Introduction to Human Nutrition

Nutrition Research Methodology 307

tabulated as proportions within categories or ranks.
Continuous variables, such as age and weight, are
customarily presented by summary statistics describ-
ing the frequency distribution. These summary statis-
tics include measures of central tendency (mean,
median) and measures of spread (variance, standard
deviation, coeffi cient of variation). The standard
deviation describes the “spread” or variation around
the sample mean.

Hypothesis testing

The fi rst step in hypothesis testing is formulating a
hypothesis called the null hypothesis. This null
hypothesis can often be stated as the negation of the
research hypothesis that the investigator is looking
for. For example, if we are interested in showing that,
in the European adult population, a lower amount
and intensity of physical activity during leisure time
has contributed to a higher prevalence of overweight
and obesity, the research hypothesis might be that
there is a difference between sedentary and active
adults with respect to their body mass index (BMI).
The negation of this research hypothesis is called the
null hypothesis. This null hypothesis simply main-
tains that the difference in BMI between sedentary
and active individuals is zero. In a second step, we
calculate the probability that the result could have
been obtained if the null hypothesis were true in the
population from which the sample has been extracted.
This probability is usually called the p-value. Its
maximum value is 1 and the minimum is 0. The
p-value is a conditional probability:

p-Value = prob(differences ≥ differences found |

null hypothesis (H 0 ) were true)

where the vertical bar (|) means “conditional to.” In a
more concise mathematical expression:

p-Value = prob(difference ≥ data | H 0 )

The above condition is that the null hypothesis was
true in the population that gave origin to the sample.
The p-value by no means expresses the probability
that the null hypothesis is true. This is a frequent
and unfortunate mistake in the interpretation of
p-values.
An example of hypothesis testing is shown in
Box 13.1. Hypothesis testing helps in deciding whether
or not the null hypothesis can be rejected. A low p-
value indicates that the data are not likely to be com-

patible with the null hypothesis. A large p-value

indicates that the data are compatible with the null

hypothesis. Many authors accept that a p-value lower

than 0.05 provides enough evidence to reject the null

hypothesis. The use of such a cut-off for p leads to

treating the analysis as a decision-making process.

Two possible errors can be made when making such

a decision (Table 13.2).

A type I error consists of rejecting the null hypoth-

esis, when the null hypothesis is in fact true. Con-

versely, a type II error occurs if the null hypothesis is

accepted when the null hypothesis is in fact not true.

The probabilities of type I and type II errors are called

alpha (α) and beta (β), respectively.

Power calculations

The power of a study is the probability of obtaining

a statistically signifi cant result when a true effect of a

specifi ed size exists. The power of a study is not a

single value, but a range of values, depending on the

Table 13.2 Right and wrong decisions in hypothesis testing

Truth (population)

Decision Null hypothesis Alternative hypothesis

Null hypothesis Right decision

(probability = 1 – α)

Type II error

(probability = β)

Alternative

hypothesis

Type I error

(probability = α)

Right decision

(power = 1 – β)

Box 13.1 Example of hypothesis testing

Among a representative sample of 7097 European men, the

authors found that each 10 unit increase in the leisure-time physi-

cal activity was associated with −0.074 kg/m^2 in BMI. Physical

activity was measured in units of MET-hours/week (1 MET-hour is

the energy expenditure during 1 resting hour).

What is the probability of fi nding, in such a sample, a BMI

0.074 kg/m^2 lower (or still lower) for those whose energy expendi-

ture is 10 MET-hours higher, if the actual difference in the whole

European population were 0? This probability is the p-value;

the smaller it is, the stronger is the evidence to reject the null

hypothesis.

In this example, the p-value was 0.001, i.e., chance would

explain a fi nding like this, or even more extreme, in only 1 out of

1000 replications of the study. The conclusion is that we reject the

null hypothesis (population difference in BMI = 0) and (provision-

ally) accept the hypothesis that states that lower physical activity

during leisure time is associated with a higher BMI. We call this the

alternative hypothesis.