What Is Sample Size? How to Determine Sample Size for Quantitative Research

What Is Sample Size

Sample size is the number of observational units selected from a population to take part in a study. In a questionnaire survey, each valid response usually represents one observational unit. If you obtain 250 valid responses, the sample size used for analysis is 250, even if you initially distributed more questionnaires because some responses contained missing data or were invalid.

You need to distinguish sample size from population size. The population may include all customers of a bank, all students at a university, or all users of an application. The sample is only the data you actually collect and include in the analysis. You can also read what is the sample size of a data sample if you are mixing up these two concepts.

The formula used to determine sample size depends on your research objective, number of observed variables, number of independent variables, population size, sampling method, and planned analysis technique. There is therefore no single number that is correct for every topic. A regression study, an EFA study, and a PLS-SEM study may require different justifications.

Why Sample Size Matters in Quantitative Research

Sample size affects the stability of results such as the mean, Cronbach's Alpha, correlation coefficient, factor loading, regression coefficient, and p-value. When the number of observations is too small, the results may change substantially because of only a few different responses. The model may fail to run, the correlation matrix may be unstable, or the statistical tests may have low reliability.

Sample size also affects your ability to test hypotheses. A relationship may exist in the population but fail to reach statistical significance when the sample is too small. Conversely, a very large sample can make small differences statistically significant even when their practical importance is limited. You therefore need to read the p-value together with effect size and the research context.

In a thesis, sample size also helps answer three questions that supervisors often ask. How many people did you select, what was the basis for that number, and how many valid observations remained after data cleaning. Your methods section should clearly report the number of questionnaires distributed, the number returned, and the final number used in SPSS or SmartPLS.

When a study contains many observed variables, the required sample often increases with the number of variables. Hair et al. recommend approximately 5 to 10 observations for each observed variable in some quantitative studies (Hair et al., 2010). This is a practical guideline, not a mandatory formula for every research design.

You also need to distinguish planned sample size from valid sample size. Suppose you plan to analyse 250 observations but obtain only 230 valid questionnaires. You cannot report the sample size as 250 in the results. The actual sample size used to run the analysis is 230.

What Sample Size Is Adequate

The question “how many respondents do I need” should be answered according to the analysis method, not with one familiar number. For regression, you can refer to the minimum sample-size rule of 50 plus 8 times the number of independent variables, represented by m (Tabachnick and Fidell, 2013). For EFA, you need to consider the number of observed variables, the expected number of factors, and the strength of the correlations between variables.

The table below helps you choose an appropriate basis for your justification. The figures are thresholds or rules stated in the relevant sources, not a guarantee that every sample meeting the threshold represents its population.

With the Yamane formula, the common form is n = N / [1 + N(e²)], where N is population size, n is the sample size to select, and e is the allowable error. You should use this formula only when you have a reasonable basis for the population size and sampling approach. If the population is unknown or data are collected by convenience sampling, inserting the formula without explaining how participants were selected will invite further questions.

For a questionnaire containing 30 observed variables, the rule of 5 to 10 observations per observed variable suggests approximately 150 to 300 observations. You should plan above the minimum to allow for invalid responses. For example, if you need 250 valid questionnaires and expect 10% to be invalid, the number to collect can be calculated as 250 / (1 - 0,10), which is approximately 278 questionnaires.

A sample that meets a numerical requirement is still not enough to conclude that the data are good. You also need to check whether respondents belong to the target population, whether questionnaires contain substantial missing data, whether respondents selected the same option throughout, and whether the data contain entry errors. A large sample with poor-quality data does not replace a carefully designed survey.

How to Read Sample Size in the Output

Sample size commonly appears in SPSS output as N, Valid N, Valid N (listwise), or the number of observations in the Descriptive Statistics table. Depending on the procedure, SPSS may use different numbers of observations. If one variable contains missing data, a table reporting each variable separately may contain more observations than a regression table using listwise deletion.

The following is illustrative output, provided only so you can recognise the shape of the output. These figures are not results from a real study.

If you run Analyze > Descriptive Statistics > Descriptives, look at the N column in the Descriptive Statistics table. If you run regression through Analyze > Regression > Linear, the number of observations shown in the Model Summary table or in the summary information may differ from the initial number of valid questionnaires.

When you run Cronbach's Alpha through Analyze > Scale > Reliability Analysis, the number of observations is usually shown in Case Processing Summary. When you run EFA through Analyze > Dimension Reduction > Factor, check the KMO and Bartlett's Test table, then compare the number of observations with the original data. When running regression, report clearly how missing values were handled because SPSS may exclude rows missing at least one variable in the model.

Do not use the final row count in an Excel file as the sample size if the file still contains blank rows, test records, or excluded questionnaires. Create a separate analysis dataset, record the exclusion criteria, and count the remaining rows. This process keeps the figures in Chapter 3, Chapter 4, and the output consistent.

What to Do When Sample Size Is Too Small

First, check how you calculated it. Many students use the number of independent variables for a regression rule but apply that rule to EFA, or use the total number of screening questions as the number of observed variables. Identify the main analysis technique, the variables entering the model, and the actual number of valid questionnaires.

