Where the population is unknown, the sample size can be derived by computing the minimum sample size required for accuracy in estimating proportions by considering the standard normal deviation set at 95% confidence level (1.96), percentage picking a choice or response (50% = 0.5) and the confidence interval (0.05 = ±5). The formula is:

n = z 2  (p)(1-p)

             c 2 

Where:

z = standard normal deviation set at 95% confidence level

p = percentage picking a choice or response

c = confidence interval

If key-variable of the population is quantitative, use n=Z2*s2/d2. Where: n - this is what are looking for (minimum sample size), Z - is the value of the distribution function (for tourism phenomenons you can calculate this value for alpha equals to 0,05), s - is the population standard deviation, and d - is acceptable standard error of the mean (it is up to you). Of course, you don't know the population (typical in tourism studies). So, I suggest to estimate s using results from pilot research. After the pilot research calculate s=s'*(n'/(n'-1))^0,5. Where: n' - is the sample size of pilot research, and s' - is the the standard deviation of sample of pilot research. I know that it's not a perfect solution. There is lot of limitations, e.g. using convenience sampling for pilot research.

Where the population is unknown, the sample size can be derived by computing the minimum sample size required for accuracy in estimating proportions by considering the standard normal deviation set at 95% confidence level (1.96), percentage picking a choice or response (50% = 0.5) and the confidence interval (0.05 = ±5). The formula is:

n = z 2  (p)(1-p)

             c 2 

Where:

z = standard normal deviation set at 95% confidence level

p = percentage picking a choice or response

c = confidence interval

Sample size  for unknown population maybe use the requirement of analysis tools. e.g. SEM or factors need minimum 100 samples or 5xn_variables and chosen by purposive way.

Tomasz Napierala's suggestion of a pilot study is appropriate. However, to avoid a very large error for small sample size estimation, use the "t" variate. "t" is dependent on the degrees of freedom, while "z" is not. Implementing a sample size equation in Excel and using equation solver to iteratively solve for 'n" with "T.inv" used for 't" is very easy to set up.

@Lloyd T. can u pls make your explanation a little more explicit. Please if u have any document that can be of help on this issue pls send to [email protected]

See Article

https://www.checkmarket.com/2013/02/how-to-estimate-your-population-and-survey-sample-size/

if you do not know the standard deviation you can apply this equation n=p(1-p)(z/E)2

p=0.50(population proportion)

z depend on the confidence interval if you choose 95% confidence interval z =1.96 and E is estimated

https://www.youtube.com/watch?v=BQGjMqhzuIg

While I agree with answer from Ishmael Mensah , More explanation can be grasped in this link below

http://success.qualtrics.com/rs/qualtrics/images/Determining-Sample-Size.pdf

           n= Z2 Pq

                 e2                                    

Valid where,

            n        =   sample size

            Z          =   the value on the Z table at 95% confidence level =1.96

            e          =   Sampling error at 5%

            p          =   maximum variability of the population at 50%. i.e. (0.5)

            q          =   1-p = 0.5

in social sciences research if we have to determine sample size from two universities then same sample size  formula will be used ?

I hope that the following article will help with the other answers.

https://www.researchgate.net/publication/315047536_SNORAN_SAMPLING_HYBRID_SAMPLING_METHOD

Working Paper SNORAN SAMPLING (HYBRID SAMPLING) METHOD

 To few researchers, if the population is unknown, a minimum of 384 responses are sufficient if EFA, CFA or SEM is applied later for data analysis. 

Your required sample size will be around 383 for your population with a 5% margin of error and a 95% confidence level.

Here’s the formula:

SS = (Z-score)² * p*(1-p) / (margin of error)²

SS = (1.96)² * 0.5*(1-0.5) / (0.05)²

SS = 3.8416 * 0,25 / 0.0025

SS = 384.16

(Z-score is 1.96 for a 95% confidence level)

Then you need to adjust it to your specific population.

SSadjusted = (SS) / 1 + [(SS – 1) / population]

Regards

Ahmed Ali it is when population size is infinite not unknown. There is a big difference between infinite population and unknown population size.

It can be estimated through Cochran's formula (please see following attachments)

see this-

Dear RG colleague,

Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.

For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.

Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).

Regards,

Calculating sample size

we can calculate our needed sample size. This can be done using an online sample size calculator or with paper and pencil.

Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:

• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576

If you choose a different confidence level, use this Z-score table* to find your score.

