Galton's problem, named after Sir
Francis Galton
Sir Francis Galton, FRS FRAI (; 16 February 1822 – 17 January 1911), was an English Victorian era polymath: a statistician, sociologist, psychologist, anthropologist, tropical explorer, geographer, inventor, meteorologist, proto- ...
, is the problem of drawing inferences from
cross-cultural Cross-cultural may refer to
* cross-cultural studies, a comparative tendency in various fields of cultural analysis
* cross-cultural communication, a field of study that looks at how people from differing cultural backgrounds communicate
*any of va ...
data, due to the statistical phenomenon now called
autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable ...
. The problem is now recognized as a general one that applies to all nonexperimental studies and to
experimental design
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...
as well. It is most simply described as the problem of external dependencies in making statistical estimates when the elements sampled are not
statistically independent.
Asking two people in the same household whether they watch TV, for example, does not give you statistically independent answers. The sample size, ''n'', for independent observations in this case is one, not two. Once proper adjustments are made that deal with external dependencies, then the axioms of probability theory concerning statistical independence will apply. These axioms are important for deriving measures of
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of number ...
, for example, or tests of
statistical significance
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the p ...
.
Origin
In 1888, Galton was present when Sir