# ILS Validity Analysis for Secondary Grade through Factor Analysis and Internal Consistency Reliability

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## Abstract

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## 1. Introduction

- To carry out a comprehensive study on the ILS validity and reliability using the data collected from different secondary schools.
- A comprehensive evaluation of psychometric analysis of ILS to investigate the learning styles of secondary-grade students.
- To explore the internal consistency reliability and construct validity using exploratory and confirmatory factor analysis of the Felder–Silverman’s ILS for the secondary grade students.
- The use of various fitting models to designate the best fit for the collected data.
- To inspect the average item correlation and exploratory and confirmatory factor analysis for the statistical evidence of validity and reliability of ILS for secondary-grade students.

## 2. Background

#### 2.1. Felder–Silverman Learning Style Model

#### 2.2. Index of Learning Styles (ILS)

#### 2.3. Assessment Tools

**Internal Consistency Reliability**: Internal consistency is an essential assessment tool to examine the uniformity of construct, whereas, reliability information illustrates the correlation among the items of the tool and is reported using the Cronbach’s alpha value [48]. It also measures the stability, consistency, and accuracy of the instrument [49]. If the scale has a high correlation between the items, the alpha ($\alpha $) value increases accordingly. Reliability is a necessary component for the instrument to be standardized, but it is not sufficient for the validity of that instrument.

**Construct Validity**: Validity measures the degree to which the instrument provides consistent results and the amount to which the test predicts other observed variables of interest [50]. According to [50] “construct validity is involved whenever a test is to be interpreted as a measure of some attribute or quality which is not operationally defined” and factor analysis is used to assess whether the test measures hypothesized learning ability. The factor analysis is the set of statistical approaches used to assess the relationships between a group of observed variables that are assessed through a number of items or questions.

**Exploratory Factor Analysis**: Exploratory Factor Analysis (EFA) is used to recognize the association between the variables to comprehend the underlying constructs [51]. The steps include examining the measure of the association and suggestion of factorability of the variables [52], extracting a set of factors from the correlation matrix, determining the number of factors using the Kaiser Criterion method and the scree plot method, rotation of factors to increase interpretability, and lastly, comprehension of results and identification of nature of factors [53].

**Confirmatory Factor Analysis**: The EFA specifies the essential quantity of factors, then the confirmatory factor analysis (CFA) confirms how well the analyzed variables characterize a smaller number of construct [49]. To cross-validate the factor structure, CFA is used to analyze the adequacy of the model. The adequacy of the model is calculated initially with Chi-square test statistics and then fit indices [53].

## 3. Literature Review

## 4. Methodology

#### 4.1. Participants

#### 4.2. Research Design

## 5. Findings

#### Internal Consistency Reliability

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Comparison of the Cronbach’s alpha value for the present study and the prior work for 11 items.

Study | N | AR | SI | VV | SG |
---|---|---|---|---|---|

[35] | 56 | 0.59 | 0.70 | 0.63 | 0.53 |

[17] | 198 | 0.51 | 0.63 | 0.64 | 0.51 |

[56] | 572 | 0.51 | 0.65 | 0.56 | 0.41 |

[31] | 584 | 0.70 | 0.76 | 0.69 | 0.55 |

[57] | 242 | 0.56 | 0.72 | 0.62 | 0.54 |

[21] | 500 | 0.87 | 0.77 | 0.77 | 0.61 |

[42] | 358 | 0.63 | 0.76 | 0.64 | 0.62 |

Present | 421 | 0.61 | 0.52 | 0.55 | 0.62 |

**Table 2.**Cronbach’s alpha values for index of learning style of the secondary-grade students for internal consistency reliability.

Learning Style | Valid Cases | Items | Mean | Variance | Cronbach Alpha ($\mathit{\alpha}$) |
---|---|---|---|---|---|

AR | 421 | 11 | 7.34 | 6.45 | 0.61 |

SI | 421 | 11 | 5.50 | 4.92 | 0.52 |

VV | 421 | 11 | 6.95 | 4.84 | 0.55 |

SG | 421 | 11 | 6.90 | 5.70 | 0.62 |

**Table 3.**The amount of factor loading (>0.3) in rotated component matrix of the 16-factor solution. The rotation method used is oblivion with Kaiser Normalization.

Learning Styles | Factors | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |

AR | 10 | 1 | 1 | 1 | ||||||||||||

SG | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||

VV | 10 | 4 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | ||||||

SI | 3 | 5 | 3 | 3 | 2 | 1 | 2 | 1 | 1 |

**Table 4.**The rotated component matrix of the 5-factor solution. The Rotation method used is Oblimin with Kaiser Normalization, Rotation converged in 11 iterations.

