Civil Engineering Reference
In-Depth Information
Fig. 8.18
Average and 95 %
lognormal confidence interval
of equivalent circular grain
size at three locations for
the as-received material in
orientation 3
The first was a two-sample
t
test with unequal sample sizes and variances
(Welch's
t
test) to verify whether the population means are equal. The test pro-
vides a
p
-value which can be compared to a level of significance. The
p
-value for
this test is calculated by using the Student's
t
distribution.
The second test is to examine the variance of two data sets to verify that they
are equal. To perform this, both the Levene test and Bartlett test were performed
and the average result is provided. The Bartlett test was designed for a nearly
normal distribution where the distribution does not affect the result of the Levene
test [
8
].
8.3.2 Summary of Statistical Analysis of Micrographs
This section provides a statistical comparison between all the samples studied in
this section, and a summary of the samples examined is provided in Table
8.6
. As
seen, there are a total of 18 samples which contain microstructure images for the
as-received material, room temperature deformation, EAF square wave testing,
EAF continuous wave testing, and incremental EAF tests. This section only con-
tains a representative analysis of these samples. For a full summary and analysis,
refer to work by Jones [
9
]. To compare the micrographs, the two-sample t test is
used to determine whether the measured means are statistically equivalent and the
Levene/Bartlett tests are used to conclude whether the grain size measurements
have equal variances. The results from these tests are summarized for all sam-
ples although not all samples are directly comparable (i.e., specific comparisons
are made for select samples in the below discussion). When comparing the micro-
graphs of the samples, orientations 1 and 2 were only examined as orientations
2 and 3 have the same axial elongation (i.e., orientations 2 and 3 are equivalent).
Hence, orientation 1 and orientation 2 are compared across all samples separately.
The average equivalent circular grain size for all samples in orientation 1
is given in Fig.
8.19
along with a 95 % lognormal confidence interval. As seen,
