http://www.kenpro.org/sample-size-determination-using-krejcie-and-morgan-table/

It depends on your context. Study objectives, study design, duration, affordability etc. are involved.

You are the best judge in qualitative research but for quantitative research you can get many formulas for random sampling.

you can use Krejcie & Morgan table

It's the basic to read a good book first.

Sampling

Before knowing the meaning of sampling, it is necessary to know the meaning of population and sample.

Population:

The collection of units or items under study is called the population or universe. The population having finite number of items is called finite population and the population having infinite number of items is called infinite population. Sometimes it is possible to examine each and every item (units) of the population under study. This is called census enumeration or complete enumeration. But sometimes it may be impossible to examine all the items of population, in such case; we take only a part of population which is called sample.

Sample: A sample is a part of population under study

Sampling: The method of selecting a sample from a population under study is called sampling.

Objective of sampling:

1. The main objective of sampling is to obtain the maximum information about the population with the minimum effort.

2. The second objective of sampling is to set up the limits of accuracy and degree of confidence to the estimates of population parameter.

3. The third objective of sampling is to test the significance of the population parameter based on sample statistics.

Census Vs Sampling (Difference between census and sampling)

A census involves the study of all the items of the population under study and sampling involves the study of a part of population under consideration.

1. A sampling technique is appropriate when the population is large but census is appropriate when the population is small.

2. A sampling technique is appropriate when the population possess homogeneous characteristics but when the population possess heterogeneous, census is appropriate.

3. Sampling gives quick result or decisions. Census method requires a long time to draw conclusion but sampling gives the decision in short time. So sampling is appropriate when the result is required in short-time.

4. The amount of cost required in sampling technique is lower than that of census.

5. Sometimes, sampling gives more accurate result than census because census accuracy may be lost because of large size of population.

6. In studying destructive nature of units (e.g. cracking strength of chalk) only sampling is possible.

7. When the population is infinite, the only way to get information is sampling method.

Types of sampling:

Sampling methods are classified into two broad categories:

(1) Probability sampling (Random sampling)

(2) Non-random sampling (non-probability sampling)

Probability sampling:

The sampling method in which each unit in the population has some definite, pre-assigned probability of being selecting in the sample is knows as probability sampling. Probability samples have the following characteristics.

(i) Each sample unit has an equal chance of being selected.

(ii) Sampling units have different probabilities of being selected.

(iii) Probability of selection of a unit is proportional to the sample size.

Types of probability sampling (Random sampling)

(i) Simple random sampling

(ii) Stratified sampling

(iii) Systematic sampling

(iv) Cluster sampling

(v) Multi-stage sampling

Non-probability sampling:

If the selection of unit from the population to form a sample is not depending upon chance but depends on the judgment or convenience of the investigator, than the sampling is said to be non-random sampling (non-probability sampling).

The types of non-probability sampling are:

1. Judgment of purposive sampling

2. Convenience sampling

3. Accidental sampling

4. Quota sampling

5. Sequential sampling.

Types of Random sampling

1.Simple random sampling:

In this method each and every unit of population has equal chance of being selected in the population. Therefore, simple random sampling is a method of selecting 'n' units out of a population of size 'N' units by giving equal probability to all units. There are two types of simple random sampling.

(i) Simple random sampling without replacement (SRSWOR)

If a unit is selected and does not return to the population before the next drawing, this procedure is called simple random sampling without replacement (SROWR).

(ii) Simple random sampling with replacement (SRSWR)

If a unit is selected and noted and return to the population before the next drawing, the procedure is called simple random sampling with replacement.

A random sample can be drawn by two ways:

(i) Lottery method

(ii) Use of random number table.

2. Stratified sampling:

When the population characteristic are heterogeneous, simple random sampling is not suitable. In this case the population is divided into different groups or classes called strata. The units are homogeneous within strata and heterogeneous between the strata. Then a simple random sampling procedure is used to draw sample from each stratum.

3. Systematic sampling:

Systematic sampling is a technique in which only the first unit is selected with the help of random number and rest gets selected automatically. Systematic sampling is commonly used if a complete and up to date list of population units is available. Suppose a population consist of units numbered from 1 to N. Let N = nk when n = sample size and k = sampling interval and a random number is selected between 1 to k. Then every kth unit will be selected automatically.

4. Cluster sampling:

A cluster sampling is a technique of random sampling in which the population is divided into different groups called clusters, in such a way that the characteristics within the cluster are heterogeneous and between the clusters are homogeneous. so that the number of sampling unit in each cluster should be approximately same. Then simple random sampling is used to select the sample unit from each cluster.

