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SAMPLE SIZE AND SAMPLING TECHNIQUE
January 13, 2023
DETERMINATION OF SAMPLE SIZE
The sample size is the number of individuals included in the research to represent the population of the study. Because the population of the study may sometimes be large, it might be difficult to collect data from; you will need to reduce the size of the population so it will be easy to collect data conveniently. The sample is a fraction (a part) of the population drawn as a sample to represent the entire population. The number arrived at (sample size) represents your total respondents (people whom you will eventually administer questionnaires to, interview or observe).
Note: If the sample size is too small it could affect the result of your study negatively (this means that your result may not be valid). Also, if your sample size is too large it could increase the cost of carrying out your study, especially during data collection.
There are several ways of determining a sample size in research. But the easiest method is with the use of the Taro Yamane Formula.
What is Taro Yamane Formula?
The Taro Yamane formula is a statistical sampling technique that is used to determine sample sizes in research methodology. It helps to improve the accuracy level in determining the chunk of a population to sample at a reasonable margin of error. It is used to arrive at an appropriate sample size in qualitative and quantitative research.
Brief History of Taro Yamane
Taro Yamane formula was invented by Dr. Taro Yamane in the early 1960s, the purpose of creating the formula was to easily and quickly ascertain the sample sizes of populations in academic research. Dr Taro Yamane was a renowned statistician and Economist who had in his lifetime published statistics books, mathematics and economic sampling theories for students and researchers. Taro Yamane formula was first introduced for social science research and market research and later to general academic research in late 1973. It is widely accepted and used by a variety of scholars globally.
In determining the appropriate sample size, the Taro Yamane formula takes into cognizance the total population size and level of significance.
We will learn how to determine a sample size using the Taro Yamane formula from the illustrations below;
Taro Yamane formula is n = N/1+N(e)2
Where; n represents the sample size
N represents the total population
e represents the level of significance
1 represents a constant value
How to Apply the Taro Yamane Method in Research
To start with, you need to do three (3) steps namely;
- Determine the individual population size
- Determine the level of significance
- Apply Taro Yamane formula
Step 1: Let’s assume the following estimated population for parents, teachers, supervisors and students, and itemize the same below.
| CATEGORY | ESTIMATED POPULATION SIZE | |
| 1 | Parents | 1,800 |
| 2 | Teachers | 145 |
| 3 | Supervisors | 65 |
| 4 | Students | 4,700 |
| Total | 6,710 |
Step 2. The level of significance is also referred to as the error limit. Statistics can never be 100 per cent accurate, so in studying a large population there is a need to adopt a margin of error. This is the measurement of statistical significance. It tells the percentage of confidence in a study (i.e., how confident you are with the results of your study). It shows the level of risk associated with a study. Studies with less than 90% level of confidence may not be considered accurate in research.
A 5% (0.05) level of significance is very safe to use. If you adopt a 5% significance level, it means that the p-value is less than 0.05, meaning that out of 100%, you have a confidence level of 95% while there is just a 5% possible error in your research.
Let’s use a 0.05 (5%) level of significance.
Step 3. Determining the sample size of parents.
n = N/1+N(e)2
n =?
N = 1,800
e = 5/100 = 0.05
Therefore:
1,800/1+1,800(0.0025)
= 1,800/5.5
n = 327.3
The sample size is therefore 327 (this represents the number of questionnaires that will be administered to respondents).
The calculations for each population in the categories (i.e. parents, teachers, supervisors, and students) should be done. The final figures arrived at have to be rounded up. When this is done, the following sample sizes will be obtained; 327, 106, 56, and 369 (see “determination of sample size of parent” as an example to calculate the other population).
After calculating for each population, you will arrive at the following sample sizes;
| S/N | POPULATION CATEGORY | SAMPLE SIZE |
| 1 | Parents | 327 |
| 2 | Teachers | 106 |
| 3 | Supervisors | 56 |
| 4 | Students | 369 |
| Total | 858 |
Sample Size Obtained from Use of Taro Yamane Formula.
Comprehensive table showing the category, estimated population and sample size after computation to obtain the sample size from the Taro Yamane Formula.
|
|
Category |
Estimated Population Size |
Sample Size |
|
1 |
Parents |
1,800 |
327 |
|
2 |
Teachers |
145 |
106 |
|
3 |
Supervisor |
65 |
56 |
|
4 |
Student |
4,700 |
369 |
|
|
Total |
6,710 |
858 |
6,710 represents the Estimated Population
858 represents the Sample Sizes
Having reduced the total population from 6,710 to 858 with the Taro Yamane Formula, Chapter four of your project which deals with Data Analysis will now rely on the information collected from the 858 respondents.
