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

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

D. Magdalene Delighta Angeline

P. Ramasubramanian

oraz

I. Samuel Peter James

| 30 gru 2020

International Journal on Smart Sensing and Intelligent Systems

Tom 13 (2020): Zeszyt 1 (January 2020)

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Article Category: Research-Article

Data publikacji: 30 gru 2020

Zakres stron: 1 - 15

Otrzymano: 04 sty 2018

DOI: https://doi.org/10.21307/ijssis-2020-035

Słowa kluczowe
Cognitive approach, Cognitive skills, Data mining, Discriminant Analysis, Effective learning, Statistical techniques

© 2020 D. Magdalene Delighta Angeline et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

eISSN:: 1178-5608
Język:: Angielski

Częstotliwość wydawania:: Volume Open
Dziedziny czasopisma:: Engineering, Introductions and Overviews, other

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

Article Category: Research-Article

Data publikacji: 30 gru 2020

Zakres stron: 1 - 15

Otrzymano: 04 sty 2018

DOI: https://doi.org/10.21307/ijssis-2020-035

Słowa kluczoweCognitive approach, Cognitive skills, Data mining, Discriminant Analysis, Effective learning, Statistical techniques

© 2020 D. Magdalene Delighta Angeline et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Słowa kluczowe
Cognitive approach, Cognitive skills, Data mining, Discriminant Analysis, Effective learning, Statistical techniques