ISSUE: There appears to be two questions here: (i) how to determine sample size, and (ii) how to justify the treatment of "couple"--counting as 1 or 2?

SAMPLE SIZE: The general rule is a sample size of 30 would allow us an adequate observation to take the benefits of the Central limit Theorem, i.e. at n = 30, we start to see the bell shape curve if the data is normally distributed. See list of references attached. However, generally the determination of sample size turns on two facts: known population and unknown population. See Agresti, attached and Nunally in reference.

(i) Finite Population Scenario: If the population (N) is known, then follow the Yamane method:

(1)   nY = N / (1 + Ne2)

... where N = known population and e = error level or % percent confidence interval or alpha level. For 0.95 confidence interval, e = 0.05. For example, if the population is 50,000, what is the minimum sample size?

nY = 50,000 / (1 + 50,000(0.0025)

nY = 50,000 / 126

nY = 396.83

Under this method for finite population, the minimum sample size is 396.83 or about 397 counts.

(ii) Non-Finite Population Scenario: A second scenario involves unknown population size, i.e. non-finite population. The following formula is used for non-finite population case:

(2)   nnf = Z2σ2 / E2

... where Z = critical value for Z; σ = estimated population standard deviation; and E = standard error which is given by: E = σ / sqrt(ntest). Under this method, a test sample (ntest) must be taken as an initial sample in order to obtain descriptive statistics and use equations (1) and (2) above to calculate the value of σ. A potential problem under this method is the assumption of normality. it may be a good idea to test the data distribution to verify whether the data is normally distributed. If it is not normally distributed, we might look to other methods for minimum sample determination.

COUNTING ELEMENTS: generally, we must define what constitute "element" of the population? If the element of the population is counted per capita or by head count, then a couple would be counted as 2, i.e. husband and wife. However, if the definition of element is constrained by the instrument, i.e. survey count, if the couple complete one (1) survey, then a couple (2 natural persons) is counted as one, i.e. one household. this explains why in a case where both husband and wife earns separate income, when reporting "household income" both incomes are combined and counted as 1.

INTERVIEW & NON-PAPER SURVEY: In case where a face-to-face or via phone or other means interviews in which both persons answer the question(s), how should they be counted? We count the unit of data collection. in this case, we count the interview to fulfill one set of question. That set of question is our count for element. Rule of thumb: look to the definition of element of population as the indicator of what is counted as an item (i) in a sample size n. For example, is a survey is used, even if the whole family completed the survey---we still count it as one survey.

REFERENCE: Some relevant article attached, others see citation below.

(1) Westland, J. Christopher (2010). "Lower bounds on sample size in structural equation modeling". Electron. Comm. Res. Appl. 9 (6): 476–487.

(2) Nunnally, J. C. (1967). "Psychometric Theory". McGraw-Hill, New York: 355.

(3) Yamane, Taro. 1967. Statistics: An Introductory Analysis, 2nd Ed., New York: Harper and Row.

ISSUE: There appears to be two questions here: (i) how to determine sample size, and (ii) how to justify the treatment of "couple"--counting as 1 or 2?

SAMPLE SIZE: The general rule is a sample size of 30 would allow us an adequate observation to take the benefits of the Central limit Theorem, i.e. at n = 30, we start to see the bell shape curve if the data is normally distributed. See list of references attached. However, generally the determination of sample size turns on two facts: known population and unknown population. See Agresti, attached and Nunally in reference.

(i) Finite Population Scenario: If the population (N) is known, then follow the Yamane method:

(1)   nY = N / (1 + Ne2)

... where N = known population and e = error level or % percent confidence interval or alpha level. For 0.95 confidence interval, e = 0.05. For example, if the population is 50,000, what is the minimum sample size?

nY = 50,000 / (1 + 50,000(0.0025)

nY = 50,000 / 126

nY = 396.83

Under this method for finite population, the minimum sample size is 396.83 or about 397 counts.

