Descriptive Statistics - Numbers used to describe information or
data or those techniques used to calculate those numbers.
Inferential Statistics - A procedure used to estimate parameters
(characteristics of populations) from statistics (characteristics of samples).
Population - All subjects or objects possessing some common
specified characteristic. The population in a statistical investigation is arbitrarily
defined by naming its unique properties.
Parameter - A measurable characteristic of a population (µ).
Sample - A smaller group of subjects or objects selected from a
large group (population).
Statistic - A measurable characteristic of a sample (x, s).
Variable - A characteristic of objects or subjects that can take
on different values.
Qualitative Variables - Characteristics which vary in quality or
Quantitative Variables - Characteristics which vary in quantity,
amount, or size.
Independent Variables - Characteristics which affect or cause
the outcome of the experiment but do not measure the results.
Dependent Variables - Characteristics which measure the effects
or results of the experimental treatment or independent variable.
Predictor Variables (x) - Measurable characteristics from which
the criterion variable (y) can be estimated.
Levels of Measurement
Nominal Scale - This simplest type of scale provides the
lowest level of quantification of the objects to be measured. A nominal scale simply sorts
objects or classes of objects into mutually exclusive categories. The number simply names
or categorizes the objects or subjects.
Ordinal Scale - Permits the sorting of objects or classes of
objects on the basis of their standing relative to each other. This scale not only
categorizes but also ranks the objects on the basis of some criterion.
Interval Scale - Indicates the exact relative position of
individuals because this type of scale uses predetermined equal intervals.
Ratio Scale - Highest level of measurement. In addition to
having equal intervals, a ratio scale measures from an absolute zero.
Hypothesis - A supposition (an educated guess) presumed to be true
for the sake of subsequent testing. In educational research, hypotheses concern the
existence of relationships between variables.
Statistical Hypothesis (Ho: Null Hypothesis) - States that there
is no (null) relationship between the variables under analysis.
Research Hypothesis (Ha: Alternative Hypothesis) - A positive
statement of the null hypothesis. It states that there is a relationship between the
variables under analysis.
Probability (p) - The chance of something happening under certain
conditions. In other words, it is the likelihood of the occurrence of any particular form
of an event, estimated as the ratio of the number of ways in which that form might occur
to the whole number of ways in which the event might occur in any other form.
Example: If an event can happen in "s" ways and fail
to happen in "f" ways, and if each of these s + f ways is equally likely to
occur, the probability of success in a single trial is p = s / (s+f)
When a statistical test reveals that the probability is rare that a set
of observed sample data is attributable to chance alone, this result is labeled as
statistically significant. If two groups are so different that only one time in 1000 would
we find such a difference by chance alone, the difference would be statistically
significant. By statistically significant, it is meant that the observed phenomenon
represents a significant departure from what might be expected by chance alone.
The level of significance (alpha) is the probability of a Type I error
that an investigator is willing to risk in rejecting a null hypothesis. Generally, it
refers to the probability of the event occurring due to chance. If alpha = .01, it is
likely that one time out of a hundred the event could occur due to chance. If you lower
the significance level from .05 to .01, you decrease the probability of rejecting a true
hypothesis but increase the probability of accepting a false hypothesis. A Type II error
(beta) occurs when an investigator fails to accept the alternative hypothesis when in fact
the alternative hypothesis was true. In other words, the null hypothesis was accepted when
it was not true.