# Tracking Studies

#### Exhibit 34.6   Required sample size at confidence level of 95%, across different margins of error, for differences in proportions.

In tracking studies where independent samples are collected at regular intervals, the focus is often on examining the change in a metric between these intervals. The standard error of the difference between two proportions, based on samples with sizes n1 and n2, with success probabilities p1 and p2 respectively, can be calculated using the formula: $$σ=\sqrt{p_1(1-p_1)/n_1+p_2(1-p_2)/n_2}$$

The upper bound for this standard error is 0.5√(1/n1+1/n2). If the sample sizes are equal (n1 = n2), this formula simplifies to σ = 1/√(2n). (Or √{2p(1-p)/n}, not assuming upper bound).

By substituting σ into the equation Z σ = e, for confidence level of 95% (Z ≈ 2), we can derive the formula for estimating the required sample size (n): $$n = \frac {2}{e^2},\; e = \sqrt {\frac {2}{n}}$$

In other words, the estimates of change have margins of error that are approximately 41% larger (multiplied by √2) compared to the corresponding estimates from individual surveys. Alternatively, to achieve the same margin of error, we would need twice the sample size.

The formula, in general, assuming p1 = p2 = p:

$$n=\frac {2p(1-p)Z^2} {e^2} ,\;e=Z \sqrt {\frac {2p(1-p)}{n}}$$

The required sample size at confidence level of 95%, across different margins of error, for differences in proportions, is shown in Exhibit 34.6.

In order to manage costs, continuous tracking studies often employ 8-weekly or 4-weekly rolling averages to track metrics. This approach helps reduce the required sample sizes to a range of 50 to 100 per wave, typically on a weekly basis. However, a drawback of using rolling averages is that they tend to smooth out the data, making it harder to detect subtle changes or variations.

Alternatively, dipstick studies may by conducted at less frequent intervals with larger samples that reveal changes more distinctly. Since they provide a snapshot in time, dipsticks are better suited for tracking the “before” and “after” impact of a marketing initiative. However, they are not typically recommended for tracking ongoing changes in the market for research programmes like advertising tracking where several brands have campaigns running across multiple media through the course of the year. For such studies, continuous tracking is better suited as it allows for establishing baselines, capturing the ongoing nature of marketing activities, and assessing their impact in the marketplace.

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