(ii) Non-Finite Population Scenario: A second scenario involves unknown population size, i.e. non-finite population. The following formula is used for non-finite population case:

(2)   nnf = Z2σ2 / E2

... where Z = critical value for Z; σ = estimated population standard deviation; and E = standard error which is given by: E = σ / sqrt(ntest). Under this method, a test sample (ntest) must be taken as an initial sample in order to obtain descriptive statistics and use equations (1) and (2) above to calculate the value of σ. A potential problem under this method is the assumption of normality. it may be a good idea to test the data distribution to verify whether the data is normally distributed. If it is not normally distributed, we might look to other methods for minimum sample determination.

COUNTING ELEMENTS: generally, we must define what constitute "element" of the population? If the element of the population is counted per capita or by head count, then a couple would be counted as 2, i.e. husband and wife. However, if the definition of element is constrained by the instrument, i.e. survey count, if the couple complete one (1) survey, then a couple (2 natural persons) is counted as one, i.e. one household. this explains why in a case where both husband and wife earns separate income, when reporting "household income" both incomes are combined and counted as 1.

INTERVIEW & NON-PAPER SURVEY: In case where a face-to-face or via phone or other means interviews in which both persons answer the question(s), how should they be counted? We count the unit of data collection. in this case, we count the interview to fulfill one set of question. That set of question is our count for element. Rule of thumb: look to the definition of element of population as the indicator of what is counted as an item (i) in a sample size n. For example, is a survey is used, even if the whole family completed the survey---we still count it as one survey.

REFERENCE: Some relevant article attached, others see citation below.

(1) Westland, J. Christopher (2010). "Lower bounds on sample size in structural equation modeling". Electron. Comm. Res. Appl. 9 (6): 476–487.

(2) Nunnally, J. C. (1967). "Psychometric Theory". McGraw-Hill, New York: 355.

(3) Yamane, Taro. 1967. Statistics: An Introductory Analysis, 2nd Ed., New York: Harper and Row.

The first question is whether your study is a study of people or couples. I guess that it's couples, so your variables are describing the couple, not the person. You will have to collect some of the data from the individuals, but the measurement is at the level of the couple. For example, if he wants more children but she does not, then the couple disagrees about family size. 

In terms of sample size, you need to tell us whether your study is qualitative or quantitative. If quantitative is it descriptive or hypothesis testing? 

If it's quantitative, I can send you a guide. You can message me.

Hello Aishah,

die needed sample size depends on the tests you want to do and the effect you expect - N produces power - the lense to see your effect.

There are some programs out there like G-Power to make statistical power analyses easy - have a look:

http://www.gpower.hhu.de/

I hope this is of some help.

All the best

T.

Paul's answer was well written, and considered several different possibilities with enough information that one could figure out if the specific suggestion was appropriate for this problem. I am curious what prompted the down vote.

I think what Paul was getting at with "Counting Elements" was the statistical problem of defining your experimental unit. Ronan provided a great example at the end of his first paragraph. The experimental unit may be different for different questions. However, since the family can't answer questions, the questions with family as the experimental unit will mostly be derived. Exceptions would be things like family income. She may earn all the income, but the family spends it.

GPower looks like a great resource. However, like all of these calculations they involve knowing a fair bit about the population being sampled. This may not be a valid assumption. Paul's suggestion of taking an initial sample is of course the correct approach, but not always (or hardly ever) used.

The assumption of normality is not exactly relevant. With a large enough sample I can usually reject this assumption. However, a large number of statistical methods are fairly insensitive to departures from normality. So you could use this assumption just to get an approximate value. Or, if you keep your sample size small, then you will not be able to reject this assumption and you can behave as if it were true.

Finally, I work with insects. I try and gather the largest sample size that I can get. No one cares if another insect dies. This is very different in working with people. If I want to test a drug that cures cancer, then the people in the control group will suffer additional mortality that could have been avoided. In this case I don't want to underpower the research, but there are also penalties for overpowering the research. If your research causes no harm, then consider gathering as much data as you possible can. It is easy to discard data, it is often much harder to go back and gather more. There is trouble in this approach. If I collect 30 surveys, I cannot quantify the effect of having more data. I may be able to estimate the effect, but the estimation may be an artifact of having only 30 surveys. If I have 30,000 surveys, I can be very confident in what will happen with only 30 surveys. If the standard approach is to collect 30, and you collect 30,000, I will probably not thank you for showing me that my last decade of research was a waste of time. So there are statistical issues, and may be ethical issues or political issues in determining sample size.