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

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

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.

Statistical distance of each observation to the mean vector.

Comparison of the final outcome with periodical assessment.

Outcome of predicted performance with Bartlett’s test.

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

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

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

Classification matrix_

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

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

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

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

Summary classification_

Correct	81.0%
Base	52.4%
Improvement	60.0%

Summary statistics_

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

Canonical correlations_

F1	F2
0.999	0.997

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

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

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

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

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

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

Fisher distances_

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

Functions at the centroids_

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

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

Summary statistics (validation)_

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

Eigenvalue_

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

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

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: Professor Subhas Chandra Mukhopadhyay

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 Professor Subhas Chandra Mukhopadhyay
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Figures & Tables

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Wilks’ Lambda test (Rao’s approximation)_

Sum of weights and prior probabilities for each class_

Pillai’s trace_

Classification matrix_

P values for Fisher distances_

Hotelling–Lawley trace_

Confusion matrix for the validation sample_

Summary classification_

Summary statistics_

Canonical correlations_

Generalized squared distances_

Roy’s greatest root_

Bartlett’s test for eigenvalue significance_

Confusion matrix for the cross-validation results_

Discriminant analysis for performance_

Matrix of variance and covariance_

Fisher distances_

Functions at the centroids_

Mahalanobis distances_

Summary statistics (validation)_

Eigenvalue_

Confusion matrix for the training sample_

Paradigm

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