Sample Size — Stratified Sampling

For stratified samples, which are the norm for retail measurement services, the formula for sample size is as follows:

$$n'_i=\left(\frac{ZS_i}{e}\right)^2 × \frac{N_i {S_i}^2}{\sum_{j=1 \, to \, k}N_j {S_j}^2} $$

Where:

n'i: Sample size for stratai (k in all)

Ni: Stratai population

Si2: Stratai population variance

Z: Standardized z value associated with the level of confidence

e: Margin of error

 

Example 2

The national universe for a retail audit comprises provision stores, minimarkets and supermarkets. Details for the provision stores are provided in Example 1 above. In the case of minimarkets, the standard deviation of the sale of the category is 100, and the average sales per store is about 400. The required minimarket sample size so that the sales estimates fall within ±6%of its true value with a confidence level of 90% is therefore equal to:

$$n_{mini}=\left(\frac{ZS}{e}\right)^2=\left(\frac{1.65×100}{0.06×400}\right)^2=47$$

The national universe comprises 200 supermarkets, 500 minimarkets and 2,000 provision stores. The standard deviation of the sales in supermarkets is 400 and average sales per store is 800. If the relative standard error at the national market breakdown is ±3%, the required sample size for minimarkets is then equal to:

$$n'_i=\left(\frac{ZS_i}{e}\right)^2 × \frac{N_i {S_i}^2}{\sum_{j=1 \, to \, k}N_j {S_j}^2} $$ $$n'_i=\left(\frac{1.65×100}{0.03×400}\right)^2 × \frac{500×100^2}{500×100^2 + 2000×80^2 + 200×400^2}=19 $$

To meet both criteria for relative standard error at the minimarket breakdown and national level, we need a minimum sample size of 47 minimarkets.

Similarly, for provision stores, n'prov = 124, and the required sample size is the maximum of nprov and n'prov, which is equal to 124.

Previous     Next

Note: To find content on MarketingMind type the acronym ‘MM’ followed by your query into the search bar. For example, if you enter ‘mm consumer analytics’ into Chrome’s search bar, relevant pages from MarketingMind will appear in Google’s result pages.







What they SHOULD TEACH at Business Schools

What they SHOULD TEACH at Business Schools


Is marketing education fluffy too?


Experiential Learning via Simulators | Best Way to Train Marketers

Experiential Learning via Simulators | Best Way to Train Marketers


Marketing simulators impart much needed combat experiences, equipping practitioners with the skills to succeed in the consumer market battleground. They combine theory with practice, linking the classroom with the consumer marketplace.