is the difference of
and
, and
…
represents
the total of each row or column.
Here, analysis of variance (ANOVA) was used to
assess the significant differences in the assessment
scores of the stimuli. The ANOVA results for the
“Ruins” sequence are shown in Table 2. The sum of
squares, degrees of freedom, and mean squares were
calculated for each factor (Fukuda, 2009). The
score is a statistical value for the F-test, and it is
obtained by dividing the mean square of a specific
factor and that of the residual factor. Further,
%
is
a critical F value for the 1% significance level. If
of the stimuli factor is greater than
%
, there is a
significant difference in the assessment scores of
stimuli. Here,
of the stimuli factor is
582.96
%
4.881. Thus, a 1% significant
difference between the stimuli is observed. Owing to
space limitations, the results for the other test
sequences cannot be shown, but all the ANOVA
results are the same in that there are significant
differences for the stimuli factor.
The significant differences in each pair of stimuli
were assessed because the ANOVA results
guarantee the significant differences of least one of
the pairs of stimuli. The yardstick values α for each
stimulus are calculated by
/2, where
is the number of observers (30) and N is the
number of stimuli (3). The yardstick values for the
“Ruins” sequence are shown in Figure 11. In Figure
11, the horizontal axis is the yardstick value, and the
marks (rhombus, square, and triangle) show the
values of each stimulus. Higher values indicate
higher assessment. The values on the arrows show
the differences between the stimuli. A critical value
of the difference in yardstick values with
significance level is calculated as follows:
Y
2
,
(1)
where
is the mean square of the residual factor
(0.26), as shown in Table 2. Further, is obtained
from the Student’s t-distribution with the degrees of
freedom for the residual factor (89) and number of
stimuli N (3). Let significance level be 0.01. Then
4.282, and thus,
.
0.164. If the difference
in yardstick values is greater than
.
, there is a
significant difference between the yardstick values.
In the results of the “Ruins” sequence, the yardstick
values in Figure 11 are the highest for NLSP, SRR,
and Lanczos, in that order. The differences in the
yardstick values of adjacent stimuli, NLSP with
SRR (α
NLSP
α
SRR
), and SRR with Lanczos (α
SRR
α
Lanczos
) are as follows:
α
α
1.60Y
.
(2)
α
α
0.00Y
.
(3)
Because α
NLSP
α
SRR
is greater than
.
, a 1%
significant difference between NLSP and SRR is
observed. The value of α
SRR
α
Lanczos
is not greater
than
.
, and thus, a significant difference between
SRR and Lanczos is not guaranteed. The asterisks
(**) in Figure 11 indicate 1% significant differences
between the stimuli. The significance level of the
difference is the error decision probability. The
complement value 99% to “**” is the probability of
the difference. Thus, a quality difference practically
exists with a 99% probability. All results have
similar tendencies; NLSP has the highest evaluation,
and there are significant differences between NLSP
and SRR as well as NLSP and Lanczos in all cases.
Significant differences between SRR and Lanczos
are obtained for “Plaza,” “Castle,” and “Cathedral.”
The results of experiment 2-B were analyzed in the
same way as those of experiment 2-A. As the
ANOVA results, the 1% significant difference
between the stimuli is observed in all test sequences.
Figure 12 show the results of yardstick values for the
“Ruins” sequence. All the results are similar to those
of experiment 2-A. The yardstick values of NLSP
are the highest of all stimuli in all cases. The
significant differences are revealed between NLSP
and the other two stimuli, SRR and Lanczos.
Significant differences between SRR and Lanczos
are obtained for “Bricks” and “Castle.”
5.3 Discussion
As a result of experiment 1, a quality difference in
resolution with and without NLSP was observed.
The reproducibility of the results was proven, and
thus, the effect of NLSP on 4K TV sets is
guaranteed. In experiment 2, the superiority of
NLSP is proven from the results of two experiments
with the same and different displays. The same
results were obtained regardless of the different
displays. The quality differences between SRR and
Lanczos are too small to guarantee because they
depend on the display and sequence. The essential
limits of the ability of SRR to improve the resolution
of the TV content were discussed (Mori, 2016), and
the results of the experiments are consistent with
these discussions. All the results prove its
reproducibility, regardless of the different displays.
Figure 10: Assessment results (experiment 1 Cherry tree).