be expected to be distributed.
The coefficients given in Table 2—i.e., 1, 2 and 3, are useful
for a quick approximation of the distribution intervals of the
population. However, since product developers typically work
with small size samples (n < 30), it is more relevant to use the
Student’s t-value5 associated with the sample size in place of
coefficients 1, 2 and 3. For example, for 95% with 10 volunteers,
the t-value equals 2.262 (see simulated example in Table 3).
In this example, 95% of consumers are expected to obtain
an SPF between 22.1 and 51.8 with product A and an SPF
between 25.1 and 42.3 with product B. Readers should note
that these distribution intervals (DI) do not draw conclusions
on the rankings of products, they only give the range of SPF
observed on the whole population of consumers sampled.
These intervals could change with an increase in the sample
size or a new test due to the changing average and/or SD.
Later, this article will show how to rigorously compare the
results of two products obtained from different tests or even
Confidence interval: To the product formulator, the CI of
SPF values gives an indication of the area in which the real
SPF is assumed to be, and can be used to estimate the real SPF
lower limit (to be used in product claims). CI represents the
95% Half Range (HR) and is also called the uncertainty (u). If
the same SPF investigation previously described is evaluated
with another set of volunteers, there is a 95% chance that the
result, as well as the real level of SPF, will be in the interval
given by the average + u; note that in the Colipa guidelines,
the letter c is used in place of u.
In in vivo SPF reports, the uncertainty value is expressed as
a percentage of the mean CI%; and since 95% is the confidence
level in this example, 17% is an acceptable level of the half
interval, expressed as a percentage of the mean SPF, per Colipa
guidelines. Another way to express this result is given by the
two limits of the CI—lower and upper.
Comparing SPF Variability
It is important that product developers compare the
variability of the results from testing two product samples to
choose the most appropriate test to compare their means, as
is explained further below. In order to compare the variability
of SPF products tested in vivo, or those assessed via different
methods—e.g., in vivo and in vitro, the SEM is provided and
is expressed as a percentage of the average (see simulated
example in Table 4).
In this example, the real level of SPF has a 95% probability
of being between 32.3 and 41.7 for product A, and between
31.0 and 36.4 for product B. For these two products, the CI
percentages—i.e., 12.7% and 8.1%—are acceptable since
both are less than 17%. Per the Colipa guidelines previously
described, to ensure a CI below 17%, the SEM for 10 volunteers
did not exceed 7.5%; 17% divided by the student’s t statistic for
9 degrees of freedom at a 95% confidence bilateral.
At this point, it is important to remember the difference
between the distribution and confidence intervals, i.e., the
DI and CI. The DI focuses on the individual values of SPF
that could be observed throughout the whole population—a
population that will never be known in its entirety. In addition,
176 | Cosmetics & Toiletries® magazine www.CosmeticsandToiletries.com
Vol. 126, No. 3/March 2011