DEFINITION OF BASIC TERMS 3

SECTION 1.2

run average of a random variable over an indefinite
number of samplings. The expected value [E(X J] of a discrete random variable X
is given by E(X) < ZXp(X) < mean of X. It should be noted from the above
definition that an expected value may be a value that the random variable could not

actually have.

Expected Value. The long-

Unbiased Estimator. An estimate of a parameter is said to be unbiased if its
expected value is egual to the parameter.

Research Hypothesis. A tentative theory or supposition provisionally adopted
to account for certain facts and to guide in the investigation of others. The terms
research hypothesis and scientific hypothesis may be used interchangeably.

Statistical Hypothesis. A statement about one or more parameters of a
population. Null and alternative hypotheses are two forms of a statistical hypothesis.

Null Hypothesis (H,). A statement concerning one or more parameters that
is subjected to statistical test.

Alternative Hypothesis (H,). The hypothesis that remains tenable when the

nuli hypothesis is rejected.

Statistical Test. A procedure whereby two mutually exclusive statistical

hypotheses are evaluated in the light of sample data. The hypothesis that dictates
the sampling distribution against which an obtained sample value is compared is

said to be the one tested.

Level of Significance (a). Probability of rejecting the null hypothesis when it is

true.

Type ! Error. Error that occurs when the experimenter rejects the null hypoth-
esis when it is true. The probability of committing a type 1 error is determined
by the level of significance (a) that the experimenter adopts.

Type ll Error. Error that occurs when the experimenter fails to reject the
null hypothesis when it is false. The probability (8) of committing a type lI error

is determined by the magnitude of the experimental effect, size of sample, magnitude

of random error, and level of significance.

Power of Test. Probability of rejecting t
hypothesis is true. If B is designated as the pro
power is egual to 1 — B.

Confidence Interval.
has some designated pro

Confidence Limits.
A set of outcomes ofa statistical test that leads to the rejection

he null hypothesis when the alternative '
bability of committing a type H error,

A range of values that, considering all possible samples,
bability of including the true population value.

Upper and lower boundaries of confidence interval.

Critical Region.
of the null hypothesis.

Replication. The collection of two or more observations under a set of

identical experimental conditions.

Degrees of Freedom (db). The number of independent observations for a source
of variation minus the number of independent parameters estimated in computing

the variation.

Experimental Error. Measure that includes all uncontrolled sources of
variation affecting a particular score.