## 3.5 Chance and variation in the response

*Natural* (chance) variation refers to variation that
cannot otherwise be explained:
even repeating a study exactly the same way every time
will not always produce the same values of the response variable.
This is called *natural variation*, *chance variation*, or just *chance*.

Natural variation makes
the influence of the explanatory variable
(which we are wanting to study)
hard to detect,
so minimising chance variation is important.
*Minimising the amount of the chance variation*,
requires using good design principles,
and measuring as many other extraneous variables
that may explain variation in the response variable
as is reasonable.

Chance can impact the values of the response variable in different ways:
each *individual* can produce different values of the response variable
each time the individual repeats the study
(*within*-individuals variation);
each individual in the study can produce different values of the
response variable compared to *other* individuals
(*between*-individuals variation):

- To estimate the amount of variation
*within*individuals: Many observations are needed from each unit of analysis (individual). - To estimate amount of variation
*between*individuals: Many units of analysis (individuals) are needed.

Since *between*-individual variation is usually more variable than the
*within*-individual variation,
using *many* individuals
is usually more important than
using a smaller number of individuals many times.

**Lemma 3.2 (Chance) **Consider the letter-typing study (Example 2.4) again.
What are the advantages and disadvantage of:

- measuring one female 30 times?
- measuring 30 different females once each?
- measuring 10 different females three times each?