European Journal of Scientific Research - EuroJournals

Determination of Sample Size 322
sample sizes remains widespread (Halpern, Karlawish & Berlin, 2002). So Rosner, (2000) described
some Practical Consequences of Mathematical Properties.
2.5. Power Analysis
In sample size calculations, appropriate values for the smallest meaningful difference and the estimated
SD are often difficult to obtain. In this case, power refers to the sensitivity of the study to enable
detection of a statistically significant difference of the magnitude observed in the study. This activity,
known as retrospective power analysis, is sometimes performed to aid in the interpretation of the
statistical results of a study. If the results were not statistically significant, the investigator might
explain the result as being due to a low power. So a lot of work is available in literature on power
analysis by Detsky & Sackett (1985); Lubin & Gail (1990); Roebruck & Kuhn (1995); Thomas (1997);
Castelloe (2000); Lenth (2001); Hoenig & Heisey (2001); Feiveson (2002).
3. Cost Function and Degree of Affordable Error
In this section, some new formulae for estimating sample size by changing affordable error in cost
function have been developed.
Let us have a cost function
C C0
C1n
+ =
Where ‘ C ’ is total cost, C 0 is overhead cost and C 1 is cost per unit.
2
Further suppose that the affordable error is of the form ε ( y − Y )
The expected loss for a sample of size ‘n’ will be:
2
S ( n)
= E[
C]
+ E ε ( y − Y )
2
εS
S(
n)
= C0
+ C1n
+
n
2
2 S
Where E(
y − Y ) =
n
After partially differentiating S (n) with respect to ‘n’ we can get:
2
1/
2
1 ⎟⎟
⎛ εS
⎞
n = ⎜
⎝ C ⎠
Similarly if error function is changed to ε y − Y with the similar cost function, then sample
size can be determined as:
⎛ 2εS
⎞
n = ⎜
5 ⎟
⎝ C1
⎠
2 / 3
Acknowledgements
The authors would like to thank Prof. Dr. Khalid Aftab, Vice Chancellor GCU for his anonymous
support behind all the research activities in GC University, Lahore (Pakistan).