Participants of the Study

Presented byKent S. Paredes

Objectives: define and differentiate population, parameter, sample, statistic; arrive at a correct sample size.

Population a complete set of person or object that possess some common characteristics that are of interest to the researcher. There are two groups of population: Target Population and Accessible Population

Target Population

is composed of the entire group of people or objects to which the researchers wishes to generalize the findings of the study.

Accessible Population

is the specific study population.

Example: Which one is the Target Population?

All people with AIDS in the metropolitan St. Louis area

All people with AIDS.

Parameter

is a numeric characteristic of a population.

Sample is a subset of the entire population or a group or individuals that represents the population.

serves as the respondents of the study.

Statistic

is a numeric characteristic of a sample.

a single member of the sample is called an element.

Ways of Determining the Statistic of a Sample Size

the larger the sample, the more reliable is the result of the study.

Factors to Consider in Determining the Sample Size

1. Homogeneity of the Population the higher the degree of

homogeneity of the population, the smaller is the sample size that can be utilized.

2. Degree of Precision Desired by the Researcher

the larger the sample size, the higher is the precision or accuracy of result.

3. Types of Sampling Procedure

probability sampling utilizes smaller sample sizes than non-probability sampling.

Considerations in Determining the Sample Sizes

1. Sample sizes as small as 30 are generally adequate to ensure that the sampling distribution of the mean will approximate the normal curve (Shott, 1990).

One of the Properties in Sample Mean Distribution stated that, If the

population is not normally distributed, but the sample size is sufficiently large,

then the sample means will have an approximately normal distribution.

Some books define sufficiently large as at least 30 and others as at least 31.

2. When the total population is ≤ 100, this same number may serve as the sample size. This is called universal sampling.

3. The Slovin’s formula is used to compute for the sample size (Sevilla, 2003)

where:

n = a sample size

N = population size

E = desired margin of error2

Nn =

1 + NE

Example:The sample size of the population

is 8,000 at 2% margin of error.

2

Nn =

1 + NE

Solution:2

Nn =

1 + NE2

8,000 =

1 + 8,000(0.02)

8,000 =

1 + 8,000(0.0004)

8,000 =

1 + 3.2

8,000 =

4.2n = 1,905

4. According to Gay (1976), the following are the acceptable sizes for the different types of research:

Descriptive Research 10% - 20% may be required

Correlational Research 30 subjects or respondents

Comparative Research 15 subjects/group

Experimental Research 15-30 subjects per group

5. Using Calmorin’s formula

2

2

NV + [S + (1 - p)]S =

NS + [V + p(1 - p)]

ss

eS sample size

N population size

V standard value (2.58) of 1%

level of probability with 0.99 reliability

S sampling error

p = the largest possible proportion

s

e

Example:Getting statistic from a parameter

of 800, Sampling error of 1%, and largest possible proportion is 0.50

2

2

NV + [S + (1 - p)]S =

NS + [V + p(1 - p)]

ss

e

Solution

2

2

NV + [S + (1 - p)]S =

NS + [V + p(1 - p)]

ss

e

2

2

800(2.58) + [(0.01) + (1 - 0.50)] =

800(0.01) + [(2.58) + 0.50(1 - 0.50)]

2,064 + [0.0001 + 0.50] =

8 + [6.66 + 0.50(0.50)]

2,064 + [0.5001] =

8 + [6.66 + 0.25]

2,064.5001 =

8 + 6.91

2,064.5001 =

14.91

S = 138.46s

Thank You !