Measurement and Statistical Terms and Their Definitions

Measurement and Statistical
Terms and Their Definitions
Stephen D. Lapan
April 2006
1. Variable- Anything on which humans can vary or can score in a
different way from one another
2. Dependent or correlated sample- Sample not drawn randomly where
there is no assumption of an equal chance to be selected
3. Independent or uncorrelated sample- Every participant in a given
population has an equal chance of appearing in the sample
4. Stratified sample- Usually randomly drawn but from predefined
substrata to be representative of important population characteristics
related to a study (e.g., rural, urban, suburban; high, medium, low
5. Convenience sample- Selecting study participants based on
availability geographically or due to volunteerism; not consider
appropriate under most circumstances
6. Purposeful sample- Participants selected, usually in interpretive
studies, who represent information-rich sources (e.g., person who
started the program, parents also working in the program)
7. Dependent variable- the variable at the end of the equation to change
as a result or outcome of some treatment, cause, or relationship,
sometimes called criterion variable
8. Independent variable- The treatment variable or variable manipulated
or expected to make a difference in the outcome or dependent
measure/variable. Usually classified as a treatment or moderator
variable and sometimes called a predictor variable
9. Nominal or dichotomous scale or variable- Labels or category names
(gender, sports jersey numbers)
10.Ordinal or ranked scale or variable- Objects or subjects are rated low
to high without being able to determine distance between each rank .
or scale point (e.g., Likert: strongly disagree= 1 to strongly agree= 5,
if other 1-n labels called “Likert-type”)
11. Interval scale or variable- Objects or subjects are ranked from low to
high and distance between each scale point is known (tests,
performance measures)
12.Ratio scale or variable- Objects or subjects are ranked from low to
high, distances between each scale point are known, and an absolute
zero point can be determined so that a score of 100 may be considered
twice that of 50 (weight, speed, time)
13. Rating scales- Instruments devised to measure the extent of some
phenomenon in some “Likert” way (see #10) or using Semantic
Differential (adjective pairs Love_ _ _Hate, Heavy_ _ _Light),
Thurstone (fully identified scale points), or Guttman (accumulative
scale points)
14.Coefficient- a score produced on a scale of +1.00 to -1.00 that
represents the relationship between two or more variables for a group
of subjects including but not limited to reliability coefficients,
correlation coefficients, predictor-criterion coefficients, and
coefficients of determination (r , square of a correlation to indicated
share variance)
15. t-test- Statistical test used when determining the difference between
two measures on one group or differences between two groups. Used
much less that in the past; replaced by structural equations (e.g.,
16. ANOVA- Analysis of Variance used when determining the statistical
difference between more than two groups. Repeated ANOVA’s are
used when groups are not randomly selected/assigned or ANCOVA
(Analysis of Covariance) to statistically equate dependent samples on
pretests before comparing on posttests
17. Factorial ANOVA- Determining statistical difference between more
than two groups involving at least one manipulated variable and one
or more moderator variables. MANOVA is used when more than one
dependent variable is included in this arrangement and MANCOVA
again to equate pretests for dependent samples
18. Degrees of freedom- Freedom to vary so that after a sample of N= 1
is drawn, each additional sample member has the opportunity to be
different than the first or variation in result found from the first N.
Thus, the degree to which a sample is free to vary is N-1. Moving
down the left hand column of a probability table, the researcher
selects the row that represents the number of subjects in the study
minus one (some use the more conservative N-2)
19. Probability- Refers to sampling or chance of error (p= .01, p< .01,
etc.). A probability sample is one drawn randomly so that every
individual in the population has an equal chance of appearing in the
sample. A probability table is used to determine the extent a particular
statistic produced in a study is considered statistically significant (e.g.,
p< .05). Also called alpha levels or levels of significance where the
figure (.10, .05, .01, .001, etc.) refers to chances out of 100 or lower
(<) that the relationship (r= correlation) or difference ( e.g., ANOVA
or F) occurred by accident or chance
20. Level of significance or p value- See Probability above
21. Type I error- It is considered a research error of judgment combined
with poor sampling that results in rejecting a null hypothesis (Ho=
there is no significant relationship or difference) when the researcher
should not have rejected it. That is, determining there is a significant
relationship or difference when it is not warranted. This is ordinarily
accomplished by setting an alpha to high, meaning setting the
standard too low (e.g., p= .10). This also can result from the use of a
less powerful statistical test such as a nonparametric measure.
22. Type II error- Setting the alpha level to low, meaning setting the
standard too high (e.g., p=.01) where it is not warranted thus failing to
reject the Ho when it should have been rejected. The researcher is
doomed to commit one error or the other. Thus, the less likely you are
to commit a Type I, the more likely you are to commit a Type II.
Special note: Avoiding Type I errors is usually accomplished by using more
powerful statistical tests and using a representative sample. But, it is also
necessary to determine which error you would prefer to commit. Is new
territory under investigation where exploratory efforts are warranted and
thus any pattern of significance should be considered grounds for rejecting
the Ho? Therefore, you would prefer to commit a Type I error. Or, is this a
well-studied topic that needs more convincing confirmation, therefore
requiring more restrictive standards for significance and increasing the
likelihood of committing a Type II error? A researcher chooses to take the
chance of making one error or the other in reasoning how to set alpha levels
(see chart).
Incorrectly Reject
Incorrectly Accept
Type I
Type II
Low Consequences
of finding significance
Rarely studied
Some study