# The Impact of Situational Test Anxiety on Retest Effects in Cognitive Ability Testing: A Structural Equation Modeling Approach

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Explanations for Retest Effects

#### 1.2. Definition of Test Anxiety

#### 1.3. Test Anxiety and Test Performance: Interference and Deficit Hypotheses

#### 1.4. A Psychological Theory for the Impact of Situational Test Anxiety on Retest Effects

## 2. A Statistical Model for the Impact of Situational Test Anxiety on Retest Effects

_{k}represent the latent ability state at Tk (k ≠ 1) and let δ

_{i}

_{+1,i}represent the latent difference variable between Ti and Ti + 1, then for all η

_{k}:

_{2,1}gives:

_{3,2}gives:

_{1}) and correlated slope variables (the latent difference variables).

^{2}test statistic of the likelihood ratio tests can be compared in size to reveal information about the magnitude of interference in a given test session. This occurs because, with every step, the same amount of additional interference effects is restricted to zero given that the number of test items is kept constant across test administrations, keeping the degrees of freedom constant across all likelihood ratio tests. The results of these successive tests can be interpreted in the light of the observed retest effects, as a comparably large retest effect between Tk − 1 and Tk should align with a comparably large Δχ

^{2}test statistic when restricting interference effects at Tk to zero. In the following, we refer to this framework as the interference reduction approach. Figure 3 depicts an example of the full interference model with three test administrations and visualizes the first step of the interference reduction approach.

## 3. An Empirical Study

#### 3.1. Method

#### 3.1.1. Sample

#### 3.1.2. Measures

#### Figural Matrices Test

#### Situational Test Anxiety

#### 3.1.3. Procedure

#### 3.1.4. Analytic Strategy

^{2}overall model fit test statistic, χ

^{2}-to-df ratio, RMSEA, CFI, and TLI. The cut-off criteria for all these fit indices were taken from West et al. [88]. For the nested models, we used likelihood ratio tests according to the Satorra method [89] for DWLS-estimated models, and the Satorra–Bentler method [90] for MLR-estimated models. Additionally, we compared CFI values. A decrease in CFI larger than 0.01 after imposing restrictions on model parameters is considered a substantial decline in model fit [91].

#### 3.2. Results

#### 3.2.1. Descriptive Statistics

_{1}= 7.658; SD

_{1}=3.110; M

_{4}= 9.938; SD

_{4}= 2.621). FOF scores decreased over the entire study length (M

_{1}= 16.582; SD

_{1}= 6.200; M

_{7}= 11.889; SD

_{7}= 6.014). Internal consistencies of all measures varied over time but always settled above 0.70 (α = 0.711–0.881).

#### 3.2.2. Ability-CFA

^{2}test statistic (χ

^{2}(3983) = 3283.490, p = 1). However, likelihood ratio tests and ΔCFI indicated a significant decline in fit with any further invariance imposition. When strong invariance was implemented, CFI and TLI just barely missed the minimum target value of 0.95 (CFI = TLI = 0.948). The χ

^{2}-to-df ratio remained under 2.00 (χ

^{2}/df = 1.627), indicating satisfying model fit. The upper 90% confidence interval bound of the RMSEA settled under 0.08 (RMSEA = 0.053, 90% CI = [0.051, 0.055]). As Chen et al. found in a simulation study, models with such high degrees of freedom are often rejected based on this criterion when estimated with an N < 400, even if the model was correctly specified [97]. Thus, we further investigated retest effects on the basis of the strong invariant model and return to this issue in the discussion.

#### 3.2.3. STA-CFA

^{2}-to-df ratios and RMSEA suggested satisfying model fit, CFI and TLI barely missed their respective thresholds of 0.95 by a maximum margin of 0.02 (TLI for the weak invariant model). Comparison of the models yielded, again, mixed results. Based on the likelihood ratio tests, only configural invariance should be assumed (Δχ

^{2}(24) = 74.028, p < 0.001). The CFI value, on the other hand, decreased by only 0.007, suggesting no substantial decline of model fit when factor loadings are restricted to being equal across test administrations.

#### 3.2.4. Retest Effects

_{2,1}= 0.72, p < 0.001). Retest effects remained positive and significantly different from zero until the fourth test administration (d

_{4,3}= 0.22, p = 0.009). Between the fourth and fifth test session, mean ability actually decreased, but this effect was small and not significant (d

_{5,4}= −0.13, p = 0.107). Compared with the first retest effect, the second decreased substantially (d

_{3,2}−d

_{2,1}= −0.56, p < 0.001). After that, the only significant change in retest effect size occurred between the third and the fourth retest effect (d

_{5,4}–d

_{4,3}= −0.35, p = 0.017). However, as already mentioned, no significant change in mean latent ability was observed between the fourth and fifth test administration.

