Question

What are methods which a statistician might use to ensure Random sampling?

Come up with a couple of these via researching the internet, and list the benefits and the possible problems of each.

Answer 1

Proper care must be exercised to ensure that the sample drawn is random and therefore, representative of the population.

A random sample may be selected by:

1)Lottery Method

2)Use of Table Of Random Numbers

Lottery Method:

• The simplest method of drawing a random sample is the lottery system. This consist in identifying each and every member or unit of the population with distinct number which is recorded on a slip or a card.
• These slips should be as homogeneous as possible in shape,size,color,etc., to avoid the bias.
• If the population is small, then these slips are put in a bag and thoroughly shuffled and then as many slips as units needed in the sample are drawn one by one.
• For example: let us suppose that we want to draw a random sample of 10 individuals from a population of 100 individuals. We assign the numbers 1 to 100, one number to each individual of the population a d prepare 100 identical slips bearing the numbers from 1 to 100.

These slips are then placed in a bag or container and shuffled thoroughly. Finally, a sample of 10 slips is drawn out one by one. The individuals bearing the numbers on these selected slips will constitute the desired sample.

Use of Table of Random Numbers:

• The lottery method described above is quite time consuming and cumbersome to use if the population to be sampled is sufficiently large.
• Moreover,in this method, it is not humanly possible to makr all the slips exactly alike and as such some bias is likely to be introduced.
• Statisticians have avoid this difficulty by considering the random smapling number series.Most of these series are the results of actual sampling operations recorded for future use.

The most practical amd inexpensive method of selecting a random sample consiat in the use of "Random Number Tables " which have been so constucted that rach of the digits 0,1,2,....9 appers with approximately the same frequency and independent of each other. If we have to select a sample from population of size N(<=99), N<=999 and so on.

The method of drawing a random sample comprises the following steps:

1. identify N units in the population with the numbers 1 to N.
2. Select at random, any page of the randomnumber table and pick up the numbers in any row or column or diagonal at random.
3. The population units corresponding to the numbers selected in step 2 constitute the random sample.