How To Determine Sample Size For Your Final Year Project

How to Determine Sample Size for Your Final Year Project

Sample size is simply the number of people, or items, you collect data from in your study. If you survey 300 students out of a population of 2,000 students, your sample size is 300. Getting this number right matters, because a sample that is too small cannot represent your population fairly, while a sample that is far too large wastes your time, your money and your respondents patience. Your supervisor and your defense panel will ask how you arrived at your number, so you need a method you can explain and defend, not a number you guessed.

This guide explains what sample size means, the four factors that decide it, the two formulas Nigerian students use most often, worked examples you can copy, and the mistakes that cost students marks in Chapter Three. By the end, you will know exactly how many respondents you need and how to justify the number in your methodology chapter.

What Is Sample Size and Why Does It Matter?

Your population is everyone your study is about. Your sample is the smaller group you actually study, chosen from that population. You study a sample because studying an entire population is usually impossible, too expensive, or simply unnecessary. A well chosen sample lets you draw conclusions about the whole population with reasonable confidence.

Sample size matters for three reasons. First, it affects how accurate your results are. Larger samples generally give more precise results, because one unusual respondent has less power to distort the average. Second, it affects whether your findings can be trusted to represent the population. A survey of 20 people cannot speak for a university of 15,000 students. Third, it is a question your defense panel will ask. If you cannot explain how you got your number, they will doubt the rest of your methodology. If you are still deciding between a survey and interviews, our guide on qualitative vs quantitative research for final year projects will help you choose the method first, because the method decides how sample size works.

The 4 Factors That Decide Your Sample Size

Before any formula, you need four pieces of information. These are the same four inputs every sample size calculator asks for.

• Population size (N). How many people are in the group you are studying? This could be all 800 students in a faculty, all 120 staff in a company, or all 45 secondary schools in a local government area. If your population is very large, or you do not know its exact size, you treat it as infinite and use the formula for large populations.
• Confidence level. How sure do you want to be that your results reflect the true population value? The standard in student research is 95 percent, which corresponds to a Z score of 1.96. A 99 percent confidence level needs a larger sample, while 90 percent needs a smaller one. Use 95 percent unless your supervisor says otherwise.
• Margin of error. How much error are you willing to accept? A margin of error of 5 percent is the standard for final year projects. It means your result could be 5 percent above or below the true value. A smaller margin, such as 3 percent, gives more precision but needs a much larger sample.
• Response distribution (p). This is your best guess of how responses will split. If you have no idea, use 50 percent. It is the most conservative choice, because it produces the largest sample size, and it is the standard assumption when you have no earlier study to rely on.

Change any one of these four and the required sample size changes. Higher confidence, a smaller margin of error, or a more diverse population all push the number up. A smaller population, or a wider margin of error, pushes it down.

Method 1: The Taro Yamane Formula for a Known Population

The Taro Yamane formula is the most common method in Nigerian universities, because it is simple and it works directly from your population size. The formula is: n = N divided by (1 + N multiplied by e squared), where n is your sample size, N is your population, and e is your margin of error, usually 0.05.

Here are worked examples with a 5 percent margin of error, so you can see the pattern:

• Population of 100: n = 100 divided by (1 + 100 multiplied by 0.0025) = 100 divided by 1.25 = 80 respondents.
• Population of 200: n = 200 divided by (1 + 200 multiplied by 0.0025) = 200 divided by 1.5 = 133 respondents.
• Population of 500: n = 500 divided by (1 + 500 multiplied by 0.0025) = 500 divided by 2.25 = 222 respondents.
• Population of 1,000: n = 1,000 divided by (1 + 1,000 multiplied by 0.0025) = 1,000 divided by 3.5 = 286 respondents.
• Population of 2,000: n = 2,000 divided by (1 + 2,000 multiplied by 0.0025) = 2,000 divided by 6 = 333 respondents.

Notice what happens as the population grows. Doubling the population from 500 to 1,000 only raises the sample from 222 to 286. Beyond a certain point, a bigger population barely changes the sample size, which is why very large populations all settle around the same number.

Method 2: The Cochran Formula for Large or Unknown Populations

When your population is very large, more than 10,000, or you do not know its exact size, use the Cochran formula. It is: n = (Z squared multiplied by p multiplied by (1 minus p)) divided by e squared. With the standard settings, 95 percent confidence (Z = 1.96), p = 0.5, and a 5 percent margin of error, the calculation is (3.8416 multiplied by 0.25) divided by 0.0025, which gives 384 respondents.

That number, 384, is worth remembering. For any large population, at 95 percent confidence and a 5 percent margin of error, 384 respondents is the standard sample size. If you then know your population is finite, you adjust it down with the finite population correction: n adjusted = n divided by (1 + (n minus 1) divided by N). For a population of 10,000, that gives 384 divided by 1.0383, which is about 370 respondents.