#### 3.2.5. Interference Reduction

^{2}(13) = 24.432, p = 0.027). However, the model CFI only reduced by 0.006 in that case. Results unambiguously suggested a decreased model fit when interference effects were additionally assumed to be absent at the first test session (Δχ

^{2}(13) = 46.045, p < 0.001, ΔCFI = 0.014).

## 4. Discussion

#### 4.1. Implications and Future Research

#### 4.2. Limitations and Future Research

#### 4.3. Deliberations on Measurement Invariance in Multiple Test Administrations

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Anxiety test (AT) model as proposed by Halpin et al. [36]. A latent cognitive ability variable (η) is measured by its respective manifest test items (three in this example: I

_{1}, I

_{2}, and I

_{3}). A latent anxiety variable (ξ) is measured by its respective manifest questionnaire items (again, three in this example: F

_{1}, F

_{2}, and F

_{3}). The arrows approaching the manifest variables from below represent their respective error terms. Regressions of the ability test items on latent anxiety are also modeled and reflect interference effects. The correlation between ability and anxiety is modeled and represents a potential deficit. Simultaneous modeling of interferences and deficits creates statistical rotational indeterminacy, rendering the model under-identified. However, strategic equality constraints among the factor loading parameters (for example: all interference effects are restricted to the same value) solve this problem.

**Figure 2.**Extension of the AT model [36] to longitudinal data (LAT model). An AT model (Figure 1) is constructed for every test session i (three in this example but it can be extended to any number of test sessions). States of latent cognitive ability (η

_{i}) are modeled to correlate between test sessions. The same is applied to latent state anxiety (ξ

_{i}).

**Figure 3.**Example of the full interference model with three test sessions. ξ

_{i}(with i = 1, 2, 3) depicts situational test anxiety at measurement occasion i. We included a latent variable η

^{*}

_{1}for a more comprehensible visualization of the model. η

_{1}regresses on η

^{*}

_{1}with a regression weight of 1 and a residual-variance of 0. Hence, η

^{*}

_{1}= η

_{1}. Note that an inclusion of η

^{*}

_{1}is not necessary for model estimation as η

_{1}can be used for the respective equations instead. By identifying the model by setting the variances of latent variables to 1, the latent differences variables δ

_{k,k−1}(with k = 2, 3) are on a standardized scale and their means can be interpreted as retest effect sizes in terms of Cohen’s d [80]. Interference effects in the third test session are depicted by dashed lines to illustrate the first step of the interference reduction approach. A model in which these coefficients are restricted to zero can be compared with the full interference model via a likelihood ratio test to test the null hypothesis that interferences disappear in the third test session.

**Figure 4.**Cognitive ability-confirmatory factor analysis (CFA). η

_{1}–η

_{7}represent the latent ability variables measured by the figural matrices test items in every test session. I

_{1,1}represents the first item in the first test session, I

_{13,7}represents the 13th item of the seventh test session, etc. (items 2–12 of any test session are not shown but are represented by the respective three dots). Factor loadings can vary without any restrictions in a configural invariant model, but the loading of any item is restricted to the same respective value across test administrations when a more restrictive from of invariance is implemented. The threshold of any test item (not shown) is also restricted to the same respective value across test administrations when strong invariance is imposed. The arrows approaching the manifest variables from below represent their respective error-terms. The model was identified by setting the factor loading of the first item at every test session to 1.

**Figure 5.**

**Situational test anxiety-confirmatory factor analysis**(STA-CFA). ξ

_{1}–ξ

_{7}represent the latent STA variables measured by the fear-of-failure (FOF) items of the “Fragebogen zur Erfassung aktueller Motivation” (FAM) at every test session. F

_{1}represents the first item of the questionnaire and F

_{5}represents the fifth item. Items 2 to 4 are not shown, but are represented by the respective three dots. Loadings from latent STA variables on the manifest items can vary without any restrictions in a configural invariant model, but the loading of any item is restricted to the same respective value across test administrations when weak invariance is implemented. The free arrows approaching the manifest variables from below represent their respective error terms. Since the same items were applied in every test administration, five item-specific latent variables [93,94] were added to the model to account for indicator specific covariance. Only indicator-specific latent variables for items 1 and 5 are shown (ζ

_{1}and ζ

_{5,}respectively), but the other three are represented by the three dots in between. The model was identified by setting the factor loading of the first item for every factor to 1.

**Figure 6.**Estimated means of the standardized latent difference variables of the full interference model, which can be interpreted as retest effect sizes in terms on Cohen’s d between two successive test administrations. To obtain these parameters, the model was identified by setting the variances of the latent variables to 1. d

_{2,1}represents the retest effect from the first to the second test administration, etc. Error-bars indicate two-tailed 95% confidence intervals. p-values at the top refer to the differences between the respective successive retest effects.