Check Excluded Data

Open the list of excluded cases and check missing values, out-of-range responses, reverse-coded variables that have not been recoded, and duplicate rows. If the problem is only an operational or data-entry error, you can correct it against the original questionnaire and record the change in a log. Do not fill missing data with an arbitrary value simply to increase N.

Collect More Data if You Still Have Time

If the sample is below the basis you selected, the easiest option to explain is to continue collecting data from the correct target population. You may use an online or in-person questionnaire, but the screening criteria must remain consistent. You can read the guide to calculating sample size to calculate how many additional questionnaires are needed after estimating the invalid-response rate.

Adjust the Scope of the Analysis for a Clear Reason

If you cannot collect more data, you can present the study as exploratory and state the limitation clearly. Reducing the number of hypotheses, removing variables, or changing the analysis technique only to make the sample appear sufficient requires approval from your supervisor. Do not randomly delete observed variables or respondents because the results are not attractive.

Your sampling method also affects how well you can justify the study. Convenience sampling is usually easier to implement but limits generalisability. If your topic requires groups or comparisons, make sure each group has enough observations instead of looking only at the total sample. The article on sampling methods can help you compare this choice with your current design.

Distinguishing Sample Size from Unit of Analysis and Population

Sample size is the number of observations used in the analysis. The unit of analysis is the object represented by each row of data, such as one customer, one employee, or one business. The population is the full set of objects that fit the scope of the study. These three concepts are related but cannot be used interchangeably.

For example, a study of customer satisfaction may define its population as customers who used a service during a specified period. The unit of analysis is each customer. If you obtain 312 valid questionnaires, the sample size is 312. The figure 312 does not mean that the population contains only 312 customers.

Sample size is also different from the number of observed variables. A questionnaire with 28 observed variables and 220 respondents has a sample size of 220, not 28 and not 248. When applying the rule of 5 to 10 observations per variable, 28 is the basis for estimating the number of respondents needed, while 220 is the actual number of observations.

You should also distinguish sample size from the number of groups in a study. If you compare three customer groups, the total sample may be 300 while each group contains only 100 people. The test of differences will then also depend on the size of each group, the balance between groups, and the assumptions of the test.

Common Errors

The first error is reporting a neat round number without a basis. The statement “the study used 200 samples because this is a common level” does not explain why 200 fits your number of variables and analysis method. State the basis, formula, or rule you used, then compare it with the number of valid questionnaires.

The second error is mixing the number of questionnaires distributed with the analysis sample. If you distribute 350 questionnaires, receive 320, and exclude 18, the final sample size is 302. Chapter 3 can describe the plan to distribute 350 questionnaires, but Chapter 4 must use 302 when reporting the results.

The third error is using several formulas without selecting a primary basis. You can check several approaches, but your thesis should clearly state which method determined the minimum sample size. The other approaches can be used for reference or cross-checking.

The fourth error is increasing the sample by retaining unreliable responses. Common signs include one respondent selecting the same option for every observed variable, an unusually short completion time, or screening information that does not fit the target population. Set your cleaning criteria before reviewing the test results so that you do not exclude data based on personal preference.

The final error is treating a large sample as proof of representativeness. A large sample cannot correct an inappropriate sampling method, leading questions, or an unclear population scope. If you need to compare random sampling methods, you can read random sampling. For software-related checks, sample size in SPSS will be useful when you need to verify N in each output.

Frequently asked questions

What sample size is good for a thesis?

There is no fixed level for every thesis. You need to base the decision on the analysis method, number of observed or independent variables, population size, and expected invalid-response rate. For regression, you can refer to the rule of n of at least 50 + 8m (Tabachnick and Fidell, 2013). For a scale, the rule of 5 to 10 observations per observed variable is commonly used as a basis (Hair et al., 2010).

Can SPSS run with a sample size of 100?

SPSS can run many procedures with 100 rows of data, but being able to run a procedure does not mean that the sample size is appropriate. Compare 100 with the number of variables, number of factors, number of independent variables, and testing objective. If the model contains many variables or you run EFA, your supervisor may ask you to provide additional justification.

What is the minimum sample size for EFA?

EFA sample size should not be determined by a number separated from the number of observed variables and the quality of the correlations between them. You can refer to the rule of 5 to 10 observations per observed variable (Hair et al., 2010) and sample-adequacy levels in factor analysis (Comrey and Lee, 1992). After running the analysis, you still need to read KMO and Bartlett's Test, communalities, and Rotated Component Matrix.

Do I need to collect more than the planned sample size?

Yes. You should collect more because some questionnaires may contain missing data, come from the wrong target population, be duplicated, or show signs of careless responding. If you need 250 valid questionnaires and expect 10% to be excluded, you can set a target of approximately 278 questionnaires. In the thesis, report the number distributed, the number returned, the number excluded, and the number used for analysis separately.

Can I delete variables to reduce the required sample size?

You should adjust the scale or model only when there is a theoretical basis, supporting test results, and agreement with your supervisor. Deleting variables only to reduce the required sample size can change the meaning of the construct and raise questions about repeated trial runs. If possible, collecting additional data from the correct target population is usually easier to justify.

When you reopen the data file, record four figures in a tracking table: the number of questionnaires distributed, the number returned, the number excluded, and the final number of observations in the output. Then compare the sample size with your analysis method and write the justification using your actual data, or use M4 data analysis to run the analysis on your own .sav or .csv file.