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.

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 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

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.

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.

1. 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.
2. 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.
3. 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.
4. 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.
5. 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 = ???

Sampling Techniques in Research

What are Sampling Techniques

Sampling techniques involve an in-depth study of a population by collecting accurate data and analyzing the said data gathered in a study. It is also known as the sampling method in research.

The sampling technique is divided into two categories which are probability and non-probability sampling techniques. The probability sampling technique is a process where every unit in the population of a study has a chance of being chosen in the sample while the non-probability sampling technique is a method where the units in the population do not all have equal chances of being selected in a sample, it is the reverse of the probability sampling technique in research.

Types of Sampling Techniques (Methods)

The various types of sampling techniques are explained below for clarity.

Probability Sampling:

Examples of probability sampling techniques include simple random sampling, systematic sampling, cluster sampling, stratified sampling and multistage sampling techniques.

Simple Random Sampling

The sampling approach is more suited for tiny, homogeneous populations that are easily accessible. Every subset within the frame has an equal chance of getting chosen. A random process is used to choose elements from a sampling frame, and each element is assigned a unique identification number. A lottery system, a table of random numbers, or other comparable methods may be employed to choose which units are chosen. The sampling method’s simplicity of comprehension is one of its main appealing aspects. The majority of methods for statistical analysis and inference assume that the data were gathered using a straightforward random sampling technique.

Nonetheless, the strategy is not impervious to certain obstacles. First, it might not be possible to create a sample frame that permits a simple random sampling for a variety of practical reasons. It may result in longer data collection times and higher costs, particularly if the study population is dispersed over wide geographic areas. When compared to other probabilistic sampling techniques, the sampling may produce findings that are less accurate and have higher standard errors. If representativeness is applied to a more diverse population, it might not be guaranteed.

Systematic Sampling

Systematic sampling depends on organizing the target population using an ordering scheme, choosing a random starting point, and then choosing further elements at predetermined sampling intervals from that ordered list. By dividing the intended sample size (n) by the entire population size (N) and rounding to the next whole integer, one can get the sampling interval. Assume, for instance, that a study aims to choose a sample of fifty out of five hundred people or components in a given population. In this instance, the sample interval (k=N/n) is 100. More specifically, a systematic sampling involves the following procedures.

Procedures:

1. Assign a number from 1 to N to each population unit.
2. Ascertain the necessary sample size.
3. Choose an interval size (k = N/n = 10) based on the preceding example.
4. Choose an integer at random from 1 to k-5.
5. Take every kth unit at the end.

Assuming that the second element is chosen at random, the 12th, 20th, and so on will be the elements that are chosen until all 50 samples have been used. With equal and known chances of selection, this sampling strategy is comparable to simple random sampling. It differs from simple random sampling, though, in that only the maximum allowable sample size (n) has an equal and known probability of being chosen. The order of the other components to be included in the sample is predetermined after the first element from the first k interval is chosen.

Because random selection is done just once, the method is simpler and less expensive than basic random sampling. Moreover, it permits the uniform distribution of samples across the whole reference population. The drawbacks include the possibility of biased sampling in cases where selection and hidden periodicity in the population occur at the same time. Evaluation of the accuracy of an estimate based on a single survey may also be challenging.

Stratified Sampling

This sampling method is suitable in situations where the population is made up of several different categories that can be grouped into several strata. After that, a separate sub-population of each stratum is sampled, from which individual components may be chosen at random. Sub-populations are non-overlapping groups, or strata, on which elements within a given sub-group are relatively homogeneous, whereas elements from distinct sub-populations exhibit heterogeneity. Stratification is frequently based on several criteria, such as socioeconomic and demographic traits, producer and consumer types, firm size, degree of vulnerability to environmental degradation, and so forth. While the researcher can choose how many strata to use, it is best to stick to no more than six because any additional expenditures related to stratification and sampling could negate any gains in precision. More generally, the study can guarantee that every distinct group within the population is represented in the sample by using stratified sampling. How proportionate or disproportionate the sampling is a crucial choice that must be made when using stratified sampling. Generally speaking, a larger stratum should have more items chosen from it. To improve precision, additional samples from strata with bigger standard errors should be obtained. Stratified sampling approaches are frequently used in socio-economic research as they can combine features of simple random sampling with possible gains in precision.

Cluster Sampling

Cluster sampling is a two-stage sampling example. Using a probability sampling technique like simple random sampling, the population is first divided into smaller, mutually exclusive groupings or segments known as clusters. The fundamental premise is that there is heterogeneity inside and homogeneity across clusters so that a cluster is seen as a smaller version of the population. Every person or component in the chosen clusters may be included in the sample, or certain components may be chosen at random from the clusters. One-stage cluster sampling is used when every element of the chosen clusters is present in the sample. Two-stage cluster sampling, on the other hand, is when samples are also randomly selected from the pre-selected clusters. There can be more than two steps in a cluster sample. While improving precision is the aim of stratified sampling, improving sampling efficiency and cutting expenses are the main goals of cluster sampling. The expenses include, among other things, those related to travel, other administrative costs, and the creation of a sampling frame. Sampling error is larger with this technique than with a conventional random sample of the same size, which is one of its drawbacks. The steps involved in cluster random sampling are as follows:

1. Separate the population into homogeneous unit clusters, typically based on geographic proximity.
2. Sampling clusters at random the number of clusters relies on the requirements of the study for each cluster that is included. Random sample units are chosen for each cluster.
3. Calculate each unit in each sample cluster. This could entail creating a sample frame for every cluster that has been chosen and drawing the same from each cluster using an easy or methodical random sampling technique.

