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Marketing textbook, chapter 4

Market research → Decision problems in the context of data collection → Selection procedure → Random selection (Chapter 4.2.3.1)

In a partial survey, the characteristic of a feature that was surveyed in the sample is used to infer the corresponding characteristic of this feature in the population (e.g. proportion of consumers who use brand X).

However, such an „extrapolation“ deviates to a greater or lesser extent from the „true“ expression of the characteristic of interest in the population. This „true“ value can be determined by means of a complete survey, but this is only possible or useful in exceptional cases. The so-called sampling error, which is also referred to as random error or maximum margin of error, indicates the random deviation of the expression of a characteristic in the sample from the „true“ expression of the characteristic in the population. The sampling error is calculated as follows:

Formula for calculating the sampling error
±e=±t√(p·q/n)±e = ±t √(p - q / n)

e = sampling error, i.e. the fluctuation range (±) in per cent around the measured sample value within which the „true“ value (in the population) lies with a certain probability.

t = indicator for the specified certainty of the inference from the sample to the population (the choice of t determines the significance level).

The following table shows at which value of t the »true« value of the characteristic lies within the interval p ± e and with what probability.

t-valueConfidence probability (significance level) (in %)
168,3
1,9695,0
295,5
399,7
3,2999,9

p = proportion of people in the population who have a certain characteristic (e.g. proportion of users of brand X).

q = proportion of people in the population who do not have a certain characteristic (e.g. proportion of non-users of brand X).
The product p - q - and thus also the sampling error - is greatest for a given sample size if p has a value of 50. This most unfavourable value in relation to the sampling error is always assumed if p is not known.

n = sample size

The following example illustrates the calculation of the sampling error: With a sample size of n = 400 and the assumption that p = 50 per cent, the sampling error is ± 5 per cent if t = 2 is selected. Accordingly, the „true“ value of p, i.e. the proportion of users of brand X in the population, is between 45 and 55 per cent with a probability of 95.5 per cent (t = 2) (cf. Ter Hofte-Fankhauser/Wälty, 2013, p. 50 f.) The calculated interval is also referred to as the confidence interval of the proportion value p. As the following figure shows, the size of the sampling error at a given significance level depends on the size of the sample on the one hand and on the value p on the other.

Sample size
n		P
q		50
50		45
55		40
60		35
65		30
70		25
75		20
80		...
...
... ........................
100 10,09,99,89,59,28,78,0...
200 7,17,06,96,76,56,15,7...
300 5,85,75,75,55,35,04,6...
400 5,05,04,94,84,64,34,0...
500 4,54,44,44,34,13,93,6...
600 4,14,14,03,93,73,53,3...
700 3,83,83,73,63,53,33,0...
800 3,53,53,53,43,23,12,8...
900 3,33,33,33,23,12,92,7...
1000 3,23,13,13,02,92,72,5...
..............................
Sample error ±e in per cent as a function of the sample size n and the distribution of p and q also in per cent (significance level: 95.5 per cent; t = 2).

Strictly speaking, the calculation of the sampling error and the confidence interval is only permitted if the following condition is met: n - p - q ≥ 9 (Bortz/Schuster 2010, p. 104 f.). This is the case in this example, as the following applies: 400 - 0.5 - 0.5 = 100. The sampling error can be calculated not only for percentage distributions, but also for sample averages of metric data (Homburg, 2015, p. 323 ff.).

Sources:

  • Bortz, J./Schuster, C.: Statistik für Human- und Sozialwissenschaftler, 7th edition, Berlin 2010.
  • Homburg, C.: Marketing Management. Strategie - Instrumente - Umsetzung - Unternehmensführung, 7th edition, Wiesbaden 2020.
  • Ter Hofte-Frankhauser, K./Wälty, H. F.: Marktforschung. Grundlagen mit zahlreichen Beispielen, Repetitionsfragen mit Lösungen und Glossar, 5th edition, Zurich 2013.

Yellow book cover with the title „MARKETING - Introduction to Theory and Practice“ in white and blue letters. At the bottom are two colourful, stylised hands that together form a heart. Authors: Andreas Scharf, Bernd Schubert, Patrick Hehn and Stephanie Glassl. Publisher: Schäffer-Poeschel.
Marketing textbook,
8th edition

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