When all four conditions are not met, researchers must use less powerful
tests known as nonparametric tests. Nonparametric statistics are used for in-
terval data that do not have a normal distribution or for data that are nominal
or ordinal in nature. Because these tests are considered to be less powerful, the
level of confidence nurses have about making inferences about the population
is not as strong as when parametric tests are used.
Another term used when talking about statistics is degrees of freedom.
Degrees of freedom (df), based on the number of elements in a sample, are
used to correct for possible underestimation of population parameters when
performing mathematical equations. Specifically, degrees of freedom refers to
the freedom of a variable’s score to vary given the other existing variables’
score values and the sum of these score values (df = N − 1) (Plichta & Kelvin,
2013). For example, suppose a data set consists of four scores: 1, 4, 4, and 7.
Before any of these scores were collected, the researcher did not know what
these scores would be. Each score was free to vary. This means that each score
was independent from the other scores. Because there are four scores, there are
four degrees of freedom. However, when the mean is calculated, one degree of
freedom is lost. This is because after the mean is known, along with three of
the scores, the fourth score is no longer free to vary. The fourth score can be
calculated, and only one value will be correct. Therefore, the data set of four
scores has three degrees of freedom, n − 1, because one degree of freedom is
lost. Many inferential statistics include degrees of freedom in their calculations.
Another concept important in the language of inferential statistics is sampling
distribution (Nieswiadomy, 2012; Plichta & Kelvin, 2013). In theory, an infinite
number of samples can be drawn from a population. Some samples are more
likely to be drawn than others are. For example, when sampling coin tosses, get-
ting half heads and half tails when tossing a coin 20 times is far more likely than
is tossing heads 20 times in a row. For many inferential tests, statisticians have
calculated the likelihood of obtaining different samples and reported them in
tables. When researchers perform certain inferential tests, they refer to these tables
to find out whether their results are likely or unlikely. Results that are unlikely
to occur as a result of chance are then considered to be statistically significant.
Nurses commonly see a number of inferential tests in the literature. Although
the study of statistical tests can seem overwhelming to some individuals, to
appraise evidence it might not be necessary to fully understand why each test
is conducted and how the calculations are performed. Nurses should be able to
discern that the correct tests were used to analyze data. This can be determined
by focusing on two broad questions: (1) “What type of question is being asked
by the researcher?” and (2) “What is the level of measurement being used to
measure the variables?” Some inferential statistical tests commonly used in
nursing research are listed in Table 13-12. Although it is beyond the scope of
KEY TERMS
nonparametric:
Inferential statistics
involving nominal-
or ordinal-level
data to make
inferences about
the population
degrees of
freedom: A
statistical concept
used to refer to the
number of sample
values that are free
to vary; n – 1
sampling
distribution:
A theoretical
distribution
representing an
infinite number of
samples that can
be drawn from a
population13.8 Using Statistical Tests to Make Inferences About Populations 363