Statistics (061541)
Introducing inference summary sheet
•
Inference is the drawing of conclusions from certain basic facts or premisses. In classical statistics,
the certain basic facts correspond largely to the sample data that we see, whereas the premisses
correspond to the mathematical model that we
believe
decribes the population (most of which
we don’t see), the sample data, and the relationship between the sample and the population.
•
The inferences that we make are generally not certain  i.e. we draw conclusions that are probably
true or probably false, or somewhere in between. One of our aims will be to quantify the validity
of the inference.
Terminology
•
A
population
is the group of people or objects of interest. It is common to call the people or
objects
units
or
subjects
.
•
A
sample
is the subset of the population actually examined.
•
A
simple random sample
(SRS) of size
n
consists of a subset of size
n
of the population, where
each unit has the same chance of being included in the sample (and indeed, every subset of size
n
has an equal chance of being included).
•
There are many other kinds of sample. In particular, the
stratified random sample
takes a SRS
from each of several strata. For example, one could take a SRS for men and for women. Quota
sampling is a further kind of sampling beloved of opinion pollsters. This kind of sample aims
deliberately to make the sample actually representative of the population.
•
Beware the many pitfalls involved in sampling. Ask yourself the questions (1) is the sample truly
random? (2) for surveys, is the wording of questions going to result in bias? (3) for voluntarily
completed questionnaires, will nonresponse lead to bias?
•
Randomisation
is essential not only as a guard against bias, but also because the process of
statistical inference
is the drawing of conclusions about the main population from the sample,
and this process depends upon the laws of
probability
, which describe
random behaviour
.
•
A
statistic
is a number that is calculated from the sample data, usually a summary. For example,
the sample mean and SD.
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 Spring '10
 Various
 Normal Distribution, Standard Deviation

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