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Determining a Sample Size when population is known
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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