**Exhibit 33.6** 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 n_{1}
and n_{2}, with success probability of success, p_{1} and p_{2}, is:

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

This has an upper bound of 0.5√(1/n_{1}+1/n_{2}) .
If n_{1} = n_{2} = n (equal sample sizes), this becomes 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 *p*_{1} = p_{2} = 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 33.6.

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 market place.

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