5. Multistage sampling:

Multistage sampling is the combination of cluster sampling and simple random sampling. Here the sampling is done in various stages. At the first stage, the population is divided into different cluster and clusters are selected by using simple random sampling. Here clusters are called primary stage units (PSU) and elements within the clusters are called second stage units (SSU). This procedure can be generalized to three or more stages and is termed as multistage sampling.

For example: In crop surveys for estimating yield of a crop in a district, VDC can be considered as primary sampling unit (PSU), the villages as the second stage units, crop fields as third stage units and a plot of fixed size as the ultimate unit of sampling.

Non-Probability sampling

1. Judgment sampling:

In this method of sampling, the choice of sample items depends upon the judgment of the investigator. In the other words, the investigator exercises his judgment in the choice and includes those items in the sample which he thinks are most important with regard to the characteristics under investigation.

2. Convenience sampling:

A convenience sample is obtained by selecting 'convenient' population units. The method of convenience sampling is also called the chunk. A chunk refers to that fraction of the population being investigated which is selected neither by probability nor by judgment but by convenience.

3. Quota sampling:

Quota sampling is a type of judgment sampling. In a quota sampling, quotas are set up according to some specified characteristics within the quotas, and the selection of sample items depends on personal judgment. For example, in radio listening survey, the interviewers may be told to interview 500 people living in a certain area and that out of every 100 persons interviewed 60 are to the housewife, 25 farmers and 15 children under age of 15 years. Within these quotas the interviewer is free to select the people to be interviewed.

4. Accidental sampling:

In this sampling, the researcher selects the sample units which, comes in hand. Suppose a researcher has to collect the information about educational status of 500 persons, he can collect the information from the any 500 persons walking in the road and willing to provide the information.

5. Sequential sampling:

In sequential sampling one can go on taking samples one after another so long as one desires. This method is generally adopted in case of acceptance sampling plan in the context of statistical quality control.

Sampling Error or Non-sampling Error

Sampling Error:

The results derived from a sample survey may not be exactly equal to the true value in the population. The reason is that estimate is based on a part of population and not on the whole population. Hence sampling gives rise to the certain errors known as sampling errors (or sampling fluctuation). However these errors can be controlled.

Following are the some reasons of sampling error:

1. Improper choice of sampling method

2. Sample size not being optimal

3. Poor sampling plan

4. Improper choice of sample statistics.

5. Improper substitution

6. Variability of population

7. Faulty method of analysis

Non-sampling error:

The data obtained in an investigation by complete enumeration, although free from sampling error, would still be subjected to non-sampling errors. The non-sampling error occurs due to a number of causes such as defective method of data collection, coding, tabulation, incomplete enumeration and etc.

More specially, non-sampling errors may arise from one or more of the following factors.

1. Inappropriate or inaccurate method of interview, observation.

2. Lack of trained and experienced investigators.

3. Lack of adequate inspection and supervision.

4. Errors due to non-response.

5. Errors in data processing operations such as coding, classification.

6. Errors committed during presentation and tabulating of data.

Hope it will be helpful

Hi Aiman Saba

Depending on the test statistic and your expected effect size you can compute the "a priori" power of different sample sizes. You can do this manually or use G.Power, which is a popular tool that is very convenient to use. I think there might also be some manuals online on how to use it to determine sample size. Of course, there are also rules of thumb for how many data points you need to estimate models of varying complexity to actually have enough statistical power to detect significant effects.

Please let me know if this helps.

G.Power: https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html

Sample size? well, a lot of factors are needed to consider in the determination/computation of sample size that may best fit your study. Such, the characteristics of your population knowing its degree of variability, the confidence level, and level of precision (margin of error) you would like to tolerate. Also, the complexity of the statistical test that you're going to utilize in your study.

The objective and type of research that you're dealing are also one of the important indicators to consider. Many supporting works of literature/studies that you can use, and methods of calculating sample size, or determining the appropriateness of sample size.

Best regards,

http://www.kenpro.org/sample-size-determination-using-krejcie-and-morgan-table/

Sample Size Rule

Sekaran (2013) wrote:

"Roscoe (1975) proposes the following rules of thumb for determining sample size:

1. Sample sizes larger than 30 and less than 500 are appropriate for most research.

2. Where samples are to be broken into sub-samples;(male/females, juniors/seniors, etc.), a minimum sample size of 30 for each category is necessary.

3. In multivariate research (including multiple regression analyses),the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.

4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size."

Reference

Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.

sample size of 30 or more is suggested because Gaussian distribution can be used instead of Student's t distribution.

Sample size should be chosen based on population variance and acceptable error. You have to take into account the benefits of being right verses the cost of being wrong. This is the reason new drug test can take so long and sample sizes are so large.

On the other hand if you are doing exploratory data analysis to find relationships that will lead to further studies, then the cost of being wrong is reduced and hopefully errors will be uncovered with further studies.