In order to answer this question/problem, several remarks have to be studied.

1. General remarks:

Research studies are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,…

In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population. A key way of achieving this is through the use of “randomization”. There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.

2. Specific remarks:

The following factors are highly affected the sample size and need to be identified:

• Population Size,
• Margin of Error,

· Confidence Level (level of significance) and

• Standard of Deviation.

Then, the sample size can be estimated by,

Necessary Sample Size = (z-score or t-value)2 * StdDev*(1-StdDev) / (margin of error)2 .

Dear Hemal,

You can still find statistically significant results with a small sample, but you need to have observed a large effect. Thus small sample sizes do not invalidate research, they just make it harder to detect associations or differences. Sample size calculations are concerned with managing the risk of not detecting results, however they need an estimate in advance of how big an effect they want to be able to detect.

Yes, I am agree with Prof. Samuels.

Hello,

Correct sample size estimation is important prior to the research, because it affects the conclusions about the parent population. You should take a preliminary sample (50 persons) out of the research population and calculate the variance for each quantitive variable and propotions (percentages). After this procedure, use the modified equations from confidence intervals. You can see http://www.statisticshowto.com/probability-and-statistics/find-sample-size/

Larger the sample size better for the statistical test

I agree with Prof. Samuels and Prof.stamatis. Thanks to give your inputs and suggested for that link.

Still i want to know that why we always use 30, 50 sample size for every research. I found that most of physiotherapy research did the same things for sample size.

Hope we find out more and more answers from this.

Sample size is critical to your experiment. It is the blood that flows through your experiment. It is the gas that powers your car. A small sample size leaves your study underpowered, and unrepeatable. It also leaves you few options if it did not go exactly as planned.

Small sample size is determined by the sample sizes from published experiments. It is often 5 to 10 in agricultural field trials, up to a few hundred in political surveys. Every discipline is different.

one sample could greatly overestimate the population standard deviation.

The optimal sample size depends on many topics as:

1. Terminable, procedural and financial factors (restricted sample size)

2. The kind of problem and the associated choice of the statistical model (necessary sample size)

3. The desired precision of the results (desired sample size) and

4. The size of the population (in general: as larger the population size as larger the sample size)

Kinds of problem can be: 1. One-, Two-, and More-sample problem (estimation and test of

parameters, comparison of parameters such as expected values) In the case of estimation of parameters the sample size depends on: the choice of the confidence level, the desired precision of the estimation

(e.g. half of the width of the confidence interval) and prior information

about the variance.

In the case of tests the sample size depends on: the probabilities of the errors of first and second kind, the desired

precision of test results (e.g. of differences of expected values) and prior

information about the variances 2. Variance and Regression analyses problems Here the necessary sample size depends on the number of effects or

parameters in the chosen statistical model (e.g. linear main component

model, linear model with interactions or quadratic model,…) and the possibility of estimating the experimental error. The desired sample size can be calculated as described in 1. (precision of

estimation of effects or regression parameters or precision of test

results).

If you have no prior knowledge and no idea about a desired precision of

the results you can think about a value relating to the standard deviation.

Many statistic programs today contain such sample size calculations as

Power analyses or it is possible to get additional modules.

Sorry for the not convenient readable format!

In order to answer this question/problem, several remarks have to be studied.

1. General remarks:

Research studies are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,…

In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population. A key way of achieving this is through the use of “randomization”. There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.

2. Specific remarks:

The following factors are highly affected the sample size and need to be identified:

• Population Size,
• Margin of Error,

· Confidence Level (level of significance) and

• Standard of Deviation.

Then, the sample size can be estimated by,

Necessary Sample Size = (z-score or t-value)2 * StdDev*(1-StdDev) / (margin of error)2 .

Sample is one of the important factor that should be considered before you go to sample survey. Sample size may also effect on the significance of data although there may be minimum difference or high difference

smaller sample sizes get decreasingly representative of the entire population.