear regression}

      ROUND {rounds each element to an integer}

      SQRT {determines the square root of each element in a vector}

      SQUARE {squares each element in a vector}

      STDEV {finds the standard deviation of each element in a vector}

      SUMABSDEV {sums the absolute deviations of one vector from another}

      SUMSQRDEV {sums the squared deviations of one vector from another}

      TIMEPLOT {plots a vector sequentially along x-axis}

      UNIFORM {randomly produces real values from a uniform distribution}

      VARIANCE {finds the variance of the elements in a vector}

      color=#663333>ADDITIONAL RESAMPLING & HOUSEKEEPING
      COMMANDS:


      CLEAR {erases contents of a vector}

      PAUSE {causes program execution to pause}

      READ {imports data from an ASCII file}

      RECODE {changes certain elements of a vector to specified value}

      SEED {sets the random number generator seed}

      SET {fills a vector with one value}

      SIZE {determines the size of a vector}

      WHILE {conditional repeat}

      WRITE {exports data to an ASCII file}


      external link