Next, plug in your Z-score, Standard of Deviation, and confidence interval into the sample size calculator or into this equation:**

Necessary Sample Size = (Z-score)2 * StdDev*(1-StdDev) / (margin of error)2

Here is an example of how the math works assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.

((1.96)2 x .5(.5)) / (.05)2 (3.8416 x .25) / .0025 .9604 / .0025 384.16 385 respondents are needed

Where the population is unknown, the sample size can be derived by computing the minimum sample size required for accuracy in estimating proportions by considering the standard normal deviation set at 95% confidence level (1.96), percentage picking a choice or response (50% = 0.5) and the confidence interval (0.05 = ±5). The formula is: n = z 2  (p)(1-p)              c 2  Where: z = standard normal deviation set at 95% confidence level p = percentage picking a choice or response c = confidence interval

where the population is infinite, like buyers, which formula should be use? according to my analysis i need 400-500 respondent

Hi

In order to answer your question, several remarks need to be incorporated:

1.The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population.

2. Cochran’s formula is considered especially appropriate in situations with large populations. A sample of any given size provides more information about a smaller population than a larger one, so there’s a ‘correction’ through which the number given by Cochran’s formula can be reduced if the whole population is relatively small.

3.The Cochran formula is:

n0=(Z square x pq/e square)

Where:

· e is the desired level of precision (i.e. the margin of error),

· p is the (estimated) proportion of the population which has the attribute in question,

· q is 1 – p.

The z-value is found in a Z table.

4. If the population we’re studying is small, we can modify the sample size we calculated in the above formula by using this equation:

n= [n0/(1+((n0-1)/N)).

5. In order to estimate the sample size, three issues need to be studied, i.e. the level of precisions, confidence or risk level and the variability. Regarding the last issue, which your questions is concentrated the degree of variability in the attributes being measured refers to the distribution of attributes in the population.

6.The more heterogeneous a population, the larger the sample size required to obtain a given level of precision. The less variable (more homogeneous) a population, the smaller the sample size.

Note that a proportion of 50% indicates a greater level of variability than either 20% or 80%. This is because 20% and 80% indicate that a large majority do not or do, respectively, have the attribute of interest. Because a proportion of .5 indicates the maximum variability in a population, it is often used in determining a more conservative sample size, that is, the sample size may be larger than if the true variability of the population attribute were used.

Regards,

Zuhair

This formula is the easiest way to do it.

tq good info

n=t^2 X P (1-P)/M^2

Where:

t=1.96

P= response rate from a pilot survey

M= .05 or .01 depending on confidence interval set at 95% or 99% confidence level

Sample Size Calculation:

Sample size refers to a number of factors, including the purpose of the study (Israel, 1992, p.3). Miaoulis and Michener (1976) have specified three main criteria to determine the appropriate sample size which are-

(1) The level of precision: It refers to the range in which the true value of the population is to be estimated (Israel, 1992, p.1). It is also called sampling error or margin of error. Generally acceptable margin of error in educational and social researches is 5% or 0.05 for categorical data, and 3% or 0.03 for continuous data (Krejcie & Morgan, 1970 quoted in Bartlett et al., 2001, p.45)

(2) The level of confidence or risk: It is based on ideas included under the Central Limit Theorem that when a population is repeatedly sampled, the average value of the attribute obtained by those samples is equal to the true population value (Israel, 1992, p.1). It is also called alpha level. The alpha level used in determining sample size in most educational research studies is either 0.05 or 0.01 (Ary, Jacobs, & Razavieh, 1996 quoted in Bartlett et al., 2001, p.45).

(3) The degree of variability: The degree of variability in the attributes being measured refers to the distribution of attributes in the population. The more heterogeneous a population, the larger the sample size required to obtain a given level of precision. The less variable (more homogeneous) a population, the smaller the sample size (quoted in Israel, 1992, p.2).

You can use g power or krejcie and Morgan (1970) table

You can refer the following video

https://www.khanacademy.org/math/ap-statistics/estimating-confidence-ap/one-sample-z-interval-proportion/v/determining-sample-size-based-on-confidence-and-margin-of-error

Mainly the sample size calculation should be according to the;

i. precision level

ii. Confidence level

iii. degree of variability

the online sample size calculation may be followed.

Also you can use Power and Precision V4 Application for this purpose. Good Luck !

