# Exploring the Influence of Item Characteristics in a Spatial Reasoning Task

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Construct Representation, Response Processes, and Explanatory Item Response Theory

#### 1.2. Object Assembly and Its Item Characteristics

#### 1.3. The Current Study

- What are the overall psychometric characteristics of an object assembly task used to assess spatial ability?
- How do the characteristics of the object assembly items contribute to item difficulty?

#### 1.4. Linear Logistic Test Model

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Instrument

#### 2.3. Data Analysis

## 3. Results

#### 3.1. Dichotomous Rasch Model

#### DIF Analysis of the Two Subgroups

#### 3.2. LLTM

## 4. Discussion

#### 4.1. What Are the Overall Psychometric Characteristics of Object Assembly?

#### 4.2. How Do the Characteristics of the Object Assembly Items Contribute to Item Difficulty?

#### 4.3. Implications

#### 4.4. Limitations

#### 4.5. Directions for Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Example of an object assembly item. The pieces to the left of the line are the item stem, and the figures (

**A**–

**D**) are the options.

**Figure 2.**Plot of standardized differences (z) in subgroup-specific item difficulty estimates between subgroups.

Item Characteristics | Description |
---|---|

Number of pieces (Npieces) | The number of pieces in the stem |

Total edges (Tedges) | The total number of edges across pieces in the stem |

Maximum edges (Medges) | The maximum number of edges on any one piece in the stem |

Curved pieces (Cpieces) | Pieces in the stem containing at least one curved edge |

Pieces with labels (Lpieces) | All pieces in the stem with clear labels (square, triangle, [pie] slice) |

Regular-shape solution (RSS) | The key has a standard shape (circle, equilateral triangle, right triangle, or square) |

Displaced pieces (Dpieces) | The number of pieces in the stem that were moved to a different location in the key |

Rotated pieces (Rpieces) | The number of pieces in the key that had to be rotated from the key to the stem to reach the correct answer |

Easily excluded distractors (EED) | The number of distractors with a different number of pieces or obviously different shapes from the stem |

Item | Npieces | Lpieces | Tedges | Medges | Cpieces | EED | RSS | Dpieces | Rpieces |
---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |

2 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |

3 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |

4 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

5 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |

6 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |

7 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |

8 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |

9 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |

10 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |

11 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |

12 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

13 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |

14 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |

15 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |

Item | n | Proportion Correct (Mean) | SD | Corrected Item–Total Correlation |
---|---|---|---|---|

1 | 123 | 0.87 | 0.34 | 0.51 |

2 | 123 | 0.82 | 0.39 | 0.60 |

3 | 123 | 0.85 | 0.36 | 0.48 |

4 | 123 | 0.77 | 0.42 | 0.59 |

5 | 123 | 0.63 | 0.48 | 0.71 |

6 | 123 | 0.69 | 0.46 | 0.58 |

7 | 123 | 0.61 | 0.49 | 0.49 |

8 | 123 | 0.43 | 0.50 | 0.49 |

9 | 170 | 0.68 | 0.47 | 0.67 |

10 | 170 | 0.65 | 0.48 | 0.52 |

11 | 169 | 0.64 | 0.48 | 0.35 |

12 | 170 | 0.46 | 0.50 | 0.53 |

13 | 169 | 0.52 | 0.50 | 0.45 |

14 | 168 | 0.50 | 0.50 | 0.53 |

15 | 170 | 0.43 | 0.50 | 0.54 |

Item | $\mathit{\delta}$ | SE | Lower CI | Upper CI | Outfit MSE | Infit MSE | Outfit z | Infit z |
---|---|---|---|---|---|---|---|---|

