Ratio preference prediction system for mouse design: Insights from golden ratio and gender differences

Abstract

This investigation aims to explore users’ accuracy in identifying computer mice designed with the golden ratio and their aesthetic preferences, with a specific focus on gender differences. First, the study used a database of 233 Genius brand mice and selected five samples with length-to-width ratios ranging from 1.42 to 1.78. A total of 99 university students (62 females and 37 males) participated in absolute and relative judgment tests. Results showed that most participants failed to correctly identify the mouse with a ratio closest to the golden ratio (approximately 1:1.62), even when provided with 2D or 3D visual references. The chi-square test showed that the difference in recognition accuracy between males (32%) and females (34%) was not statistically significant (p = 0.34). In addition, there was no correlation between aesthetic preference and whether the mouse followed the golden ratio. These findings suggest that golden ratio design is neither easily recognizable nor a key factor in product preference, and designers need not overly rely on it to enhance product appeal. Finally, polynomial regression analysis was employed to investigate the effect of the ratio on the preferences of all participants. The model fit was very high (R² = 99.91%, p-value = 0.038), showing that the mouse ratio was associated with all participants’ preferences. According to the results, if a ratio/preference prediction system for mouse design is developed in the future, a mouse design with an aspect ratio of 1.5 to 1.56 can serve as an important reference indicator for preference prediction.

Keywords

Golden ratio mouse design recognition accuracy gender differences relative judgment absolute judgment prediction system

Introduction

In design education, students are often taught the principles of aesthetic form, which include repetition, gradation, symmetry, balance, proportion, contrast, harmony, unity, and rhythm. Among these, proportion is a particularly important feature in three-dimensional form design. The golden ratio (approximately 1:1.62) is often regarded as a proportion that evokes visual pleasure.

The golden ratio is omnipresent¹ and has long captured the attention of mathematicians, artists, architects, sculptors, musicians, and designers.² From the Parthenon of ancient Greece to Da Vinci's Mona Lisa during the Renaissance, the golden ratio has been widely applied in art, architecture, and design,³ exemplifying harmony between nature and human-made forms.

However, there is little research on whether applying the golden ratio to consumer electronics—such as input devices—actually attracts consumers. Moreover, it is also unknown whether males and females differ in their ability to recognize golden ratio designs in such products. This study addresses these gaps by focusing on the field of consumer electronics, form aesthetics, and user psychology. Based on years of data from Genius brand mice, I selected five samples for testing. Participants attended the survey in the classroom to identify golden ratio proportions under both relative judgment and absolute judgment conditions, investigating their recognition accuracy and aesthetic preference.

Literature review

Relative judgment and absolute judgment

Researchers often use simplified product form representations, such as contours, sketches, and other two-dimensional depictions, to study customer preferences.⁴ Visual attributes and their combinations influence consumers’ judgments. Consistent with aesthetic theory, the most important main effect is the product's contour.⁵

Two judgment methods can be used: relative judgment and absolute judgment. Relative judgment occurs when two or more stimuli can be compared, and decisions are made based on their differences. Absolute judgment, on the other hand, is made without the opportunity for comparison.⁶ For example, consider squid-fishing boats, which are lined with light bulbs. If I want to determine whether the boat lights are brighter than a lighthouse, but only one is visible at a time, my judgment must rely on past experience and memory—this is absolute judgment. However, if both the fishing boat and the lighthouse are visible at the same time, I can make a direct relative judgment using my visual comparison ability.

The golden ratio

The golden ratio is typically denoted by the lowercase Greek letter Phi (φ), representing an irrational number approximately equal to 1.61803.⁷ Artists often regard the golden ratio as aesthetically pleasing.⁸ Similar terms include the “golden section” or “golden rectangle.” The golden section has a long-standing history in both the arts and sciences.⁹ It is often represented as a golden rectangle, where the ratio between the longer and shorter sides equals the golden ratio.

Related application fields include interaction design,¹⁰ furniture design,¹¹ visual design,¹² product design,¹³ architecture,⁷ and home appliance design.¹⁴ The golden ratio has inspired thinkers across all disciplines and holds a unique position in the history of mathematics. Two quantities, a and b, are said to be in a golden ratio φ if:

φ = \frac{1 + \sqrt{5}}{2} \approx 1.61803

Prediction system based on regression analysis

Prediction systems have been developed for decades and are widely applied in various domains. In the medical field, for instance, prediction models have been used to assess the risk of heart disease,¹⁵ hepatitis infection,¹⁶ and thyroid disease.¹⁷ These systems are deeply intertwined with statistical methods and machine learning techniques, which provide the analytical foundation for identifying patterns and generating accurate forecasts.

