Overview Resampling, also known as bootstrapping, uses brute computer power to estabish confidence intervals for any statistical procedure, based not on assumptions such as multivariate normal distributions but rather based on repeated samples from the researcher's own data. That is, rather than use generic distribution tables to compute approximate p probability values, resampling generates a unique sampling distribution based on the actual data at hand and uses experimental rather than analytic methods. Unlike approximation with generic distribution tables, resampling yields unbiased estimates because it is based on unbiased samples of all possible outcomes in the data being studied.

Contents Key concepts and terms Assumptions Frequently asked questions Bibliography




Key Concepts and Terms

Histogram of z values. Computer packages like Resampling Stats will run a thousand or more samples of a researcher-supplied dataset, each time generating a statistic (ex., correlation) requested by the researcher. It will then present the results in a bar chart (the histogram) which shows the sampling distribution of that statistic for the data at hand. Each bar may be called a "bin." There will be a table of the values of the statistic (ex., correlation) at bin centers, with percent and cumulative percent. As with a normal distribution table, one may find the value of the statistic at the point at which the cumulative percent is .05. Suppose that point was r = .30. We could then state that any correlation higher than .30 would be significant at the .05 level.




Assumptions

• This is an experimental approach which sidesteps all parametric assumptions about the nature of the underlying data stribution.

• While there is no specific sample size requirement, the larger the sample, the more reliable the confidence intervals generated by resampling. Likewise, the smaller the sample size, the more likely that confidence limits will be fitted misleadingly to noise in the data rather than to a true underlying distribution.




Frequently Asked Questions

• How do I do resampling in terms of computer software?
  A convenient package is Resampling Statistics (Resampling Stats Inc., 612 N. Jackson Ave., Arlington, VA 22201; email stats@resample.com; or visit http://www.statistics.com). This is reviewed in Social Science Computer Review, Vol. 15, No. 3 (Fall, 1997:: 305-308.

• What is the command code for doing bootstrapping in SPSS?
  The following code works with employee data.sav, an example file supplied with SPSS:

  ***oms_bootstrapping.sps***.
  ***if c:\temp is not a valid drive\path, replace all instances of c:\temp
     with a valid drive\path.
  
  PRESERVE.
  SET TVARS NAMES.
  
  *first OMS command just suppresses Viewer output.
  OMS /DESTINATION VIEWER=NO /TAG='suppressall'.
  
  *select regression coefficients tables and write to data file.
  OMS /SELECT TABLES
      /IF COMMANDS=['Regression'] SUBTYPES=['Coefficients']
      /DESTINATION FORMAT=SAV OUTFILE='c:\temp\temp.sav'
     /COLUMNS DIMNAMES=[ 'Variables'  'Statistics']
     /TAG='reg_coeff'.
  
  *define a macro to draw samples with replacement and
   run Regression commands.
  DEFINE regression_bootstrap (samples=!TOKENS(1)
                                       /depvar=!TOKENS(1)
                                       /indvars=!CMDEND)
  
  COMPUTE dummyvar=1.
  AGGREGATE
    /OUTFILE = * MODE = ADDVARIABLES
    /BREAK=dummyvar
    /filesize=N.
  !DO !other=1 !TO !samples
  SET SEED RANDOM.
  WEIGHT OFF.
  FILTER OFF.
  DO IF $casenum=1.
  - COMPUTE #samplesize=filesize.
  - COMPUTE #filesize=filesize.
  END IF.
  DO IF (#samplesize>0 and #filesize>0).
  - COMPUTE sampleWeight=rv.binom(#samplesize, 1/#filesize).
  - COMPUTE #samplesize=#samplesize-sampleWeight.
  - COMPUTE #filesize=#filesize-1.
  ELSE.
  - COMPUTE sampleWeight=0.
  END IF.
  WEIGHT BY sampleWeight.
  FILTER BY sampleWeight.
  REGRESSION
    /STATISTICS COEFF
    /DEPENDENT !depvar
    /METHOD=ENTER !indvars.
  !DOEND
  !ENDDEFINE.
  
  g***insert any valid path\data file name***.
  GET FILE='c:\Program Files\SPSS13\Employee data.sav'.
  
  ***Call the macro, and specify number of samples,
     dependent variable, and independent variables.
  regression_bootstrap
     samples=100
     depvar=salary
     indvars=salbegin  jobtime .
  
  OMSEND.
  
  GET FILE 'c:\temp\temp.sav'.
  
  FREQUENCIES
    VARIABLES=salbegin_B salbegin_Beta jobtime_B jobtime_Beta
    /FORMAT NOTABLE
    /PERCENTILES= 2.5 97.5
    /HISTOGRAM NORMAL.
  
  RESTORE.
  




Bibliography

• Cirincione, C. and G. A. Gurrieri (1997). Research methodology: Computer intensive methods in the social iences. Social Science Computer Review, Vol. 15, No. 1: 83-97. A good overview of resampling and related methods.

• Efron, Bradley (1982). The jackknife, the bootstrap, and other resampling plans. SIAM. This is the classic reference.

Copyright 1998, 2008 by G. David Garson.
Last updated 3/29//08.