Multistage Sampling

Multistage sampling often uses a variety of sample techniques. Usually, it entails putting different probability approaches together most effectively and efficiently. Using the most suitable techniques at each stage, the sample procedure is carried out step by step. There may be two, three, four, or more stages involved. A researcher may employ three stages of sampling: the first stage would involve selecting a sample of districts within a region; the second stage would involve selecting villages within districts; and the third stage would involve selecting households within each village. characteristics of each chosen village’s households (third stage). One benefit of multistage sampling is that it allows the selection of final units (households, for example) at the last step to be surveyed.  Through a hierarchy of higher-level stages for sampling or study.

Not as efficient as actual random sampling, but it likely addresses more of the issues that arise from random sampling. This tactic works well because it makes use of several randomizations. As such, it is quite beneficial. Moreover, multistage sampling avoids the significant—and maybe needless—expense of typical cluster sampling by not using all sample units in all chosen clusters.

Non-Probability Sampling:

Non-probability sampling Methods are sampling strategies that rely on the researcher’s subjective opinion rather than following the logic of probability theory. In other words, the selection of samples is not done at random; rather, it is done for a variety of reasons, including convenience, judgment, and the subjective inclusion of components or units with specific characteristics in the population. Convenience sampling, quota sampling, purposeful sampling, judgmental sampling, and snowballing are examples of non-probability sampling procedures.

Examples of non-probability sampling techniques are purposive, quota, judgmental, convenience and snowballing sampling techniques.

Convenience Sampling

This is sometimes known as grab or chance sampling, unintentional, or haphazard sampling. During the data collection process, the researcher chooses study units that are readily available or, even better, draws the sample from the conveniently available portion of the population. This is known as a sampling approach. Such a sample would not be sufficiently representative for the researcher to be able to conclude the entire population from it in a scientific manner. However, they are still in use, particularly in cases when respondents refuse to be interviewed or where basic random sampling may not be effective for practical reasons. For instance, the interviewer could only speak with those present at the designated time if the survey was conducted early on a particular day at a shopping centre. This would mean that the opinions of other members of the community in that region would not be represented. This method is frequently applied in student surveys, street interviews, mall/supermarket intercept interviews, etc. The example method is less time- and money-consuming. However, there are certain drawbacks to the strategy, like selection bias. They might not be appropriate for causal study, but they can be helpful in exploratory research to generate ideas or hypotheses.  Pilot testing is the best application for this kind of sampling but is also being used in large surveys for the reason mentioned.

Quota Sampling

The population is first segmented like in the case of stratified sampling, into smaller groups. After that, the researcher determines, using a predetermined proportion, which components or units to choose from each section. For instance, an interviewer might be instructed to select 600 men and 400 women between the ages of 55 and 70. The technique is a non-probability sampling technique because of this second stage. Compared to convenience sampling, the approach may produce a more representative sample. To ensure that all of these qualities are represented, quota sampling makes sure that a predetermined number of sample units from various categories with predetermined features appear in the sample. It sets aside amounts for various population groupings and then uses convenience or purposeful sampling to complete each quota. Used only when hurried and unrefined outcomes will make sense practically.

Purposive Sampling

Purposive sampling is also referred to as selective or judgmental sampling. This sampling strategy involves choosing the units or items to sample based on expert opinion or personal experience. The sampling technique selects a sample to highlight specific traits within the population. As an illustration, limiting the group to individuals who have embraced a specific technology or employed a particular methodology. Based on the respondents’ ability to provide the necessary data—such as pig, rice, or poultry farmers—a purposive sample may be selected. A sample of places or individuals can be purposefully selected based on a set of distinguishing traits. Because the sample deviates inexplicably from the intended purpose, purposeful sampling is weak.  Typically, we would be looking for one or more particular, preset groupings. If the distinctive characteristics of the respondents are prevalent in the area, the researcher can choose a study area purposefully. For instance, since farmers in oil-producing regions are more likely to experience oil spills, it will be simpler to do a study on the impact of spills on agricultural products in those areas. Essentially, confirming that the respondent satisfies the requirements for inclusion in the sample will probably be one of the first tasks a researcher employing purposive sampling will perform. When sampling for proportionality is not the main goal and you need to swiftly attain a desired sample, purposeful sampling can be quite helpful. You can obtain the opinions of your target population with a purposive sample, but the more easily accessible segments in your population will probably be over-represented.

Snowball Sampling

Snowballing is a chain-referral sampling technique, in which the respondents (subjects) under study select potential subjects for future correspondence from their social network. Using the snowball sampling technique, a first respondent or group of respondents is chosen at random, and after being questioned, they are asked for advice on how to find further respondents who fall into the target population. This approach can be helpful when a researcher wants to look at traits that are uncommon in the community or socially sensitive or touching topics that make people reluctant to come out and volunteer information without hesitation. One desirable aspect of this approach is that, as the referral process advances, it significantly increases the likelihood of finding the desired features in the population. Examples of such issues include HIV/AIDS, cocaine use, or other practices that are not socially acceptable, such as using certain government or social services that are stigmatized in society.

Read more about the examples of probability and non-probability sampling techniques.

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