Components | Components | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | ||

AR1 | 0.636 | 0.137 | −0.009 | 0.076 | 0.054 | SG8 | 0.117 | 0.503 | 0.109 | −0.119 | 0.129 |

AR5 | 0.595 | −0.019 | 0.115 | −0.016 | 0.163 | SG12 | −0.014 | 0.407 | −0.167 | 0.027 | 0.186 |

AR9 | 0.684 | 0.104 | −0.117 | −0.127 | −0.079 | SG16 | 0.101 | 0.560 | 0.064 | −0.018 | −0.124 |

AR13 | 0.633 | 0.111 | 0.096 | −0.026 | 0.072 | SG20 | 0.155 | 0.562 | −0.046 | 0.049 | 0.006 |

AR21 | 0.479 | −0.066 | −0.061 | 0.061 | −0.298 | SG24 | 0.022 | 0.726 | 0.039 | 0.029 | 0.007 |

AR25 | 0.551 | 0.151 | −0.084 | −0.069 | 0.109 | SG28 | −0.084 | 0.512 | −0.193 | 0.223 | 0.115 |

AR29 | 0.534 | −0.004 | −0.068 | −0.076 | −0.099 | SG32 | −0.080 | 0.557 | −0.001 | 0.029 | −0.112 |

AR33 | 0.610 | −0.080 | −0.022 | −0.057 | 0.069 | SG36 | 0.100 | 0.600 | −0.063 | 0.182 | −0.170 |

AR37 | 0.666 | −0.003 | 0.169 | −0.038 | −0.195 | SG40 | −0.112 | 0.513 | 0.024 | −0.018 | −0.155 |

AR41 | 0.474 | −0.004 | 0.142 | 0.039 | −0.108 | SG44 | 0.148 | 0.411 | −0.036 | 0.128 | −0.279 |

AR17 | 0.09 | 0.218 | −0.079 | 0.197 | 0.155 | SG4 | 0.104 | −0.129 | 0.170 | 0.052 | 0.357 |

VV3 | −0.055 | 0.061 | 0.407 | −0.057 | 0.274 | SI2 | −0.151 | −0.043 | −0.002 | 0.442 | 0.094 |

VV7 | 0.069 | −0.110 | 0.480 | 0.240 | 0.077 | SI6 | 0.039 | 0.179 | 0.157 | 0.310 | −0.213 |

VV11 | −0.142 | −0.133 | 0.560 | 0.058 | −0.200 | SI14 | −0.150 | 0.054 | 0.218 | 0.450 | 0.178 |

VV15 | −0.177 | −0.047 | 0.477 | 0.142 | 0.040 | SI18 | 0.145 | −0.030 | 0.025 | 0.480 | −0.173 |

VV19 | 0.085 | 0.120 | 0.483 | −0.014 | 0.084 | SI22 | −0.071 | 0.208 | 0.171 | 0.337 | 0.003 |

VV27 | 0.052 | 0.017 | 0.600 | −0.088 | 0.130 | SI30 | −0.180 | 0.046 | −0.024 | 0.462 | 0.269 |

VV31 | 0.082 | −0.130 | 0.629 | 0.079 | −0.157 | SI34 | −0.070 | 0.098 | −0.144 | 0.550 | −0.084 |

VV35 | 0.053 | 0.070 | 0.319 | 0.125 | 0.126 | SI38 | −0.064 | −0.038 | 0.141 | 0.364 | 0.120 |

VV39 | 0.240 | −0.023 | 0.321 | 0.262 | −0.257 | SI10 | 0.054 | −0.115 | 0.145 | 0.141 | 0.559 |

VV23 | 0.113 | 0.062 | 0.126 | 0.504 | 0.128 | SI26 | −0.122 | −0.031 | 0.021 | 0.297 | 0.425 |

VV43 | 0.153 | 0.073 | 0.044 | 0.367 | −0.248 | SI42 | −0.112 | 0.072 | −0.299 | 0.245 | −0.345 |

**Table 5.**The distribution of loading ($>\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}0.3$) of the 5-factor solution. The rotation method used is Oblimin with Catell’s scree test. Rotation converged in 11 iterations.

Learning Styles | Factors | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

AR | 10 | ||||

SG | 10 | 1 | |||

VV | 9 | 2 | |||

SI | 8 | 3 |

Factors | Items | Label | Factors Explained |
---|---|---|---|

1 | 1, 5, 9, 13, 21, 25, 29, 33, 37, 41, 17 | AR | Action first or reflection first |

2 | 17, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 | SG | Linear VS sequential or random VS holistic thinking |

3 | 3, 8, 11, 15, 19, 27, 31, 35, 39 | VV | Information format preferred as input or memory |

4 | 23, 43, 2, 6, 14, 18, 22, 30, 34, 37 | SI | Information format preferred and preference of concrete or abstract information |

5 | 4, 10, 26, 42 | SI-SG | Conceptual VS factual and detail VS theme |

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**MDPI and ACS Style**

Mirza, M.A.; Khurshid, K.; Shah, Z.; Ullah, I.; Binbusayyis, A.; Mahdavi, M.
ILS Validity Analysis for Secondary Grade through Factor Analysis and Internal Consistency Reliability. *Sustainability* **2022**, *14*, 7950.
https://doi.org/10.3390/su14137950

**AMA Style**

Mirza MA, Khurshid K, Shah Z, Ullah I, Binbusayyis A, Mahdavi M.
ILS Validity Analysis for Secondary Grade through Factor Analysis and Internal Consistency Reliability. *Sustainability*. 2022; 14(13):7950.
https://doi.org/10.3390/su14137950

**Chicago/Turabian Style**

Mirza, Munazza A., Khawar Khurshid, Zawar Shah, Imdad Ullah, Adel Binbusayyis, and Mehregan Mahdavi.
2022. "ILS Validity Analysis for Secondary Grade through Factor Analysis and Internal Consistency Reliability" *Sustainability* 14, no. 13: 7950.
https://doi.org/10.3390/su14137950