Taking Supplemental Samples

We have assumed in drawing our sample that we know exactly how big a particular population or subpopulation will be. But this is not always the case. For example, suppose that we want to sample books that are stored on shelves. The shelves have been numbered from 1 to 355 but each shelf may contain anywhere from five to thirty books. In this case we have to draw numbers that allow for the biggest possible population (number of books per shelf) and then throw away values that are too big. So we need to set up the sample to draw a shelf number and then a book number from one to thirty. If there are not as many books on a shelf as the book number drawn then the value is discarded. It would not be correct to continue counting onto the next shelf, since that would give books at the start of a shelf a greater chance of being selected. In this case, some of our original sample will be discarded, because the population (the exact number of books on a shelf) was not known so that we did not know the range of random numbers to be drawn.

Discarding values gives us problems when we are using an ordered list. We might decide to draw an extra big sample because we know that we will not get to use some numbers. This would be acceptable as long as we remember that when we are drawing from an ordered list we cannot stop just because we have as many data points as we would like To be sure of random selection, we have to include all items on the list.

Another, perhaps better, way of dealing with this problem is to draw several small supplemental samples of say five or ten percent of the sample size. After collecting data from our main sample we would count how many more books need to be drawn and then draw a supplemental sample of that size or perhaps a bit larger. Since the supplemental sample, like the main sample, must give every unselected item an equal chance of being selected, the use of supplemental samples adds the requirement that we make sure the same book is not selected in both samples. The program will take care of this for us if we follow the correct steps.

If we think we may want to draw a supplemental sample we need to select the choice menu before drawing the sample. In practice it is probably best always to retain the raw sample. To do so only uses up some extra disk space for the raw file. This file can always be deleted later if we don't need it. We then select item r "-- retain the raw sample ..." from the choice menu. The program then lets us name the file and describe it.

   What do you want to call the raw sample file?

We might decide to call the file "Raw1 Book Study." (obviously this is a Macintosh name not an IBM name) The program then lets us save a description of this file by prompting:
   You may enter up to two lines to describe this design

We might type "A study of books on the shelves of our library" and the press the return key. If we have no need for a second line, we press return again.
                            SET THE CHOICES
   The following options may be set or changed by typing the letter
   s -- sort the sample when it is drawn
                     the sample will be sorted
   p -- print the sample as it is generated.
                     the sample will not be printed.
   t -- save the sample to a file for use in other programs.
                  the sample will be saved in a file named Book Study 1
   d -- draw a supplemental sample
                     a supplemental sample is not being drawn.
   r -- retain the raw sample in case a supplement is needed.
                   the raw sample will be retained in the file Raw1 Book Study 
   To quit this menu just press return.

The entry for option r in the choice menu has changed to show that the raw file will be saved. The t option shows that we are saving the sample in a file called Book Study 1. We now go ahead and draw the sample by choosing p from the main menu. When the sample is complete the program will give us a message indicating that the raw file has been saved.
   Results saved for other uses in Book Study 1
   Save of Raw1 Book Study completed.

To draw a supplemental sample, we again return to the choice menu, this time using the command d. The program asks:
   Enter a name of the raw file to be supplemented.

We respond with the name of the raw file created above. In this case we would type "Raw1 Book Study." This step restores the sample design that was used for the original sample so that we do not need to type the sample description again. It also repeats the descriptive lines that we entered when the file was created.
   A study of books on the shelves in our library

   Category 1 -- Shelf numbered from 1 to 938
   Category 2 -- Book numbered from 1 to 60

The following example shows what the choice menu would look like if, when the initial sample had been drawn, the raw sample was retained in a file called Raw File 1. This file is specified as the source in option d. We have also asked that a new raw file, incorporating both the original sample and the supplement be saved as Raw File 2 in case we should need an additional supplement. Remember, if you create a new raw file while drawing a supplemental sample, it supersedes the old raw file. For any sampling study, you need keep only the most recently created raw file. You might want to throw the others away to prevent confusion Note that we have specified that the supplemental sample be stored for use in the file Sample Two.
                           SET THE CHOICES
   The following options may be set or changed by typing the letter
   s -- sort the sample when it is drawn
                     the sample will be sorted
   p -- print the sample as it is generated.
                     the sample will not be printed.
   t -- save the sample to a file for use in other programs.
                  the sample will be saved in a file named Sample Two
   d -- draw a supplemental sample
                   a supplemental sample is being drawn using Raw1 Book Study
   r -- retain the raw sample in case a supplement is needed.
                   the raw sample will be retained in the file Raw File 2 
   To quit this menu just press return.



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