Descriptive Statistics | Correlations | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

FM | FOF | ||||||||||||||||||

Measure | Test session | Mean | SD | Min | Max | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

FM | 1 | 7.658 | 3.11 | 1 | 13 | 0.776 | |||||||||||||

2 | 9.187 | 2.63 | 0 | 13 | 0.700 *** | 0.711 | |||||||||||||

3 | 9.631 | 2.69 | 0 | 13 | 0.640 *** | 0.684 *** | 0.761 | ||||||||||||

4 | 9.938 | 2.621 | 1 | 13 | 0.584 *** | 0.705 *** | 0.660 *** | 0.754 | |||||||||||

5 | 9.782 | 3.043 | 0 | 13 | 0.579 *** | 0.616 *** | 0.738 *** | 0.687 *** | 0.819 | ||||||||||

6 | 9.791 | 3.058 | 0 | 13 | 0.619 *** | 0.690 *** | 0.695 *** | 0.681 *** | 0.714 *** | 0.819 | |||||||||

7 | 9.822 | 2.905 | 0 | 13 | 0.594 *** | 0.639 *** | 0.707 *** | 0.643 *** | 0.736 *** | 0.768 *** | 0.798 | ||||||||

FOF | 1 | 16.582 | 6.2 | 5 | 31 | −0.157 * | −0.104 | −0.088 | −0.05 | −0.042 | −0.067 | −0.054 | 0.84 | ||||||

2 | 15.116 | 6.352 | 5 | 34 | −0.197 ** | −0.094 | −0.087 | −0.032 | 0.023 | −0.033 | −0.037 | 0.785 *** | 0.881 | ||||||

3 | 13.569 | 6.001 | 5 | 32 | −0.177 ** | −0.131 | −0.099 | −0.062 | 0.005 | −0.033 | −0.057 | 0.729 *** | 0.864 *** | 0.868 | |||||

4 | 12.929 | 5.95 | 5 | 28 | −0.148 * | −0.058 | −0.04 | −0.035 | 0.02 | −0.013 | −0.002 | 0.700 *** | 0.826 *** | 0.888 *** | 0.867 | ||||

5 | 12.48 | 6.15 | 5 | 28 | −0.148 * | −0.11 | −0.085 | −0.1 | −0.013 | −0.011 | −0.014 | 0.633 *** | 0.812 *** | 0.882 *** | 0.891 *** | 0.878 | |||

6 | 12.36 | 6.005 | 5 | 30 | −0.159 * | −0.124 | −0.107 | −0.116 | −0.068 | −0.069 | −0.077 | 0.574 *** | 0.759 *** | 0.826 *** | 0.838 *** | .906 *** | 0.875 | ||

7 | 11.889 | 6.014 | 5 | 28 | −0.133 * | −0.106 | −0.057 | −0.072 | −0.013 | −0.057 | −0.04 | 0.594 *** | 0.749 *** | 0.851 *** | 0.853 *** | 0.861 *** | 0.864 *** | 0.877 |

Implemented Invariance | Δχ^{2} (df) | p | χ^{2} (df) | p | χ^{2}/df | RMSEA [90% CI] | CFI | TLI |
---|---|---|---|---|---|---|---|---|

Configural | - | - | 3283.490 (3983) | 1 | 0.824 | 0.000 [0.000, 0.000] | 1.000 | 1.000 |

Weak | 168.960 (72) | <0.001 | 6038.581 (4055) | <0.001 | 1.489 | 0.047 [0.044, 0.049] | 0.960 | 0.960 |

Strong | 727.390 (71) | <0.001 | 6712.612 (4126) | <0.001 | 1.627 | 0.053 [0.051, 0.055] | 0.948 | 0.948 |

Implemented Invariance | Δχ^{2} (df) | p | χ^{2} (df) | p | χ^{2}/df | RMSEA [90% CI] | CFI | TLI |
---|---|---|---|---|---|---|---|---|

Configural | - | - | 845.657 (504) | <0.001 | 1.678 | 0.055 [0.049, 0.061] | 0.945 | 0.935 |

Weak | 74.082 (24) | <0.001 | 913.722 (528) | <0.001 | 1.731 | 0.057 [0.051, 0.063] | 0.938 | 0.930 |

**Table 4.**Standardized interference effects and correlations of latent ability and anxiety (deficit effects) of the full interference model.

