The Discriminant Analysis Approach for Evaluating Effectiveness of Learning in an Instructor-Led Virtual Classroom

D. Magdalene Delighta Angeline; P. Ramasubramanian; I. Samuel Peter James

doi:10.21307/ijssis-2020-035

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The Discriminant Analysis Approach for Evaluating Effectiveness of Learning in an Instructor-Led Virtual Classroom

International Journal on Smart Sensing and Intelligent Systems

Volume 13 (2020): Issue 1 (January 2020)

By: D. Magdalene Delighta Angeline, P. Ramasubramanian and I. Samuel Peter James

Open Access

|Dec 2020

Figures & Tables

Analysis of learning with various approaches.

Overall percentage of cognitive skills when applied with various learning approaches in an instructor-led virtual classroom.

Table 1.

Discriminant analysis for performance.

Sample summary	Sample size	Internal 1 mean	Internal 2 mean	Attendance mean
Average	5	54	51.2	89
Good	11	78	77	90.54545455
Poor	5	19.4	25.2	73.8

Table 2.

Classification matrix.

Classification matrix	Average	Good	Poor	Correct
Average	5	0	0	100
Good	3	8	0	72.7272727
Poor	1	0	4	80

Table 3.

Matrix of variance and covariance.

Matrix of vars and covars	PA 1	PA 2	Attendance
Average
PA 1	126.5	243.5	96.5
PA 2	243.5	472.7	178
Attendance	96.5	178	100.5
Good
PA 1	258	163.6	10.4
PA 2	163.6	152.2	7
Attendance	10.4	7	22.27273
Poor
PA 1	237.8	190.4	126.85
PA 2	190.4	268.7	107.8
Attendance	126.85	107.8	92.2
Pooled
PA 1	224.289	187.31	55.41111
PA 2	187.311	249.31	67.4
Attendance	55.4111	67.4	55.19596

Table 4.

Summary classification.

Correct	81.0%
Base	52.4%
Improvement	60.0%

Statistical distance of each observation to the mean vector.

Comparison of the final outcome with periodical assessment.

Table 5.

Summary statistics.

Variable	Categories	Frequencies	%
Predicted performance	Average	68	34.171
	Good	62	31.156
	Poor	69	34.673

Table 6.

Summary statistics (validation).

Variable	Categories	Frequencies	%
Predicted performance	Average	0	0.000
	Good	0	0.000
	Poor	1	100.000

Table 7.

Sum of weights and prior probabilities for each class.

Class	Sum of weights	Prior probabilities
Average	68.000	0.342
Good	62.000	0.312
Poor	69.000	0.347

Table 8.

Mahalanobis distances.

Class	Average	Good	Poor
Average	0	1,526.947	1,257.661
Good	1,526.947	0	2,554.130
Poor	1,257.661	2,554.130	0

Table 9.

Generalized squared distances.

Class	Average	Good	Poor
Average	2.147594	1,529.279	1,259.779
Good	1,529.094	2.332341	2,556.248
Poor	1,259.809	2,556.462	2.118397

Table 10.

Fisher distances.

Class	Average	Good	Poor
Average	0	6.580	5.723
Good	6.580	0	11.082
Poor	5.723	11.082	0

Table 11.

P values for Fisher distances.

Class	Average	Good	Poor
Average	1	0.021	0.028
Good	0.021	1	0.006
Poor	0.028	0.006	1

Table 12.

Wilks’ Lambda test (Rao’s approximation).

Lambda	0.000
F (observed value)	7.018
F (critical value)	2.551
DF1	384
DF2	10
P value	0.001
alpha	0.05

Table 13.

Pillai’s trace.

Trace	1.992
F (observed value)	7.610
F (critical value)	2.310
DF1	384
DF2	12
P value	0.000
alpha	0.05

Table 14.

Hotelling–Lawley trace.

Trace	596.480
F (observed value)	7.256
F (critical value)	3.923
DF1	384
DF2	6
P value	0.011
alpha	0.05

Table 15.

Roy’s greatest root.

Root	426.213
F (observed value)	13.319
F (critical value)	3.691
DF1	192
DF2	6
P value	0.002
alpha	0.05

Table 16.

Eigenvalue.

	F1	F2
Eigenvalue	426.213	170.267
Discrimination (%)	71.455	28.545
Cumulative %	71.455	100.000

Table 17.

Bartlett’s test for eigenvalue significance.

	F1	F2
Eigenvalue	426.213	170.267
Bartlett’s statistic	1125.651	516.894
P value	0.000	0.000

Table 18.

Canonical correlations.

F1	F2
0.999	0.997

Table 19.

Functions at the centroids.

	F1	F2
AVERAGE	−1.441	17.951
GOOD	27.354	−8.465
POOR	−23.159	−10.085

Outcome of predicted performance with Bartlett’s test.

Table 20.

Confusion matrix for the training sample.

From/to	AVERAGE	GOOD	POOR	Total	% correct
AVERAGE	68	0	0	68	100.00
GOOD	0	62	0	62	100.00
POOR	0	0	69	69	100.00
Total	68	62	69	199	100.00

Table 21.

Confusion matrix for the validation sample.

From/to	POOR	Total	% correct
AVERAGE	0	0	0.00
GOOD	0	0	0.00
POOR	1	1	100.00
Total	1	1	100.00

Table 22.

Confusion matrix for the cross-validation results.

From\to	AVERAGE	GOOD	POOR	Total	% correct
AVERAGE	23	26	19	68	33.82
GOOD	16	36	10	62	58.06
POOR	5	8	56	69	81.16
Total	44	70	85	199	57.79

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Articles in this issue

DOI: https://doi.org/10.21307/ijssis-2020-035 | Journal eISSN: 1178-5608

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Language: English

Page range: 1 - 15

Submitted on: Jan 4, 2018

Published on: Dec 30, 2020

Published by: International Journal on Smart Sensing and Intelligent Systems

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Cognitive approach,

Cognitive skills,

Data mining,

Discriminant Analysis,

Effective learning,

Statistical techniques

Related subjects:

Engineering,

Introductions and overviews,

Engineering, other

© 2020 D. Magdalene Delighta Angeline, P. Ramasubramanian, I. Samuel Peter James, published by International Journal on Smart Sensing and Intelligent Systems
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 13 (2020): Issue 1 (January 2020)

The Discriminant Analysis Approach for Evaluating Effectiveness of Learning in an Instructor-Led Virtual Classroom

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Paradigm

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