You can also cross check your result against the Krejcie and Morgan table, published in 1970 and still used in many departments. For a 95 percent confidence level and a 5 percent margin of error, the table gives 80 for a population of 100, 132 for 200, 217 for 500, and 278 for 1,000. These are very close to the Taro Yamane results above, which is a good sign. If your formula result and the table disagree wildly, check your arithmetic before you write the number into Chapter Three.

How to Determine Sample Size in 5 Steps

Step 1. Define your population clearly

Write down exactly who your study covers, and count them. For example, all 450 final year students in the Faculty of Social Sciences, or all 86 registered pharmacies in Enugu metropolis. If you cannot count the population, say so, and use the Cochran formula for an unknown population instead.

Step 2. Choose your confidence level and margin of error

Use 95 percent confidence and a 5 percent margin of error unless your supervisor asks for something different. Write these choices down, because you will need to state them in Chapter Three.

Step 3. Pick the formula that fits your situation

Use Taro Yamane when you know your population size. Use Cochran when the population is very large or unknown. Use the Krejcie and Morgan table as a cross check. Do not mix formulas in the same study, and do not switch formulas after seeing the result.

Step 4. Calculate, then add a buffer for non response

Not everyone you give a questionnaire to will return it. Add 10 to 20 percent extra to your calculated sample to cover non response and incomplete questionnaires. If your formula gives 222, plan to distribute about 250 questionnaires so that you still end up with at least 222 usable responses. Report the final number of usable responses in your analysis, not just the number you distributed.

Step 5. Write it up properly in Chapter Three

In your methodology chapter, state the population, the formula you used, the confidence level and margin of error, the calculation, and the final sample size. A sentence like, "The population of the study was 500 students. Using the Taro Yamane formula with a 5 percent margin of error, the sample size was determined as 222 respondents," is exactly what a supervisor wants to see. Our guide on how to write Chapter One of a final year project shows how your population, objectives and method should line up from the start.

What About Qualitative Research?

Sample size works differently in qualitative research, because you are not trying to represent a population statistically. You stop collecting data when you reach saturation, which means new interviews stop giving you new information. In practice, qualitative studies typically use 6 to 30 participants, chosen purposively because they have relevant experience, not because they represent a whole population. If your project is interview based, do not apply the Taro Yamane or Cochran formula to it. Explain in Chapter Three that you used purposive sampling and stopped at saturation, and say how many participants that gave you.

Common Mistakes Students Make With Sample Size

• Guessing the number. Writing "a sample of 100 respondents was used" with no formula, no population and no justification is the most common error, and it is one supervisors notice first.
• Using a tiny sample for a survey. Surveying 20 people and reporting percentages as if they represent a whole university is not valid. If your sample is small, either increase it or reconsider whether a qualitative design fits better.
• Confusing sample size with population. Your population is everyone the study covers. Your sample is the part you actually study. State both numbers, and never use them interchangeably.
• Forgetting non response. If you need 222 usable responses and you distribute exactly 222 questionnaires, you will fall short. Always distribute more than your target.
• Copying another study's sample size. A sample size of 384 was right for that study's population and settings, not automatically for yours. Calculate your own number from your own population.
• Using the wrong formula for the design. Applying Taro Yamane to an interview study, or quoting a qualitative sample of 15 participants as if it represented a population statistically, will draw questions at defense. Match the method to the design, and practise your answers with the 25 most common project defense questions and answers on ProjectNG.

Frequently Asked Questions About Sample Size

How many respondents do I need for my final year project?

It depends on your population. With a 5 percent margin of error at 95 percent confidence, a population of 500 needs about 222 respondents, a population of 1,000 needs about 286, and a very large population needs about 384. Calculate your own number from your population using the Taro Yamane or Cochran formula.

What is the Taro Yamane formula?

It is n = N divided by (1 + N multiplied by e squared), where N is your population and e is your margin of error, usually 0.05. It is the most widely used sample size formula in Nigerian universities for a known population.

Can I use an online sample size calculator instead?

Yes. Online calculators such as Raosoft use the same formulas and are a good way to cross check your hand calculation. Still write the formula, the inputs and the result in Chapter Three, because a calculator screenshot alone does not explain your method to a supervisor.

What if my population is very small?

If your population is small, for example 40 people, do not sample at all. Study the whole population. This is called a census, and it is the correct choice when the population is small enough to reach everyone. State in Chapter Three that you used the entire population because of its size.

Calculate It, Justify It, Then Collect Your Data

Determining sample size is not guesswork. Define your population, choose 95 percent confidence and a 5 percent margin of error, apply the Taro Yamane formula for a known population or the Cochran formula for a large one, add 10 to 20 percent for non response, and write the whole calculation into Chapter Three. A number you can explain is worth far more than a bigger number you cannot defend. Once your sample size is settled, you can move on to designing your questionnaire and collecting data with confidence.

If you have not yet defined the problem your project will solve, start with our guide on how to identify a research gap for your final year project, so your population and your sample size follow from a question that is worth answering.

Sources: OmniCalculator, Sample Size Calculator; Youth Research Journal, Sample Size Calculator; Sample Size Determination lecture notes, Cochran and Fisher formulas; EduProjectTopics, How to Write a Research Methodology.