Tracking Services (Continuous Parameters)

As mentioned earlier, research programmes like surveys or ongoing tracking services like retail measurement do not have margins of error. Parameters do. It is for the parameters measured by these service that we need to set confidence levels and confidence intervals.

BUT how do we then set the sample size of services like retail measurement that continually track sales in stores, or for services like consumer panels that track purchases by households. These services are tracking hundreds of product categories, and hundreds of thousands of items. The mean and variance of each of these items varies very significantly.

Reverting to the discussion on relative standard deviation (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. However the relative standard deviation is quite similar.

This is generally true. Since it is scale-invariant, the relative standard deviation of item sales or purchases varies much less than their mean or variance.

Based on the equation for sample size, as expressed in terms of proportion of parameter value, i.e. RSE and relative margin of error, the sample size required to measure the sales of items is dependent on RSE, which varies much less than the standard deviation:

$$n=\frac {ZS'}{e'}^2,\;\;e'= \frac{ZS'}{\sqrt n}$$

Assuming a large population of stores, if the relative standard deviation of 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.

To design the sample for a retail tracking service such as the RMS, one of the standards an agency needs to set is the acceptable precision level in terms of the relative margin of error. But, what is also required is the RSE, and this is not known at the onset of the service.

For a company such as Nielsen that conducts retail audits in over 100 countries, it is not a complex task to use the information that they obtain from a retail census in a new market, match it with global indicators and benchmarks, to estimate the range of RSE of items across product categories. Moreover, tracking service samples are adjusted on a periodic basis. So once the agency starts tracking, they use real data to refine their estimates and improve their sample designs.

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