Thus, I applied regression analysis to build a prediction system. Among various statistical models, linear regression analysis has demonstrated promising results due to its reasonable accuracy and relatively simple implementation compared to other methods.¹⁸ The selected metrics are subsequently used in regression analysis to generate multiple mathematical equations. The equation with a p-value less than 0.05 and both R-squared and adjusted R-squared values exceeding 90% is chosen as the preferred prediction model.¹⁹

Beyond the medical field, prediction systems are also utilized in other areas—for example, in estimating dye concentration in industrial processes,²⁰ stock market trend,²¹ accelerometer-based surface roughness,²² summertime precipitation,²³ tool wear,²⁴ and waste collection vehicles travel time.²⁵ Moreover, relevant applications have emerged in the field of product design—for instance, in predicting the outcomes of product design competitions such as the product design award,²⁶ customer utility,²⁷ product design decision making,²⁸ user satisfaction.²⁹

Research method

Experiment prototypes

The input devices sampled in this study, shown in Figure 1, include five mouse models: (A) Micro Traveler 330s, (B) GX Gaming Maurus X, (C) NX-Micro, (D) Navigator 365, and (E) Traveler 9000. Micro Traveler 330s is a small-sized, three-button wireless mouse. GX Gaming Maurus X is a wired gaming mouse with a more striking appearance and ergonomic design. NX-Micro is a wired Bluetooth mouse with two tail-light-like features on its rear. Navigator 365 is a hybrid game controller and mouse featuring a hinge design that allows it to unfold into a controller or fold into a mouse. The Traveler 9000 is a wireless input device featuring an integrated cover and button structure, classified as a mid-range mouse.

Figure 1.

The five tested input devices in this study: (A) Micro Traveler 330s, (B) GX Gaming Maurus X, (C) NX-Micro, (D) Navigator 365, (E) Traveler 9000 (Source: Photographed by the author).

Participants

Ninety-nine participants (62 females and 37 males) were recruited for this study. All were students in the Department of Product Design, ranging from first-year undergraduate to master's program level, and aged between 18 and 29 years old.

Experiment procedure

The experiment was conducted in a classroom M410 at the School of Design, using a questionnaire-based approach. SurveyCake was used as the platform. Participants completed the questionnaire using their mobile phones, and the test took approximately 10 min to complete.

Golden ratio in mouse design

Artists often regard the golden ratio (φ ≈ 1.618) as aesthetically more pleasing. However, it remains unclear whether computer mice designed with this ratio are perceived as more attractive by general college users. Some literature suggests that the golden ratio has become a traditional standard of aesthetic judgment.

In this study, mice of the Genius brand were used as a case. I analyzed length-to-width ratios from years of Genius product catalogs. Among the 233 Genius mouse models collected, their ratios ranged from 1.0 to 2.18. The widest model was the Easy Trak Mouse (1996), with a ratio of 1.0. The longest and narrowest was the Navigator 535 Laser (2006), with a ratio of 2.18. The mouse with the ratio closest to the golden ratio was the NX Micro (2011), with a ratio of 1.617 and a length of 67 mm, categorized as a small mouse. Another example with a close to golden ratio was the Ergo 520 (2007), with a ratio of 1.608 and a length of 127 mm, categorized as a large mouse, shown in Figure 2.

Figure 2.

Mouse designs close to the golden ratio (based on genius brand).

The study selected five models (A–E) from the database of 233 Genius mice, with ratios of 1.42, 1.50, 1.62, 1.70, and 1.78. These ratios are approximately evenly spaced, allowing us to illustrate a gradual progression from low to high while minimizing the influence of non-proportional factors (e.g., complexity) on recognition results. Notably, 1.62 is close to the golden ratio (1.618), facilitating the comparison of golden-ratio-like preferences.

Survey questions

The mouse models used in this experiment vary in their length-to-width ratios, as illustrated in Figure 3. The questionnaire comprises ten items: the first five involve absolute judgment, the following four involve relative judgment, and the final question (question 10) assesses aesthetic preference.

Figure 3.

Length-to-width ratios of mouse test models.

Questions 1 to 5 require participants to identify which of the five mouse designs (A to E) best reflects the golden ratio. These are absolute judgment tasks, in which no reference objects are provided. Questions 6 and 7 mark the beginning of relative judgment tasks. In question 6, participants are asked to evaluate the front view of the mouse models to determine which one corresponds to the golden ratio. In question 7, participants judge based on a 3D perspective view of the same models.

