Tracking Services (Continuous Parameters)

As mentioned earlier, 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 we need to set confidence levels and confidence intervals.

Services like retail measurement and consumer panel continually track many product categories, and several thousand items. So, for these services, theoretically, there are several thousand parameters to be considered in the sample design.

Since the descriptive statistics of each of these items differ, researchers need to set criteria, and design samples such that the majority of the items that are tracked meet the service specifications.

Reverting to the discussion on relative standard error (RSE), consider sales of item I and II, and 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

The mean and variance of item II is about 10 times greater than item I. The RSE (σ'), however, since it is scale-invariant, generally varies much less than the mean or variance. And, since the sample size (n) to measure the sales of items (see equation) is dependent on RSE, the sample requirement does not vary drastically across items: $$n=\frac {ZS'}{e'}^2,\;\;e'= \frac{ZS'}{\sqrt n}$$

Assuming a large population of stores, since RSE of the two items, I and II, is 0.550 and 0.546, Z = 1.65 (90% confidence level) and e' = ±6% of sales level, then the required sample size for item I is 229, and that for item II is 225.

Knowledge of the RSE of items to be tracked by a retail tracking service or a consumer panel, is not known at the onset of the service. Relying on retail census data and information gleaned from similar services across the globe, data scientists at research firms such as NielsenIQ, are able to form thumb rules and RSE benchmarks, which are used in designing the sample for the pilot service. The sample design is then finalized based on real data obtained from the pilot.

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