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SECTION 1.3 PLANS FOR COLLECTION AND ANALYSIS OF DATA 9
AN ODNO,

(se) E ka )
6? JAdf, t 3
NM ILINL IE Ee
Efficiency < CA (AL IV

( 65 Mae ga )
where 6? — estimate of experimental error per observation, n — number of
subjects, C — cost of collecting data per subject, df — experimental error
degrees of freedom, and the subscripts designate the two experimental
designs (Federer, 1955, 13). If the ratio is less than one, the second design
is more efficient than the first. The converse is true if the ratio is greater
than one. The formula calls attention to four factors that are related to
the efficiency of experimental designs. Unfortunately, an experimental
design that is advantageous with respect to one factor may not be advan-
tageous with respect to the others. For example, if a design has the desirable
attribute of a small experimental error, it may have a high cost per subject
or a small number of degrees of freedom for experimental error, or it may
reguire a large number of subjects. The problem facing an investigator is
to select an experimental design that represents the best compromise
obtainable within the constraints of his research situation.

DETERMINATION OF SAMPLE SIZE

Once the independent and dependent variables are specified, the
number of subjects reguired for the experiment must be determined.
This is one of the more perplexing problems in experimental design. Five
factors must be considered in specifying a sample size that is adeguate for
testing a statistical hypothesis: (1) minimum treatment effects an experi-
menter is interested in detecting, (2) number of treatment levels, (3) popula-
tion error variance, (4) probability of making a type I error, and (S) prob-
ability of making a type II error. In general, the population error variance
is unknown. It may be possible to make a reasonable estimate of the popula-
tion error variance on the basis of previous experiments or a pilot study.
If the above information can be specified, the size of the sample necessary
to achieve a given power can be calculated. The power of a research
methodology is defined as the probability of rejecting the null hypothesis
when the alternative hypothesis is true. Power is egual to 1 — (probability
of committing a type II error).

The procedure described here for calculating power was developed
by Tang (1938). It assumes that the observations are normally distributed
with a common error variance <— o2. The parameter b is defined as

k
|xu; - p)'/k

be TT