Questions 8 and 9 provide a golden ratio reference figure alongside the mouse models. In question 8, a 2D reference is presented with the front view, while in question 9, a 3D reference model is shown. Participants are asked to use these references to help identify which mouse design adheres most closely to the golden ratio. Finally, in question 10, participants are asked to select the mouse design they consider the most aesthetically pleasing.

Case analysis and discussion

The study included both absolute and relative judgment tests. A judgment based on past impressions or memory of the mouse ratios is classified as an absolute judgment, whereas a judgment made by simultaneously observing and comparing two mouse ratios is classified as a relative judgment.

Absolute judgment test results

Based on the absolute judgment questionnaire (Questions 1–5), the results showed that the highest number of participants identified Mouse D as having the golden ratio (55.6%), followed by Mouse A (43.4%), Mouse E (34.3%), Mouse C (33.7%), and Mouse B (21.2%), as shown in Figure 4.

Figure 4.

Results of the absolute judgment test.

However, the experimental results showed that Mouse D, which most participants believed to have the golden ratio, was not the one closest to it. According to the measurements, Mouse D has a length-to-width ratio of 1.70, whereas Mouse C has a ratio of 1.62, making it the one closest to the golden ratio. Therefore, in the absolute judgment experiment, public perception did not align with mathematical reality. Notably, more participants misjudged Mouse C (66.7%) than those who correctly identified it (33.3%).

Relative judgment test results

In the relative judgment questionnaire (questions 6–9), results showed that in the 2D front-view condition. Mouse D was most frequently believed to have the golden ratio (42.4%), followed by Mouse C (20.2%), Mouse B (19.2%), Mouse E (12.1%), and Mouse A (6.1%).

The difference compared to absolute judgment lies in the order of choices. In absolute judgment, the perceived golden ratio ranking was: D > A > E > C > B. In relative judgment, it was: D > C > B > E > A. However, results showed that in 2D images, whether using absolute or relative judgment, participants still often failed to identify the correct mouse (Mouse C) as closest to the golden ratio.

In question 7, which used 3D perspective images, the perceived ranking was: D > B > C > E > A. However, the proportion of participants choosing Mouse D increased, suggesting a higher rate of incorrect judgments. Meanwhile, the correct identification of Mouse C decreased slightly from 20.2% to 17.2%. This indicates that 3D imagery did not improve participants’ ability to recognize the golden ratio in mouse designs.

In question 8, I added a 2D front-view golden ratio reference image. The test scene is shown in Figure 5. This was designed to see whether the inclusion of a reference would help participants make more accurate decisions. The results, however, showed no improvement in accuracy. Comparing question 6 (no reference) and question 8 (with 2D reference): In question 6, 42.4% believed Mouse D was the golden ratio. In question 8, this increased to 51.5%, even though Mouse D is not the golden ratio.

Figure 5.

2D front view with golden ratio reference.

Meanwhile, in question 6, 20.2% believed Mouse C was the golden ratio. In question 8, that dropped to 19.2% — despite Mouse C being the correct answer. Thus, adding a 2D reference image increased the incorrect identification of Mouse D and decreased the correct identification of Mouse C. The conclusion is that 2D references did not help participants make more accurate decisions. In question 9, a 3D golden ratio reference was included alongside 3D images of the mice, as shown in Figure 6. Also, there was no improvement in accuracy.

Figure 6.

3D view with golden ratio reference.

Next, comparing question 7 (without 3D reference) and question 9 (with 3D reference). In question 7, 52.5% chose Mouse D as the golden ratio. In question 9, this rose to 62.6%—again, an incorrect choice. Meanwhile, in question 7, 17.2% chose Mouse C. In question 9, it unchanged at 17.2%, despite being correct. In conclusion, even with a 3D golden ratio reference, participants did not improve in correctly identifying the mouse that adhered to the golden ratio.

In summary, the inclusion of either 2D or 3D golden ratio reference visuals did not assist participants in making more accurate decisions. In both cases, the error rate increased for the incorrect option (Mouse D), while the selection rate for the correct golden ratio design (Mouse C) decreased or remained unchanged. These results suggest that visual reference aids, in the context of this study, were ineffective in supporting accurate identification of the golden ratio.

Results of mouse ratio preference survey

The final survey examined participants’ aesthetic preferences toward the mouse ratio. The results indicated that Mouse B was the most preferred, selected by 46.5% of participants. This ranking was B > C > E > A = D. Notably, Mouse B was neither the most commonly perceived as having the golden ratio nor the mouse with an actual length-to-width ratio closest to the golden ratio. The mouse most frequently perceived as having the golden ratio was Mouse D, while the actual closest match was Mouse C. These findings suggest that participants’ aesthetic preferences for mouse appearance were not correlated with the presence or proximity of golden ratio proportions.

