380
11.4.3.3 Kaiser-Meyer-Olkin (KMO) and Bartlett’s Test
The KMO measures the sampling capability which should be greater than 0.5 for
acceptable factor analysis to proceed. If any pair of variables has a value less than
this, it may be considered the declining one of them from the investigation. The all
off-diagonal elements should be very Small (close to zero) in a good model. Looking
at the table below, the KMO measure shows values 0.359 for Patibania Island, 0.331
for Fredric Island and 0.361 for Henry’s Island after the calculation.
The Bartlett’s test is an additional indication of the power of the relationship
along with variables. These trials represent the null hypothesis that the correlation
matrix is a distinctive matrix. An identity matrix is the matrix in which all of the
diagonal elements are 1 and all off-diagonal elements are 0. For which one can
desire to reject this null hypothesis. From the same table (Table 11.9), one can see
that the Bartlett’s test of sphericity is significant, and at the same time its connected
probability is less than 0.05. In fact, it is actually measured for Patibania Island is
0.655, is 0.304 for Fredric Island and 0.457 for Henry’s Island; by which the significance level is small enough to reject the null hypothesis in this experiment
(Table 11.9).
11.4.3.4 Communalities
The next item from the output is a table of communalities which shows how much
of the ariance in the variables has been accounted for by the extracted factors. For
instance, over 93.5% of the variance in Hypersalinity is accounted for while 65% of
the variance in Human uses is accounted for Patibania Island. Similarly, over 95%
of the variance in Human Uses is accounted for while 74.5% of the variance in
Strom Effect is accounted for Fredric Island, and over 93% of the variance in
Sediment Deposition is accounted for while 73% of the variance in Land Erosion is
accounted for Henry’s Island (Table 11.10).
Table 11.9 KMO and Bartlett’s test for seven major factors of three sample islands
Tested substance
Patibania
Island
Fredrick
Island
Henry’s
Island
Kaiser-Meyer-Olkin measure of sampling adequacy
0.359
0.331
0.361
Bartlett’s test of
sphericity
Approx. Chi-square
17.903
23.782
21.037
df
21
21
21
Sig.
0.655
0.304
0.457
A.K. Paul et al.
11.4.3.3 Kaiser-Meyer-Olkin (KMO) and Bartlett’s Test
The KMO measures the sampling capability which should be greater than 0.5 for
acceptable factor analysis to proceed. If any pair of variables has a value less than
this, it may be considered the declining one of them from the investigation. The all
off-diagonal elements should be very Small (close to zero) in a good model. Looking
at the table below, the KMO measure shows values 0.359 for Patibania Island, 0.331
for Fredric Island and 0.361 for Henry’s Island after the calculation.
The Bartlett’s test is an additional indication of the power of the relationship
along with variables. These trials represent the null hypothesis that the correlation
matrix is a distinctive matrix. An identity matrix is the matrix in which all of the
diagonal elements are 1 and all off-diagonal elements are 0. For which one can
desire to reject this null hypothesis. From the same table (Table 11.9), one can see
that the Bartlett’s test of sphericity is significant, and at the same time its connected
probability is less than 0.05. In fact, it is actually measured for Patibania Island is
0.655, is 0.304 for Fredric Island and 0.457 for Henry’s Island; by which the significance level is small enough to reject the null hypothesis in this experiment
(Table 11.9).
11.4.3.4 Communalities
The next item from the output is a table of communalities which shows how much
of the ariance in the variables has been accounted for by the extracted factors. For
instance, over 93.5% of the variance in Hypersalinity is accounted for while 65% of
the variance in Human uses is accounted for Patibania Island. Similarly, over 95%
of the variance in Human Uses is accounted for while 74.5% of the variance in
Strom Effect is accounted for Fredric Island, and over 93% of the variance in
Sediment Deposition is accounted for while 73% of the variance in Land Erosion is
accounted for Henry’s Island (Table 11.10).
Table 11.9 KMO and Bartlett’s test for seven major factors of three sample islands
Tested substance
Patibania
Island
Fredrick
Island
Henry’s
Island
Kaiser-Meyer-Olkin measure of sampling adequacy
0.359
0.331
0.361
Bartlett’s test of
sphericity
Approx. Chi-square
17.903
23.782
21.037
df
21
21
21
Sig.
0.655
0.304
0.457
A.K. Paul et al.