Sampling Technique and Determining Sample Size

SAMPLING - is a process or procedure of taking samples from a population

Probability Sampling – is a random sampling technique that each element in a population has an equal chance of being selected.

Non-probability Sampling – is a non-random sampling technique that each element in a population has no equal chance of being selected.

How big should the sample size be?

A sample should be big enough to answer the research question, but not so big that the process of sampling becomes expensive.

Too big a sample does not increase the precision of testing your question beyond costs and trouble incurred in getting that size sample.

An important consideration in conducting research is the size of your sample. It must be large enough so that erratic or inconsistent behavior of very small samples will not produce misleading results.

A large sample is not necessarily a good sample. Although it is important to have a sample that is sufficiently large, it is more important to have a sample in which the respondents have been chosen in an appropriate way, such as random selection.

Use a sample size large enough so that we can see the true nature of any effects or phenomena, and obtain the sample using an appropriate method, such as one based on randomness.

Stratified Sampling – entails subdividing the population according to a certain characteristic, then selecting the samples from every subgroup or stratum.

This is resorted to when it is important to get response per subgroup or stratum.

It is useful if there is a need to differentiate the characteristics of a heterogeneous population and the elements or respondents are geographically concentrated in a given area

n = minimum sample size

N = population size

e = margin of error due to sampling

(0.05 or 0.025 or 0.10)

21 Ne

Nn

Find a minimum sample n if a population size N is 5000 with a margin of error due to sampling of 5%.

Given : N = 5000 e = 5% = 0.05

37037.3705.13

5000

5.121

5000

)05.0)(5000(1

5000

1 22

Ne

Nn

n = sample sizeN = population sizep = 0.50 (proportion of getting a good sample) 1 – p = 0.50 (proportion of getting a poor sample)d = 0.025 or 0.05 or 0.10 (your choice of sampling error) Z = 1.96 (95% reliability in obtaining the sample size)2.33 (99% reliability in obtaining the sample size)

)1(

)1(22

2

ppzNd

ppNzn

Letting the proportion of getting a good sample and proportion of getting a poor sample equal 0.50, then the formula becomes

n = sample sizeN = population sizep = 0.50 (proportion of getting a good sample) 1 – p = 0.50 (proportion of getting a poor sample)d = 0.025 or 0.05 or 0.10 (your choice of sampling error) Z = 1.96 (95% reliability in obtaining the sample size) 2.33 (99% reliability in obtaining the sample size)

22

2

)25.0(

)25.0(

zNd

Nzn

Find a minimum sample n if a population size N is 5000 with a margin of error due to sampling of 5% and a 95% reliability in obtaining the sample size.

Given: N = 5000 d = 5% = 0.05

z = 1.96 (95% reliability)

9604.05.12

4802

)96.1)(25.0()05.0)(5000(

)96.1)(5000)(25.0(22

2

n

35775.3564604.13

4802n

Slovin’s Formula Lynch et. al Formula

N = Population Sizen = sample sizee = margin of error (0.10, 0.05, or 0.01)

Z = value of the normal variable for a reliability level Z = 1.645 (90% reliability in obtaining the sample size)) Z = 1.96 (95% reliability in obtaining the sample size) Z = 2.33 (99% reliability in obtaining the sample size)p = 0.50 (proportion of getting a good sample)(1 – p) = 0.50 (proportion of getting a poor sample)d = 0.01, 0.025, 0.05, or 0.10 (choice of sampling error) N = population sizen = sample size

21 Ne

Nn

22

2

)25.0(

)25.0(

ZNd

NZn

Table 1 shows the total population from 5 selected provinces in Luzon (2010). Find the sample size for each province/district using:

(a) Slovin’s Formula with 5% margin of error due to sampling (b) Lynch et al. with 5% margin of error due to sampling and a 95%

reliability in obtaining the sample size.

Province/District Total

NCR 11,855,975

CAR 1,616,687

CALABARZON 12,609,803

MIMAROPA 2,744,671

CENTRAL LUZON 10,137,737

Overall Total N = 38,964,873

Table 2 shows the total population by sex from 5 selected districts/provinces in Khon Kaen. Find the sample size by sex for each province/district using:

(a) Slovin’s Formula with 5% margin of error due to sampling (b) Lynch et al. with 5% margin of error due to sampling and a 95%

reliability in obtaining the sample size.

  Sex  Province/District Male Female Row Total

NCR 4,742,390 7,113,585 11,855,975CAR 727,509 889,178 1,616,687CALABARZON 5,296,117 7,313,686 12,609,803MIMAROPA 1,235,101 1,509,570 2,744,671CENTRAL LUZON 4,561,982 5,575,755 10,137,737

Column Total 16,563,099 22,401,774 N = 38,964,873