calculation of sample size for qualitative variables

8/3/2019 Calculation of Sample Size for Qualitative Variables

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CALCULATION OF SAMPLE SIZE FOR QUALITATIVE VARIABLES

Calculation of sample size is important because the results obtained from the sample are

to be applied to the whole population. If there is an error in calculating the sample size, it affects

the entire results. Therefore, while calculating sample size investigator should take proper care.

For calculation of sample size for estimate of qualitative variables the investigator should

be provided with the following information on the basis of which the investigator can calculate

sample size.

1. The investigator should be provided with possible presence of test positive animal or should

have rough idea about the prevalence of disease in population, such an idea or base about the

causative reactor of disease is called as P hat represented by symbol P^, while using this P hat

in statistical calculation, it is always written in 0 to 1 frequency.

2 The confidence level should be given to investigator because formulae are different for

preparation of sample size for qualitative variable at 95% and 99% confidence level.3 The investigator should be provided with allowable error (required precision) in the result. It is

represented by L. In statistical calculation, The allowable error to be used in 0 to 1 frequency.

Formula for calculation of sample size at 95% confidence level

n = 4PQ

L2

Where P = approximate prevalence

Q = 1- P

For 95% confidence level, Z = 1.96, and therefore 4; which is approximate

square of Z is taken

L = Allowable error (required precision)

Formula for calculation of sample size at 99% confidence level

n = 6.6PQ

L2

If the required sample size is actually more as compared to actual population then in such case,

sample size can be corrected by using reciprocal of

1 = 1 + 1

n n* N

Where, n = required sample size to be calculated for animal population

n* = calculated sample size

N = Population size


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Example calculation no. 1:

Available incidence suggest that 30% of the cow population having positive antibody

titre against enzootic bovine leucosis. Also assume that the investigator would like to survey the

estimate within 6% allowable error. Calculate the sample size for both the confidence level of

95% and 99%.

P = positive Ab titre

100 (cow population)

P = 30

100

= 0.30

Q = (1 - P) = (1 - 0.30) = 0.70

L

2

= 6100

= 0.06

a. At 95% confidence level:n = 4 PQ

L2

= 40.30.7

(0.06)2

= 0.84

0.0036 = 233Approximately 233 cows would be needed for survey.

b. At 99% confidence leveln = 6.6 PQ

L2

= 6.6 0.3 0.7

(0.06)2

= 385

Approximately 385 cows would be needed for survey.

If N = 150, calculate the corrected sample size at 95% and 99% confidence level

1 / n = 233 (at 95% level)

1 / N = 150

1 = 1 + 1

n n* N

= 1/ 233 + 1 / 150

= 0.004291 + 0.006666


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1/n = 0.01095

n = 91.3242

The required sample size is approximately 91 animals.

1 / n = 385 (at 99% level)

1 / N = 150

1 = 1 + 1

n n* N

= 1/ 385+ 1 / 150

= 0.0025 + 0.0066

1/n = 0.009197

n = 108.73

The required sample size is approximately 108 animals.

Exercise no. 1:According to one survey, prevalence of Hypophosphatemia in buffaloes of Marathwada

region is 15%. The investigator wants prevalence to be within 5% of true level (allowable error).

Calculate the sample size for both 95% and 99% confidence level.

P = 15

100

= 0.15

Q = (1 - P) = (1 - 0.15) = 0.85

L2= 5

100= 0.05

c. At 95% confidence level:n = 4 PQ

L2

= 40.150.85

(0.05)2

= 0.51

0.0025 = 204

Approximately 204 buffaloes would be needed for survey.

d. At 99% confidence leveln = 6.6 PQ

L2

= 6.6 0.15 0.85

(0.05)2

= 336.6 = 337

Approximately 337 cows would be needed for survey.


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Exercise no. 2:

A survey is to be carried out to investigate prevalence of dog erythrocytic Antigen (DEA

1.1) in Parbhani canine population. An earlier survey indicated that the prevalence of this

antigen in Chennai was 40%. The allowable error is 1%. Calculate sample size for both 95% and

99% level of confidence.


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Exercise no. 3:

Prevalence of Canine Parvo virus gastroenteritis in Parbhani city is known to be around

0.5%. The investigator wants to be within 10% of true level. Find out the sample size for 99%

confidence level. If the dog population of the city is 75,000. What will be sample size.


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calculation of sample size for qualitative variables

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