# Tracking Studies

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

For tracking studies where independent samples are taken at regular intervals, the change of a metric between intervals is of prime interest. The standard error of the difference between two proportions of samples n1 and n2, with success probability of success, p1 and p2, is:

$$σ=\sqrt{p_1(1-p_1)/n_1+p_2(1-p_2)/n_2}$$

This has an upper bound of 0.5√(1/n1+1/n2) . If n1 = n2 = n (equal sample sizes), this becomes σ = 1/√(2n). (Or √{2p(1-p)/n}, not assuming upper bound).

Substituting σ in the equation Z σ = e, for confidence level of 95% (Z ≈ 2):

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

In other words, change estimates have margins of error that are 41% (times √2) larger than the corresponding estimates from the individual surveys. Or, for the same margin of error, we 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.

To contain costs, continuous tracking studies use 8 weekly or 4 weekly rolling averages to track metrics. This helps to reduce sample sizes to 50 to 100 per wave (usually per week). The drawback is that since rolling averages flattens the data, it is harder to detect changes.

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. They are not usually recommended for studies where the objective is to track ongoing changes occurring in the market. For instance, in advertising tracking where several brands have campaigns scattered over multiple media through the course of the year, continuous tracking is better suited for establishing baselines, and capturing the ongoing nature of marketing activities and their impact in the marketplace.

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