Statistical Analysis for Education and Psychology Researchers

from a defined population with a view to describing prevalence (total number of
occurrences), incidence rate (new occurrences in specified time period) or, for example,
what subjects think or feel about an issue, such as the Gallup Polls. In an explanatory
survey the purpose and subsequent analysis would focus on explaining interrelationships
between or among phenomena.

Sampling

Selection of a sample is an integral part of most survey designs. Samples may be
characterized as one of two main types, probability samples, sometimes called random
samples, where every member of the population has some probability of being selected
for the sample (not necessarily equal probability) and non-probability samples in which
some section of the population may not be represented (non-random). Statistical
techniques for estimating precision of sample statistics which are based on probabilistic
reasoning should be used cautiously with non-probability samples. Examples of non-
probability sampling approaches include:

• Convenience subjects selected on basis of availability


• Quota subjects sampled in proportion to population proportions on key variables


• Purposive subjects selected on the basis that they are known to have certain attributes


• Dimensional subjects selected to represent similar or dissimilar
  dimensions


• Snowball subjects identified by sample members


• Critical case subjects selected that will give an overall assessment

The degree of representativeness of a sample depends upon how the sample is selected. If
the population was not carefully specified or a non-probability sampling procedure was
used then a non-representative sample may be drawn and one’s confidence in estimating
characteristics of the target population from the selected sample would be limited.
Survey and correlational studies are generally characterized by the absence of planned
change and control of variables. They cannot therefore show cause-effect relationships.
In these studies variables are not manipulated and it is unwise to attribute causality to
variables that change jointly or covary. Variables are said to covary if, say, high values
on variable ‘A’ are associated with (but do not cause) high values on another variable ‘B’
or, alternatively, if lower values on variable ‘A’ are associated with (but do not cause)
higher values on variable ‘B’. Correlation is a special case of covariation when the
degree of relationship between two variables is expressed on a common scale of
measurement or standard scores (see Chapters 7 and 8). If values of two variables covary
in survey and correlational designs then the relationship is said to be concomitant rather
than causal. Covariation of two variables in surveys could be attributed to a common
third variable, the effect of a number of confounding variables or causation. Only an
experimental design would be able to establish causation as an explanation for the
observed covariation. Correlational surveys are designed with the specific purpose of
gaining insight into the extent of the relationship between two or more quantifiable
variables and in this sense are distinct from typical self-report questionnaires or
observational studies. If variables are found to be related or correlated then scores on one
variable may be used to predict scores on another variable. This would be an example of

Statistical analysis for education and psychology researchers 8