occur if the null hypothesis were true. Observed and expected frequencies are
entered into contingency tables, and a Chi-square statistic is calculated. Using
the calculated Chi-square statistic, the degrees of freedom, and the alpha level,
researchers consult Chi-square tables to determine the critical value and judge
whether the critical value is statistically significant. In the literature, notations
for Chi square, such as X^2 = 1.89, df = 1, p < .05, appear reported with de-
grees of freedom and significance. Another reason Chi squares are frequently
used is that they can be calculated without the use of computers. However,
the sample size must be adequate because there must be at least five or more
observed frequencies in each cell of the table. If this minimum is not met, then
a variation of the Chi square, known as Fisher’s exact probability test, is used.The t Statistic
The t statistic is another inferential statistical test that is frequently reported in
nursing research. Commonly known as the t test, or Student’s t test, this para-
metric measure is used to determine whether there is a statistically significant
difference between two groups (Hayes, 1994; Plichta & Kelvin, 2013).
There are two variations of the t test. One variation, known as the correlated
t test or paired t test, is used when there are only two measurements taken on
the same person (one group) or when the groups are related. For example, a
paired t test would be used to assess for differences between subjects’ morn-
ing and evening blood pressure readings. The other variation is known as an
independent t test and is used when data values vary independently from
one another.
In experimental and quasi-experimental designs, the t test is used to determine
whether the means of two groups are statistically different. Suppose a researcher
is measuring the effectiveness of applying ice for pain reduction in patients
with a new cast applied for fracture of the tibia. The mean pain intensity rating
for the experimental group, which received the ice application, is 5.6, whereas
for the control group, which did not get the ice, it is 6.0. As with a Chi-square
test, researchers calculate the t statistic and consult tables using the statistic,
degrees of freedom, and alpha levels to find the critical value. The critical value
is obtained and a decision about its statistical significance is made. In reports,
the t test information provided includes t, indicating the statistical test done,
number of degrees of freedom, actual t value obtained, and significance level,
which is reported in the following manner: t(2)= 2.54, p < .01.Analysis of Variance
Analysis of variance (ANOVA) is used when the level of measurement is in-
terval or ratio and there are more than two groups or the variable of interest isKEY TERMS
t statistic:
Inferential
statistical test to
determine whether
a statistically
significant
difference between
groups exists
correlated t test:
A variation of the
t test used when
there is only one
group or when
groups are related;
paired t test
independent t test:
A variation of the
t test used when
data values vary
independently from
one another
analysis of
variance: Inferential
statistical test used
when the level of
measurement is
interval or ratio
and more than two
groups are being
compared366 CHAPTER 13 What Do the Quantitative Data Mean?