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Stat 211 Prof Parzen CHAPTER 1
STATISTICAL DATA ANALYSIS
Statistical methods seek to learn patterns from a data set
by computing, comparing,
and interpreting
statistical summaries, including mean, median, quartiles, mid-
quartile, inter-quartile range, standard deviation, box plot, QQ quantile plot, scatter
diagram.
1.1
DATA, VARIABLES, QUANTITATIVE, CATEGORICAL, FREQUENCY
By data or a sample we mean a set of n observations or measurements , denoted by
capital letters X or Y with subscripts (for example
1
,
,
n
Y
Y
⋯
or X_1,…,X_n). We
assume data
to be observations on a variable (denoted
by capital letters
,
,
Y X
etc.)
which represents a population which was sampled to collect the data.
HISTORY: A fascinating story
can be told about the first published example of a
statistical data analysis by John Graunt
around 1660
DESIGN OF DATA COLLECTION:
Statisticians
distinguish between
(1) random samples which are representative of a population, and
(2) samples from volunteers (called convenience samples) which may not yield
conclusions valid about a population because the sample is not representative of the
population.
EXAMPLE: To collect data on opinions of workers in a factory one could (1)
randomly select a sample of workers to interview from a complete list of workers,
(2) use as a sample workers who sign up on a list osted on a bulletin board
requesting volunteers for the survey.
EXAMPLE:
A
grocery store company asks a consultant
to estimate how much
money is lost by an average grocery store
due to shoplifting by choosing
(by
statistical random methods) a representative sample
rather than conveniently
choosing
a few local
grocery stores who are asked to report their
losses due to
shoplifting.
Statisticians
distinguish between (1) data from experiments, and (2) data from
observational studies.
One often observes two groups: (1) control group, (2)
treatment group.
An experiment is called (1) blind
if subjects do not know which
group they are in, (2) double blind if both subjects and investigators do not know
whether a subject is in the treatment or control (placebo) group.
EXAMPLE: Does earting dark cholate lower blood pressure
in men? Two large
groups of men are entrolled in an experiment for many months. Control group eats