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Chapter 3

Fundamentals of Statistical

Studies

Definition of Statistics

• Statistics is the study of variation, interactions

and, operational definitions.

• Statistics is the study of data to provide a

basis for action on a population or process.

Enumerative Studies

• Basic Concepts

• A population (or universe ) is the totality of units,

items, or people of interest that exist in a given

time period and/or given location Administration.

• A frame is a list of the items in a population.
• The gap is the difference between the frame and

the population.

• A sample is a portion of the frame under

investigation, and is selected so that information

can be drawn from it about the frame.

• Basic Concepts
  • Nonrandom samples are selected on the basis of

convenience ( convenience sample ), the opinion

of an expert ( judgment sample ), or a quota to

ensure proportional representation of certain

classes of items, units, or people in the sample

( quota sample ).

• All nonrandom samples have the same shortcoming they're subject to an unknown degree of bias in their results.
• This bias is caused by the absence of a frame.
• Nonrandom samples should be used only when better information is too costly to obtain.

• Seven steps are involved in selecting a simple random sample: - Step 1. Count the number of elements in the frame, N. - Step 2. Number the elements in the frame from 1 through N. If N is 25, then the elements in the frame should be numbered from 01 through 25. All elements must receive an identification number with the same number of digits.

• Step 3. Select a page in a table of random numbers. For example, selecting a page and starting point yields.

• Step 5. Determine the necessary sample size.
• Step 6. From the chosen column on the selected page, select the first six two-digit numbers between 01 and 25, inclusive. If a number is encountered that is smaller than 01 (e.g., 00) or larger than 25 (e.g., 31), ignore the number and continue down the column. If an acceptable number appears more than once, ignore every repetition and continue moving down the column until six unique numbers between 01 and 25 have been selected. If the bottom of the page is reached before six unique random numbers are obtained, go to the top of the page and move down the next two-digit column.
• Step 7. Finally, analyze the information as a basis for action.

• Two important points to remember are:

1. different methods of measurement will also

yield different results.

2. different samples of size six will yield different

results, and

• Random samples, however, don't have

bias, and the sampling error can be held

to known limits by increasing the sample

size.

• Step 1. Specify the reason(s) you want

to conduct the study (for example, to

estimate the average number of sick

days per employee in the XYZ

Company in 2002). If this average is

greater than 8.0 days, then a new

health care plan will be instituted. If it is

less than or equal to 8.0 days, the

current plan will be maintained.

• Step 2. Specify the population to be

studied. In our example, the population

would be all full-time employees in the XYZ

Company in 2002. An employee is considered full-time in 2001 if he had full-

time status designation at any time during the year.

Step 4. Perform secondary research

(such as the examination of pre-

published data) to determine how much

information is already available about

the problem under investigation. For

example, check the Human Resources

Department's records.

Step 5. Determine the type of study to be

conducted (for example, mail survey,

personal interviews, analysis of units).

In this example, we would analyze

employee absentee cards for 2002.

Step 7. Establish the sampling plan to be

used, determine the amount of

allowable error in the results, and

calculate the cost of the sampling plan.

At this stage, Steps 1 and 2 may need

revisions due to cost considerations.

For example, we may decide to draw a

simple random sample of employee

absentee cards using random numbers,

at a cost of $1 per card, assuming an

allowable error of one quarter of a day

in the estimate.

Step 7 requires a random sample. The

result of a nonrandom sample in an

enumerative study is worth no more

than the reputation of the person who

signs the report.