Krejcie Morgan Table: How to Choose a Sample Size for Quantitative Research

What is the Krejcie Morgan table in quantitative research

You may have a population of 2,000 students or 450 customers to survey, but you cannot ask every person. The Krejcie Morgan table lets you quickly look up the minimum number of responses needed from a finite population. It supports sample-size selection for a survey, but it does not replace decisions about the target population, sampling method, or response rate.

The table is usually used when you know or can estimate the population size N. Find the value of N in the corresponding column or row, then read the sample size S. If the population lies between two levels in the table, select the higher sample-size level so that you are less likely to fall short after cleaning the data.

In your thesis, you should also distinguish this table from the sample size formula, the Slovin formula, and the separate requirements of EFA or regression. Each approach is based on a different logic. A sample size that is adequate for the population can still be inadequate for a model with many indicators or independent variables.

How to determine sample size with the Krejcie Morgan table

Krejcie and Morgan developed the lookup table from a formula for determining the sample size of a finite population. The formula is commonly written as follows:

S = χ²NP(1 - P) / [d²(N - 1) + χ²P(1 - P)]

Here, S is the required sample size, N is the population size, P is usually set at 0,5 to produce a conservative sample-size requirement, d is the accepted margin of error, and χ² is the Chi-square value corresponding to the selected confidence level. When you use the lookup table, you do not need to calculate every row yourself. Understanding these components still helps you explain the method in Chapter 3.

The finite-population sample-size formula can be compared with (Yamane, 1967). If your study examines a proportion in a large population or a population whose size is not clearly known, the approach in (Cochran, 1977) may be more appropriate. Do not put all three approaches in the thesis and then choose the lowest number simply to reduce the number of questionnaires you need to distribute.

The table below shows commonly used lookup levels. These figures are reference sample sizes from the Krejcie Morgan table, while the final decision must also consider your analytical model and your ability to recover valid questionnaires. This is an illustrative output.

For example, your population contains 2.000 students. The table gives a reference sample size of approximately 322. If you expect 10% of questionnaires to be invalid, the number to distribute is not 322. You can calculate it as 322 / 0,90, which gives approximately 358 questionnaires. This is the number to distribute, while the analytical sample size is the number of valid observations remaining after cleaning.

If you have not finalised the method, also review EFA sample size. For a study with many indicators, the requirements of EFA, regression, or PLS-SEM may make the required sample size higher than the number obtained from the population table.

Designing the questionnaire for this objective

The Krejcie Morgan table answers how many observations you need. It does not tell you whom to survey, which variables to measure, or whether the questionnaire measures the intended construct. Before distributing the questionnaire, connect the sample size to your research model, hypotheses, and set of indicators.

The first part of the questionnaire should contain screening questions. For example, if your study examines the shopping experience on an e-commerce platform, respondents should have purchased from that platform during the period you specify. A person who does not meet the condition should be directed to the end of the questionnaire or excluded from the analytical sample.

The measurement section commonly uses a 5-point or 7-point Likert scale. The Likert scale originated from the attitude-measurement technique described by (Likert, 1932). State the meaning of each level clearly, such as 1 meaning strongly disagree and 5 meaning strongly agree. Do not change the direction of the interpretation between groups of indicators, because this can create data that is difficult to check.

Each construct should have enough indicators for you to assess scale reliability and validity. Assign variable codes while designing the questionnaire, such as PU1, PU2, and PU3 for Perceived Usefulness. These codes must remain consistent across the questionnaire, Excel file, .csv or .sav file, and SPSS results tables.

A practical questionnaire usually has the following structure:

Before official data collection, run a small pilot to identify unclear wording, missing answer options, and an excessive completion time. This checks the questionnaire. It does not support a claim that the scale has already been validated on the official sample.

Implementing data collection

You need to identify where the population comes from. If N is the number of students in a department, record the source of the list or the way you estimated it. If N represents customers of a platform and you do not know the exact number, state clearly that the population is treated as large or unknown. Then select an appropriate sample-size method instead of assigning an arbitrary value to N.

Your collection target should be higher than the minimum sample size. Respondents may leave items blank, complete the questionnaire too quickly, select the same level for every indicator, or fail the screening condition. Track the number of people who open the questionnaire, complete it, and produce valid responses, but include only valid questionnaires in the analysis.

DoThesis has fillform.info, our form tool for creating Vietnamese questionnaires and collecting online responses. Google Forms is a familiar alternative. Whichever tool you use, check the column structure after downloading the data, because form software does not decide automatically which responses are valid for your study.

You can review the guide to online survey questionnaires to check question layout, the collection link, and data export. When respondents come from several groups, track the number in each group so that the actual sample does not move too far from the target population.

A common mistake is to stop collecting as soon as the number of responses reaches the lookup value in the table. If you need 322 valid observations, you may have to distribute 350 to 380 questionnaires depending on the exclusion rate. This reserve is not a fixed threshold in the table, so record how you estimated it in the research method.

Cleaning data before importing it into SPSS

After closing the survey, save one copy of the raw data and create a second copy for cleaning. Do not edit the original file and then try to remember which rows you removed. Every excluded questionnaire should have a reason and a row identifier so that you can explain the decision if your supervisor asks.

Start by checking incomplete questionnaires. If a respondent leaves many measurement indicators blank or stops before the main section, exclude the response according to a criterion defined in advance. For a few blank cells, the treatment depends on the missing-data rate and your analysis plan. Do not automatically replace every blank cell with 3 on a Likert scale.