Taro Yamane Formula Example 2
There are several ways of presenting Taro Yamane’s calculations, one of which includes the tabular format. This format helps the researcher assemble data in a simple table of about seven(7) rolls and a few columns of which the population of the study (also known as a category), the total estimated numbers and arithmetic are displayed and calculated to arrive at an acceptable sample size.
This is the easiest and most appreciated method of arriving at the sample size which is represented as “n” as shown in the table below. The “N” and “e” represent the total population and significance level respectively. At the end of the calculation, the sample sizes from each of the respondents which in this case are “land surveyors, engineers, builders, residents and landlords” are totalled to arrive at a grand total of the sample size.
As shown in the example below, the total population of the study is 10,402 while the sample size arrived at is 951 (the respondents that will provide data for the analysis in chapter 4 or 5 of a research paper).
Analysis of Computation of Estimated Population and Sample Sizes of the Study
|
S/N |
Category |
N |
(e)2 |
1+ N (e)2 |
N/1+ N (e)2 |
Sample Size (n) |
|
1 |
Land Surveyors |
56 |
0.0025 |
1.14 |
49.12 |
49 |
|
2 |
Engineers |
123 |
0.0025 |
1.31 |
93.89 |
94 |
|
3 |
Builders |
211 |
0.0025 |
1.53 |
137.91 |
138 |
|
4 |
Residents |
9,000 |
0.0025 |
23.5 |
382.98 |
383 |
|
5 |
Landlords |
1,012 |
0.0025 |
3.53 |
286.69 |
287 |
|
|
Total |
10,402 |
|
|
|
951 |
Summary of Population and Sample Sizes obtained from the example in the above table. This summary is necessary for easy presentation and reference during a study. It gives the ordinary man a clear picture of what the sample sizes from the selected population are like.
|
S/N |
Categories of the Population Adopted for the Study |
Estimated population of the Study |
Sample Sizes Obtained |
|
1 |
Land Surveyors |
56 |
49 |
|
2 |
Engineers |
123 |
94 |
|
3 |
Builders |
211 |
138 |
|
4 |
Residents |
9,000 |
383 |
|
5 |
Landlords |
1,012 |
278 |
|
|
Total |
10,402 |
951 |
Problems Associated With the Use of Taro Yamane Formula in Research
Although the Taro Yamane formula is accepted globally, there are still some arguments about the application of the formula in research. These arguments which have been in existence for years emanated to provide a more accurate result from an in-depth study.
- Some scholars think that the Taro Yamane formula appears simple which might impact the accuracy rate of results arrived at eventually. It is suggested that more sophisticated models should be invented to tackle advanced research endeavours.
- Since the Taro Yamane formula can be conveniently applied to all types of research irrespective of the diversity, some researchers are worried that the universality of the formula may not accurately represent the true outcome of heterogeneous data in a research exercise.
- Some researchers think that the formula adopts a fixed margin of error e.g. 5% when in the real sense a large population may require a higher margin of error.
- Because Taro Yamane relies solely on data inputted and applied in calculating an appropriate sample size, when figures are erroneously inputted, it could also affect the outcome of the result, meaning that the sample size arrived at may not be reliable at the end of the day.
- Some researchers also think that too much reliance on the Taro Yamane formula might discourage students from trying other formulas that produce similar or better results. It is suggested that other formulas should be tried to determine the sample sizes of specialized studies.
Why is Taro Yamane Important in Research?
The main advantages that the Taro Yamane formula enjoys over other methods or models include; ease of use, convenience, flexibility, accurate figures, universally accepted and used, providing a simplified formula, the formula is easy to remember and apply, being used in both qualitative and quantitative research among others.
In summary, it is important to note that Taro Yamane should be used only when the population of the study is known, a suitable level of significance is adopted and the sample size sought after is unknown.
for example;
population = XYZ
level of significance = xyz but,
sample size = ???
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2 Replies to “SAMPLE SIZE AND SAMPLING TECHNIQUE” .
This illustration ws very helpful. Thank you and God bless you
Thank you Temitope.