Overview of Taro Yamane Formula
The Taro Yamane Formula was formulated by an American-Japanese economist known as Taro Yamane in 1967. It is statistically used to determine a finite population in research methodology. A finite population is a population whose size can be determined.
The formula is majorly used to determine the sample size from a heterogynous population.
When to Use the Taro Yamane Formula
You can use the formula only when the population is known (i.e. finite), and it is also used to determine the sample size from a heterogynous population, that is, the individuals or items used in the study are different from one another.
The Taro Yamane Formula
The Merit of the Taro Yamane Formula Compared to Other Methods of Sample Size Determination.
- The formula gives a reasonable amount of sample that can be studied in a population
- It is simple to use in determining sample size compared to other methods of sample size determination.
- It is the most widely used formula for determining sample size compared to other methods.
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Working Examples
Example 1
A researcher is researching the topic “Utilization of Community-Based Resources for Funding Agricultural Education Programme in Higher Institutions in North Central, Nigeria. The study population consists of 2334 individuals, including Lecturers and Students from all the Universities offering Agricultural Education Programme in Higher Institutions in North Central, Nigeria. The researcher desires to test the hypotheses at a 0.05 level of significance, (95 % probability that the sample is distributed in the same way as the population). Calculate the perfect sample size that the researcher can study using the Yamane Formula.
N= N
1+N (E) 2
Where:
N=the sample size
N=the finite population
E= Status of significance
1= unite (a constant value)
Solution
The population is 2334 and
E the status of significance is 0.05
n= 2334/
1+2334(0.05)2
=2334/
1+2334(0.0025)
Note: to get 0.0025, you have to square (0.05)2 or multiply 0.05 by 0.05 to get 0.0025
2334
1+2334(0.0025) =5.835
Multiply 2334 by 0.0025
2334/
1+5.834
Add 1 to 5.834 to 6.835
2334/
6.835
Divide 2335 by 6.835
= 341.4
This means that if your population is 2334, then you can sample 341 out of 2334. The 341 sampled are adequate to represent the entire population based on the formula.
Working Example 2
A researcher is conducting a study on the topic “Assessment of Teacher Methodology on Students Interest and Academic Achievement in Senior Secondary School Chemistry Students in Delta State, Nigeria. The population for the study is 1205, consisting of Chemistry Teachers and Chemistry Students from all Secondary Schools offering Chemistry in Delta State. The researcher wishes to test the hypotheses at a 0.05 level of significance, (i.e. 95 % likelihood that the sample is distributed in the same way as the population). Determine the ideal sample size that can be studied using the Yamane Formula.
N = N
1+N (E) 2
Where:
N=the sample size
N=the finite population
e= status of significance
1=unite (a constant value)
Solution
The population is 1205 and
E the status of significance is 0.05
n= 1205/
1+1205 (0.05)2
=1205/
1+1205 (0.0025)
Note: to get 0.0025, you have to square (0.05)2 or multiply 0.05 by 0.05 to get 0.0025
1205/
1+1205 (0.0025) =3.013
Multiply 1205 by 0.0025
1205/
1+3.013
Add 1 to 3.013 to 4.013
1205/
4.013
Divide 1205 by 4.013
= 300.3
This means that, if your population is 1205, you can sample 300 out of the 1205. The 300 sampled are satisfactory in representing the absolute population based on the formula.
Working Example 3
A researcher is interested in investigating the effectiveness of teaching technical drawings by comparing the 3rd angle projection and 1st angle projection for effective academic achievement in technical schools at Delta State, Nigeria. The study is made up of both the experimental and control groups with a total population of 1532 participants. The researcher wishes to test the hypotheses at a 0.05 level of significance, which means a 95 % chance that the sample will be distributed in the same way as the population. Find the ideal sample size for the study using the Taro Yamane Formula.
N= N
1+N (E) 2
Where:
N =the sample size
N=the finite population
E= status of significance
1=unite (a constant value)
Solution
The population is 1532 and
E the level or status of significance is 0.05
n= 1532/
1+1532 (0.05)2
=1532/
1+1532 (0.0025)
Note: to get 0.0025, you have to square (0.05)2 or multiply 0.05 by 0.05 to get 0.0025
1532/
1+1532 (0.0025) =3.83
Multiply 1532 by 0.0025 to get 3.83
1532/
1+3.83
Add 1 to 3.83 to 4.83
1532/
4.83
Divide 1532 by 4.83
= 317.1
This means that, if your population is 1532, you can sample 317 individuals out of 1532, which is sufficient to represent the entire population of the study.
References
Emaikwu, S.O (2013) Fundamentals of Research Methodology and Statistics. Kaduna, Datura Publishing Company LTD Nigeria.