Next, check for straight-lining, where a respondent selects the same level for most or all indicators. This pattern is not always invalid, because the respondent may genuinely agree with all the statements. Combine completion time, attention-check items, open responses, and the plausibility of the information before deciding to exclude the record.

You should also check respondents outside the target population, duplicate records, invalid ages, and values outside the scale range. If the Likert scale runs only from 1 to 5 but the file contains 6 or 0, trace the questionnaire or coding rule before running SPSS.

When you import the file into SPSS, each row is usually one respondent and each column is one variable. You can retain the respondent ID column for tracing, but do not include it in Cronbach's Alpha, EFA, or regression. Time columns, email addresses, and personally identifying data should also stay out of the model unless they are research variables.

If you are selecting a sample for EFA, review the Slovin formula as another reference approach, then state clearly why the final method fits your study. Do not combine a Krejcie Morgan response count with another formula without explaining the decision.

How to report it in Chapter 3

The methods section should tell the reader who the population is, how its size was determined, how the Krejcie Morgan table was used, how many questionnaires you distributed, and how many valid observations remained. The valid sample size and the number of questionnaires distributed are different figures, so report them separately.

How to write this in your thesis: “The study population consisted of [N] [target respondents] within [research scope]. Based on the Krejcie Morgan table, the corresponding minimum sample size was [S] observations. The research team distributed [number distributed] questionnaires to allow for invalid responses and received [number received], of which [number valid] valid questionnaires were used for data analysis. The valid sample met the identified minimum and was appropriate for the [SPSS/EFA/regression/PLS-SEM] method.”

If you do not know N precisely, do not write a specific population figure simply to match the table. Describe the limits of the available data, explain the sampling decision, and add reasoning based on the number of indicators or the analytical technique. For regression, a commonly cited guideline is a sample size of 50 + 8m or more, where m is the number of independent variables (Tabachnick and Fidell, 2013). This is a separate basis, not a number to add arbitrarily to the Krejcie Morgan table.

In Chapter 4, you can report the number of excluded questionnaires and the reasons. For example, you distributed 360 questionnaires, received 348, excluded 21 because of missing data or failure to meet the conditions, and retained 327 valid questionnaires. These figures must match the final data file and the descriptive statistics table in SPSS.

Common mistakes when using the Krejcie Morgan table

The first mistake is confusing population size with sample size. If the population has 500 people, 217 is the reference sample size, not the number of people to exclude or the number of questionnaires to distribute. You should also avoid using the row for 500 when the population has only 240 people if the table contains a closer level.

The second mistake is treating the lookup sample size as a guarantee for every analysis. A sample may be adequate for the population and still be weak when the model has many independent variables, several comparison groups, or many indicators for EFA. Check the requirements of the analytical technique before finalising the number of questionnaires.

The third mistake is reporting only the number of questionnaires distributed. The committee will usually want to know how many were actually used, what the exclusion criteria were, and whether the final data match the SPSS file.

The fourth mistake is using the Slovin formula, Cochran, and Krejcie Morgan at the same time without explaining which one takes priority. Select one primary basis, state its assumptions, and explain if the practical sample size was increased because of analytical requirements.

Finally, do not alter the data to reach the exact table-based sample size. If you have 327 valid questionnaires while the planned minimum is 322, keep all 327 if they meet the criteria. If you have only 290, consider collecting more data or reporting the limitation. Do not create additional rows in the file.

Read more: survey topic.

Frequently asked questions

What is the Krejcie Morgan table used for?

It is a sample-size lookup table based on the size of a finite population. You use it to estimate the minimum number of observations when you know or can estimate the number of units in the research population.

The table does not replace decisions about the sampling method, valid-response criteria, or the requirements of EFA, regression, and PLS-SEM.

How large should the sample be for a population of 1.000 people according to the Krejcie Morgan table?

The common reference level is approximately 278 valid observations. If you expect some questionnaires to be excluded, distribute more than 278 and draw your conclusion from the number that meets the criteria after cleaning.

You should also check the number of indicators and the analytical technique. If the model requires more observations, use the higher requirement as the practical basis.

Is the Krejcie Morgan sample size the same as the Slovin formula?

Both approaches can be used to estimate a sample size from a finite population, but their presentation and assumptions may differ. Select one primary method instead of choosing the lower result simply to reduce the work of collecting data.

If your supervisor requires a specific formula, present that formula accurately and explain why it fits the scope of the study.

Can you use the table when the population size is unknown?

You can use a table level close to an estimated population size when you have a reasonable basis for the estimate, but you should not assign N arbitrarily. When the population is very large or unknown, consider another calculation method and state the limits of the estimate.

In every case, the required number of questionnaires also depends on the model and analytical method. The lookup table is only one part of the sample-size argument.

What should you do if you collect fewer responses than the table indicates?

First, check the number of valid questionnaires and the reasons for the shortfall. If you still have time, continue collecting responses from the correct target group. If you cannot collect more, report the actual sample honestly, state the limitation, and ask your supervisor which analytical approach is appropriate.

You must not duplicate data rows, fill in answers yourself, or delete valid questionnaires simply to produce a cleaner number.

Open your data file now and record population N, the minimum sample size, the number of questionnaires distributed, and the number of valid questionnaires separately. Then compare these four figures with the descriptive table in Chapter 3. If you need help running the analysis on a .sav or .csv file, use DoThesis M4 data analysis.