1 | −1.92 | 0.29 | −1.35 | −2.49 | 0.36 | 0.73 | −1.28 | −1.70 |

2 | −1.43 | 0.27 | −0.92 | −1.95 | 0.35 | 0.65 | −1.77 | −2.80 * |

3 | −1.66 | 0.28 | −1.12 | −2.21 | 0.85 | 0.81 | −0.15 | −1.24 |

4 | −1.02 | 0.25 | −0.53 | −1.51 | 0.52 | 0.79 | −1.46 | −1.70 |

5 | −0.01 | 0.23 | 0.44 | −0.46 | 0.52 | 0.70 | −2.44 | −2.70 |

6 | −0.41 | 0.24 | 0.05 | −0.87 | 0.77 | 0.90 | −0.83 | −0.82 |

7 | 0.16 | 0.23 | 0.61 | −0.29 | 1.26 | 1.15 | 1.16 | 1.16 |

8 | 1.35 | 0.23 | 1.81 | 0.90 | 1.21 | 1.10 | 0.86 | 0.80 |

9 | −0.29 | 0.23 | 0.17 | −0.75 | 0.62 | 0.79 | −1.62 | −1.85 |

10 | 0.16 | 0.23 | 0.61 | −0.29 | 1.18 | 1.15 | 0.85 | 1.16 |

11 | −0.29 | 0.23 | 0.17 | −0.75 | 1.32 | 1.36 | 1.20 | 2.70 |

12 | 1.52 | 0.23 | 1.97 | 1.06 | 1.13 | 1.01 | 0.56 | 0.11 |

13 | 0.65 | 0.23 | 1.10 | 0.21 | 1.26 | 1.20 | 1.22 | 1.51 |

14 | 1.41 | 0.23 | 1.86 | 0.96 | 1.15 | 1.05 | 0.62 | 0.44 |

15 | 1.79 | 0.23 | 2.24 | 1.33 | 1.04 | 1.01 | 0.22 | 0.16 |

M | 0.00 | 0.24 | 0.47 | −0.47 | 0.90 | 0.96 | −0.19 | −0.32 |

SD | 1.19 | 0.02 | 1.15 | 1.22 | 0.35 | 0.21 | 1.26 | 1.65 |

Item | ${\mathit{d}}_{1}$ | ${\mathit{se}}_{1}$ | ${\mathit{d}}_{2}$ | ${\mathit{se}}_{2}$ | z | p |
---|---|---|---|---|---|---|

3 | −2.81 | 0.96 | −1.61 | 0.29 | −1.20 | 0.23 |

4 | −2.81 | 0.96 | −0.86 | 0.28 | −1.96 | 0.05 * |

5 | −0.43 | 0.40 | 0.01 | 0.30 | −0.86 | 0.39 |

6 | −1.03 | 0.48 | −0.36 | 0.29 | −1.19 | 0.23 |

7 | 0.49 | 0.33 | −0.36 | 0.29 | 1.92 | 0.05 * |

8 | 1.46 | 0.30 | 0.82 | 0.36 | 1.38 | 0.17 |

9 | −0.80 | 0.45 | −0.27 | 0.29 | −0.99 | 0.32 |

10 | −0.12 | 0.37 | 0.11 | 0.31 | −0.47 | 0.64 |

11 | 0.26 | 0.35 | −0.86 | 0.28 | 2.53 | 0.01 * |

12 | 1.69 | 0.30 | 0.82 | 0.36 | 1.87 | 0.06 |

13 | 0.88 | 0.31 | 0.11 | 0.31 | 1.75 | 0.08 |

14 | 1.46 | 0.30 | 0.97 | 0.37 | 1.04 | 0.30 |

15 | 1.76 | 0.30 | 1.50 | 0.44 | 0.51 | 0.61 |

Item Characteristic | $\mathit{\eta}$ | SE | Lower CI | Upper CI |
---|---|---|---|---|

Npieces | −0.85 | 0.29 | −1.41 | −0.29 |

Lpieces | 1.20 | 0.25 | 0.71 | 1.68 |

Tedges | 1.54 | 0.28 | 0.99 | 2.08 |

Medges | 0.64 | 0.19 | 0.27 | 1.01 |

Cpieces | 1.02 | 0.20 | 0.62 | 1.41 |

EED | −1.19 | 0.23 | −1.65 | −0.74 |

RSS | −0.39 | 0.32 | −1.02 | 0.25 |

Dpieces | 1.89 | 0.32 | 1.25 | 2.52 |

Rpieces | −0.44 | 0.22 | −0.88 | −0.01 |

Item | ${\mathit{\delta}}^{\prime}$ | SE | Lower CI | Upper CI |
---|---|---|---|---|

1 | −0.94 | 0.42 | −1.77 | −0.11 |

2 | −0.94 | 0.42 | −1.77 | −0.11 |

3 | −0.57 | 0.45 | −1.45 | 0.32 |

4 | −0.05 | 0.57 | −1.16 | 1.07 |

5 | 1.32 | 0.44 | 0.45 | 2.18 |

6 | 0.94 | 0.55 | −0.14 | 2.02 |

7 | 0.76 | 0.56 | −0.33 | 1.86 |

8 | 2.04 | 0.55 | 0.97 | 3.11 |

9 | 0.12 | 0.50 | −0.87 | 1.11 |

10 | 0.98 | 0.39 | 0.22 | 1.74 |

11 | 1.05 | 0.46 | 0.16 | 1.95 |

12 | 1.50 | 0.42 | 0.68 | 2.31 |

13 | 1.57 | 0.45 | 0.68 | 2.45 |

14 | 2.51 | 0.50 | 1.54 | 3.48 |

15 | 2.07 | 0.52 | 1.05 | 3.10 |

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**MDPI and ACS Style**

Shi, Q.; Wind, S.A.; Lakin, J.M.
Exploring the Influence of Item Characteristics in a Spatial Reasoning Task. *J. Intell.* **2023**, *11*, 152.
https://doi.org/10.3390/jintelligence11080152

**AMA Style**

Shi Q, Wind SA, Lakin JM.
Exploring the Influence of Item Characteristics in a Spatial Reasoning Task. *Journal of Intelligence*. 2023; 11(8):152.
https://doi.org/10.3390/jintelligence11080152

**Chicago/Turabian Style**

Shi, Qingzhou, Stefanie A. Wind, and Joni M. Lakin.
2023. "Exploring the Influence of Item Characteristics in a Spatial Reasoning Task" *Journal of Intelligence* 11, no. 8: 152.
https://doi.org/10.3390/jintelligence11080152