Test Session | Item | r_{η,ξ} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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

1 | −0.300 ** | 0.088 | −0.272 * | 0.041 | −0.095 | −0.377 *** | −0.347 *** | −0.340 *** | −0.159 | −0.395 *** | −0.188 | −0.106 | −0.116 | −0.060 |

2 | −0.041 | 0.064 | −0.302 ** | −0.074 | −0.168 | −0.014 | −0.037 | −0.014 | −0.254 ** | −0.236 ** | −0.127 | 0.022 | −0.229 ** | 0.134 |

3 | −0.039 | −0.178 | −0.274 * | −0.118 | −0.129 | −0.137 | −0.290 ** | −0.153 | −0.087 | 0.065 | 0.032 | −0.071 | 0.021 | −0.006 |

4 | −0.039 | −0.170 | −0.196 | −0.094 | −0.042 | −0.246 * | 0.026 | −0.339 ** | −0.133 | −0.041 | −0.038 | 0.120 | −0.166 | 0.132 ** |

5 | −0.109 | −0.049 | −0.21 | −0.100 | −0.065 | −0.012 | −0.037 | −0.003 | −0.195 * | −0.024 | 0.053 | 0.067 | 0.047 | 0.031 |

6 | −0.194 | 0.016 | −0.078 | 0.009 | 0.052 | −0.237 * | −0.168 | 0.002 | −0.037 | −0.007 | −0.148 | −0.015 | −0.021 | −0.032 |

7 | −0.046 | 0.117 | −0.188 | 0.034 | −0.215 * | 0.010 | 0.017 | −0.048 | −0.315 ** | −0.144 | −0.078 | 0.059 | −0.086 | −0.035 |

Threshold | −1.019 | −0.933 | −1.062 | −0.702 | −0.760 | −0.821 | −0.536 | −0.493 | −0.549 | −0.447 | −0.248 | 0.059 | 0.025 |

_{η,ξ}= Correlation between latent ability and latent anxiety. Thresholds reflect item difficulties, which were restricted to be equal across test sessions. The model was identified by setting the variances of the latent variables to 1. Significant interference effects are printed in bold. * p < 0.05; ** p < 0.01; *** p < 0.001.

**Table 5.**Model fit and comparisons of nested models of interference effects in the interference-reduction approach.

Test Sessions with Modeled Interference Effects | Δχ^{2} (df) | p | χ^{2} (df) | p | χ^{2}/df | RMSEA (90% CI) | CFI | TLI |
---|---|---|---|---|---|---|---|---|

1 to 7 | - | - | 9766.433 (7753) | <0.001 | 1.230 | 0.034 [0.032, 0.036] | 0.971 | 0.971 |

1 to 6 | 16.882 (13) | 0.205 | 10,079.649 (7766) | <0.001 | 1.300 | 0.036 [0.034, 0.038] | 0.967 | 0.966 |

1 to 5 | 11.459 (13) | 0.572 | 10,272.688 (7779) | <0.001 | 1.321 | 0.038 [0.036, 0.040] | 0.964 | 0.964 |

1 to 4 | 9.749 (13) | 0.714 | 10,423.506 (7792) | <0.001 | 1.338 | 0.039 [0.037, 0.041] | 0.962 | 0.962 |

1 to 3 | 20.410 (13) | 0.085 | 10,790.511 (7805) | <0.001 | 1.383 | 0.041 [0.039, 0.043] | 0.957 | 0.957 |

1 and 2 | 18.128 (13) | 0.153 | 11,126.464 (7818) | <0.001 | 1.423 | 0.043 [0.042, 0.045] | 0.952 | 0.952 |

1 | 24.432 (13) | 0.027 | 11,581.707 (7831) | <0.001 | 1.479 | 0.046 [0.044, 0.048] | 0.946 | 0.946 |

None | 46.045 (13) | <0.001 | 12,525.000 (7844) | <0.001 | 1.597 | 0.052 [0.050, 0.053] | 0.932 | 0.932 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jendryczko, D.; Scharfen, J.; Holling, H.
The Impact of Situational Test Anxiety on Retest Effects in Cognitive Ability Testing: A Structural Equation Modeling Approach. *J. Intell.* **2019**, *7*, 22.
https://doi.org/10.3390/jintelligence7040022

**AMA Style**

Jendryczko D, Scharfen J, Holling H.
The Impact of Situational Test Anxiety on Retest Effects in Cognitive Ability Testing: A Structural Equation Modeling Approach. *Journal of Intelligence*. 2019; 7(4):22.
https://doi.org/10.3390/jintelligence7040022

**Chicago/Turabian Style**

Jendryczko, David, Jana Scharfen, and Heinz Holling.
2019. "The Impact of Situational Test Anxiety on Retest Effects in Cognitive Ability Testing: A Structural Equation Modeling Approach" *Journal of Intelligence* 7, no. 4: 22.
https://doi.org/10.3390/jintelligence7040022