The Morgan table: sample size with the Krejcie and Morgan method

Robert Krejcie and Daryle Morgan published this table in 1970 in a paper titled "Determining Sample Size for Research Activities" in Educational and Psychological Measurement. Their aim was to let researchers read the sample size off the population size without any calculation. Every number in the table comes from one formula:

• χ²: chi-square value with one degree of freedom at the chosen confidence level; 3.841 for 95%, i.e. 1.96 squared.
• P: proportion of the trait in the population; set to 0.5 to give the largest sample size.
• d: precision or margin of error; 0.05 in the table.
• N: population size.

The table rounds to the nearest whole number. If you apply the same formula to all 90 population sizes you get exactly the printed table; the table on this page is generated with this formula and checked row by row against the original paper.

1. 1

   Define the population precisely

   The population is everyone you generalise the results to; for example the 850 employees of one organisation, not every employee in the country.

2. 2

   Take the same or the next larger row

   If your exact number is not in the table, the safest choice is the next larger row: for 820 people, the 850 row, i.e. 265 people. Or type the exact number into the calculator, which gives 262 people for 820.

3. 3

   Allow for attrition

   The table gives the number of complete, usable questionnaires. If you expect 15% of responses to be incomplete or unusable, divide the table value by 0.85: for a population of 850, distribute at least 312 questionnaires.

4. 4

   State the sampling method

   The table only gives the sample size, not how to select it. Even with the right number, a convenience sample does not represent the population; state the sampling method (simple random, stratified, cluster) in your methods chapter.

Morgan's formula and Cochran's formula with the finite population correction are mathematically the same. Divide the numerator and denominator of Morgan's formula by d² and you get n₀ × N ÷ (N − 1 + n₀), exactly as in Cochran. They differ in only two details: Morgan uses χ² = 3.841 while Cochran uses z² = 3.8416, and Morgan rounds to the nearest whole number while Cochran is usually rounded up. That is why the two methods differ by one person at most.

If you need a different confidence level or margin of error, or the population is unknown, calculate the sample size with Cochran's formula. The calculator on this page also accepts other confidence levels and margins, but with non-default settings the result is no longer "the Morgan table value"; call it a calculation with the Krejcie and Morgan formula.

Before data collection, also check the questionnaire's reliability on a pilot sample; Cronbach's alpha calculator takes the data straight from Excel. To collect the responses, build an online questionnaire so you know exactly how many complete responses you have and when you have reached the table value.