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
N 1 Ne
n = minimum sample size N = population size e = margin of error due to sampling (0.05 or 0.025 or 0.10)
2
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
n
N 1 Ne
2
5000 1 (5000 )( 0.05 )
2
5000 1 12 .5
5000 13 .5
370 .37
370
n
Nz 2 p (1 p) 2
Nd
2
z
p (1 p)
n = sample size N = population size p = 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)
Letting the proportion of getting a good sample and proportion of getting a poor sample equal 0.50, then the formula becomes
n
(0.25 ) Nz 2 Nd 2 (0.25 ) z 2
n = sample size N = population size p = 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)
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)
n
n
(0.25 )( 5000 )(1.96 ) 2 (5000 )( 0.05 )
4802 13.4604
2
(0.25 )(1.96 )
356.75 357
2
4802 12 .5 0.9604
Slovin’s
n
Formula
N 1 Ne
N = Population Size n = sample size e = margin of error (0.10, 0.05, or 0.01)
2
Lynch et. al Formula
n
(0.25 ) NZ 2 2
Nd (0.25 ) Z
2
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 size n = sample size
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
11,855,975
CAR
727,509
889,178
1,616,687
CALABARZON
5,296,117
7,313,686
12,609,803
MIMAROPA
1,235,101
1,509,570
2,744,671
CENTRAL LUZON
4,561,982
5,575,755
10,137,737
