As previously mentioned, research programmes like
surveys or ongoing tracking services like retail measurement do not have margins of error. It
is for the parameters measured by these services that require the setting of confidence levels
and confidence intervals.
Services like retail measurement and consumer panel continually track numerous
product categories, and several thousand items. Therefore, theoretically, there are several
thousand parameters to be considered in the sample design for these services.
Since the descriptive statistics of each item differ, researchers need to
establish criteria and design samples in a way that the majority of the tracked items meet the
service specifications.
With reference to relative standard error
(RSE), let us examine the sales of two items, item I and item II, along with their
descriptive statistics:
Sales of item I in 10 stores: {1,2,3,4,5,6,7,8,9,10}
- mean (μ)= 5.5,
- variance (σ2) = 9.17,
- standard deviation (σ)= 3.03,
- relative standard deviation, RSE (σ') = σ/μ = 3.03/5.5 = 0.550
Sales of item II in 10 stores: {11,19,31,42,49,58,71,80,91,99}
- μ = 55.1,
- σ2 = 904
- σ=30.1,
- σ'= 0.546
Although the mean and variance of item II are approximately 10 times greater
than those of item I, the RSE (σ') varies much less since it is scale-invariant. Consequently,
the sample requirement, which is dependent on RSE, does not vary drastically across items:
$$n=\frac {ZS'}{e'}^2,\;\;e'= \frac{ZS'}{\sqrt n}$$
Assuming a large population of stores and a 90% confidence level (Z = 1.65),
with e' set as ±6% of the sales level, the required sample size for item I is 229, and for item
II, it is 225.
The knowledge of RSE for items to be tracked by a retail tracking service or a
consumer panel is not initially known. Data scientists at research firms like NielsenIQ rely on
retail census data data and insights gained from
similar services worldwide to establish thumb rules and RSE benchmarks. These benchmarks are
then used in designing the sample for the pilot service, with the final sample design being
refined based on real data obtained from the pilot.