Power and Precision V4 application is also a good approach, agree with Mohammadreza Bachari Lafteh

Cochran’s Sample Size Formula

The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population.

Cochran’s formula is considered especially appropriate in situations with large populations. A sample of any given size provides more information about a smaller population than a larger one, so there’s a ‘correction’ through which the number given by Cochran’s formula can be reduced if the whole population is relatively small.

The Cochran formula is:

📷

Where:

• e is the desired level of precision (i.e. the margin of error),
• p is the (estimated) proportion of the population which has the attribute in question,
• q is 1 – p.

The z-value is found in a Z table.

For unknown population to calculate the sample size the population parameter is always taken as 50% with 5% margin of errors (p), z= 1.96 of 95% confidence interval

The sample size will therefore be

n = z2p(100-p)

ε2

Where

n= required sample size

Z= Critical value of the standard normal distribution for the 95% confidence interval around the true proportion which is 1.96

P= expected proportion of interest to be studied which is 50%, which is the prevalence for unknown previous prevalence.

ɛ= accepted margin of error on Proportion which is set at 3% (if the expected prevalence is above 20% and below 80%. The expected margin of error is set at 5% If the expected

if the expected prevalence is below 20% and above 80%. The expected margin of error is set at 3% . Therefore, since the previous prevalence is 50% of the unknown population which is above 20%, and below 80% the margin of error will be 5%.

Substituting in the above formula you get the final sample size for unknown population

For unknown population to calculate the sample size the population parameter is always taken as 50% with 5% margin of errors (p), z= 1.96 of 95% confidence interval The sample size will therefore be n = z2p(100-p) ε2 Where n= required sample size Z= Critical value of the standard normal distribution for the 95% confidence interval around the true proportion which is 1.96 P= expected proportion of interest to be studied which is 50%, which is the prevalence for unknown previous prevalence. ɛ= accepted margin of error on Proportion which is set at 3% (if the expected prevalence is above 20% and below 80%. The expected margin of error is set at 5% If the expected if the expected prevalence is below 20% and above 80%. The expected margin of error is set at 3% . Therefore, since the previous prevalence is 50% of the unknown population which is above 20%, and below 80% the margin of error will be 5%. Substituting in the above formula you get the final sample size for unknown population

I think that we should also consider the design effect(DE) and Non-Response Rate(NRR) while calculating sample size. So, there would be a slight variation in formula suggested by Mr. Brajesh i.e., a general formula used by most of the researchers. I would recommend you to read the book written by Leslie Kish on Survey Sampling. This would help you to use appropriate formula.

https://drive.google.com/open?id=0B_oYgB0kyn-9b2lQQkJNbU0tMDg

Best,

Vijay Kumar Mishra

Actually I was not first come here to answer the question as it was also mine. But I couldn't able to write a question for my self and decided to continue here.

My research title is related to cultural tourism where my primary sample population will be both domestic and international tourists who use to visit different cultural heritage sites. Thus, they are unknown and I need your support to draw clear and easy sample size formula to determine the unknown sample size. Thank you!

The sample size was determined using single population formula for estimating single population proportion from the infinite population. The formula for calculating the sample size (n) would be:

n = (zα/2)square P (1-P)

d(Square)

P is the assumed highest population proportion prevalence

d is margin of error

z (a/2) is the Z-score at 95% confidence interval = 1.96

Can anyone justify the difference between Cochran's formula and a single population proportion formula?

(Z value)^2 X standard deviation (1-standard deviation)/(margin of error)^2 = n

Cochran formula allows you to calculate p value is the estimated proportion of an attribute that is present in the population.q =1-p ..

Pand q are the estimate of the variance

https://www.surveysystem.com/sscalc.htm

This is an online calculator that helps you to calculate the needed sample size. All you need to know first are the Confidence Level and Confidence Interval.

Please use the infinite population sample size'

s = z2*p*(1-p)/m2

s= sample size for infinite population

z= Z score. It is determine based on confidence level. If we consider confidence level 95% then Z score=1.96.

p= % of population probability (assumed to be 50%=0.5)

m= Margin of error. It means miscalculation or change of circumstances. It will take 5%=0.05.

Download and use G-power sampling calculator

This attached articles are helpful for sample determination.

just use G-Power software

May be this article helps you

G power calculation is more reliable compared to Z score method given the credit in terms of either of the populations i.e. Known and unknown population