Selecting Samples with More than one Category

At times we need finer gradations than just days, for taking our sample. We may need to sample specific times in terms of hours and minutes. The program lets us do this without having to type in sixty minutes for every hour. In the example above we drew a sample of hours from 9am to 4pm. If we were trying to select times of day to the nearest minute we would need to complete each number by drawing a separate category of a number of minutes from zero to fifty nine (note that this means that the earliest time drawn would be 9:00am and the latest time that could be drawn is 4:59pm.) We could have just as easily decided to draw minutes from one to sixty, giving a range from 9:01am to 4:60 (i.e. 5:00pm) but that would produce some times, like 4:60, that required a second look to understand. What we must not do is to select minutes from zero to sixty. This selection would give even hours twice the chance of being selected of any other time, since an even hour could be drawn by selecting either zero (10:00) or sixty (9:60). Here our design has two categories:

   Category 1 -- Hour named 9am  10am  11am  12noon
          1pm  2pm  3pm  4pm
   Category 2 -- Minute numbered from 0 to 59

A sample based on this design will look like this:
Hour	9am	Minute 	8	
Hour	10am	Minute 	17	
Hour	10am	Minute 	29	
Hour	11am	Minute 	15	
Hour	11am	Minute 	56	
Hour	12noon	Minute 	36	
Hour	1pm	Minute 	11	
Hour	2pm	Minute 	38	
Hour	2pm	Minute 	47	
Hour	3pm	Minute 	1	
Hour	3pm	Minute 	58	
Hour	4pm	Minute 	30	


As you can see from the example above, when there is more than one category a single sample point consists of one selection from each category. In this example when the program selected a sample point it first randomly selected an hour and then randomly selected a number of minutes. The sample points were sorted after they were selected.

One of the limits of the program is that a number may not exceed 32,000. If you try to create the design:

Category 1 -- Big Stuff numbered from 0 to 70000

The program will simply refuse to accept the description. You can work around this by changing the design to:
Category 1 -- Thousands numbered from 0 to 70
Category 2 -- Hundreds numbered from 0 to 999

The program will accept this design. When the sample is drawn you will have to read numbers that look like:
Thousands    43        Hundreds    137

Which means draw item 43,137. You are particularly likely to have a need for this sort of design if you are sampling a large data base by sampling record numbers. This would be the case if you were picking your sample from an automated card catalog where your sample consisted of record numbers.



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