308 Introduction to Human Nutrition

assumption about the size of the effect. The plot of
power against size of effect is called a power curve.
The calculations of sample size are based in the prin-
ciples of hypothesis testing. Thus, the power of a
study to detect an effect of a specifi ed size is the com-
plementary of beta (1 − β). The smaller a study is, the
lower is its power. Calculation of the optimum sample
size is often viewed as a rather diffi cult task, but it is
an important issue because a reasonable certainty that
the study will be large enough to provide a precise
answer is needed before starting the process of data
collection (Box 13.2).
The necessary sample size for a study can be
estimated taking into account at least three inputs:

● the expected proportion in each group and, conse-

quently, the expected magnitude of the true effect

● the beta error (or alternatively, the power) that is

required

● the alpha error.

The p-value has been the subject of much criticism

because a p-value of 0.05 has been frequently and

arbitrarily misused to distinguish a true effect from

lack of effect. Until the 1970s most applications of

statistics in nutrition and nutritional epidemiology

focused on classical signifi cance testing, involving a

decision on whether or not chance could explain the

observed association. But more important than the

simple decision is the estimation of the magnitude of

the association. This estimation includes an assess-

ment about the range of credible values for the asso-

ciation. This is more meaningfully presented as a

confi dence interval, which expresses, with a certain

degree of confi dence, usually 95%, the range from the

smallest to the largest value that is plausible for the

true population value, assuming that only random

variation has created discrepancies between the true

value in the population and the value observed in the

sample of analyzed data.

Options for statistical approaches to

data analysis

Different statistical procedures are used for describing

or analyzing data in nutritional epidemiology (Table

13.3). The criteria for selecting the appropriate

procedure are based on the nature of the variable

considered as the outcome or dependent variable.

Three main types of dependent variable can be

considered: quantitative (normal), qualitative (very

often dichotomous), and survival or time-to-event

variables.

Within bivariate comparisons, some modalities

deserve further insights (Table 13.4).

The validity of most standard tests depends on the

assumptions that:

● the data are from a normal distribution

● the variability within groups (if these are com-

pared) is similar.

Tests of this type are termed parametric and are to

some degree sensitive to violations of these assump-

tions. Alternatively, nonparametric or distribution-

free tests, which do not depend on the normal

Box 13.2 Example of sample size calculation

Let us suppose that we want to compare the proportion of subjects

who develop a given outcome depending on whether they have

been assigned to diet A or diet B. We expect that 5% of subjects in

the group assigned to diet A and 25% of those assigned to diet B

will develop the outcome of interest. We are willing to accept a

type I error with a 5% probability and a type II error with a 10%

probability. A simplifi ed equation* for sample size (n) calculation

would be:

n

zzpq

pp

n

AB

=

()+

()−

=()+ ××

()−

αβ 2

2

2

2

2

1 96 1 28 2 0 15 0 85

005 025

.. ..

..^22

n= 65

where zα/2 and zβ are the values of the normal distribution corre-

sponding to alpha 0.05 (zα/2 = 1.96) and beta 0.10 (zβ = 1.28),

PA and PB are the expected proportions, p is the average of both

proportions (0.05+0.25/2 = 0.15) and q = 1 − p. Therefore, in this

example:

zα/2 = (^) 0.05 (^) (two tailed) = 1.96
zβ = (^) 0.10 (one tailed) = 1.28
pA = 0.05 (q 1 = 0.95)
pB = 0.25 (q 2 = 0.75)
These values are substituted in the equation and thus the required
sample size for each group is obtained (65). Therefore, we shall
need 130 participants, 65 in each group.
*When the outcome is a quantitative variable, sample means (xA
and xB) replace proportions in the denominator, while the product
terms pAqA and pBqB are replaced by the respective variances (s^2 ) of
the two groups in the numerator:
n
zzSS
xx
AB
AB

()+ ⎣ +⎡ ⎤⎦
()−
αβ 2
(^222)
2