Gender differences in recognition accuracy

In this study, regarding the accuracy in identifying the mouse closest to the golden ratio (Mouse C), a gender difference was observed. The recognition accuracy for male participants was 32%, whereas for female participants, it was 34%, indicating a 2% higher accuracy among females, shown in Figure 7. For other mice, there is no gender difference in recognition. Furthermore, when assessing aesthetic preferences for mouse appearance, no significant gender difference was detected. The data on gender differences in recognition accuracy for the five mice are presented in Table 1.

Table 1.

Gender differences in recognition accuracy.

Mouse	A	B	C	D	E
Ratio	1.42	1.50	1.62	1.70	1.78
Male	0.43	0.32	0.32	0.46	0.35
Female	0.44	0.15	0.34	0.61	0.34
Total	0.43	0.21	0.34	0.45	0.34

However, based on the chi-square test, the p-value was 0.343, which exceeds the conventional significance threshold of 0.05. Therefore, the null hypothesis cannot be rejected. This result indicates that there is insufficient statistical evidence to support a significant association between gender and the ability to recognize the golden ratio in mouse design. In other words, based on the current data, there is no statistically significant difference between male and female participants in identifying golden ratio proportions in the test models.

Figure 7.

Gender differences in recognition accuracy of golden ratio mouse.

Summary

In this study, I derived the following seven summaries from the analysis of the questionnaire results. (A)

In absolute judgment tasks, participants’ intuitive assumptions about which mouse conformed to the golden ratio were often incorrect, with more participants misidentifying the mouse C than correctly recognizing it.

(B)

In 2D image-based tasks, whether under absolute or relative judgment conditions, the mouse most frequently identified as having the golden ratio was incorrect, even by design students. This result suggests that recognizing golden ratio proportions from 2D visuals is not easy or reliable.

(C)

The use of 3D perspective renderings did not improve recognition accuracy, indicating that even 3D model presentations do not help users more accurately judge whether a mouse design adheres to the golden ratio.

(D)

When 2D golden ratio reference images were provided alongside the test samples, there was no improvement in the accuracy of participants’ judgments. This result implies that additional 2D visual references do not significantly assist in recognizing the golden ratio.

(E)

Similarly, when 3D golden ratio reference images were presented alongside the 3D mouse models, no improvement in correct identification was observed. Thus, an additional 3D reference also failed to enhance decision-making.

(F)

Participants’ aesthetic preferences for the mouse ratio designs were not associated with whether the mouse was close to the golden ratio. In other words, a golden ratio design did not guarantee user preference.

(G)

Recognition accuracy did not differ by gender, with male and female participants showing nearly identical performance in identifying the mouse that matched the golden ratio.

Nonlinear prediction model of ratio and participants’ preference

The study examined how aspect ratio influences gender-based preferences in mouse design and conducted separate polynomial regression analyses for male and female participants. The ratio of the mouse models served as the independent variable, and preference values were treated as the dependent variable. Based on the updated data, both male and female participants showed their highest preference within the ratio range of 1.5 to 1.6, corresponding to Models B (1.50) and C (1.62). Although their exact preference levels differed slightly—males showing a stronger peak at 1.50 and females showing a broader peak spanning 1.50–1.62—the general trend remained nonlinear. Table 2 presents the data on gender differences in ratio preferences across the five mice.

Table 2.

Gender differences in mouse ratio preference

	A	B	C	D	E
Ratio	1.42	1.50	1.62	1.70	1.78
Preference	0.08	0.46	0.28	0.08	0.09
Male Preference	0.05	0.59	0.24	0.08	0.03
Female Preference	0.10	0.39	0.31	0.08	0.13

For female participants, the cubic polynomial model showed a strong fit (R² = 97.41%, adjusted R² = 89.62%), yet it did not reach conventional statistical significance (P = 0.204). Although none of the individual terms were statistically significant, the cubic term (F = 19.49, P = 0.142) remained the primary contributor to the model, indicating that female participants exhibit a nonlinear perceptual response to proportion, but the limited sample size likely reduced statistical power.

For male participants, the model also demonstrated a high degree of fit (R² = 95.36%, adjusted R² = 81.44%) but similarly failed to reach statistical significance (P = 0.272). Sequential analysis showed that the cubic term (F = 10.17, P = 0.193) accounted for most of the explained variance, suggesting that male participants likewise display a nonlinear response pattern to proportion, even though the relationship was not statistically reliable.

In contrast, the model for all participants combined showed both an exceptional fit and statistical significance (R² = 99.91%, adjusted R² = 99.65%; P = 0.038). Crucially, the cubic term was the only statistically significant predictor (F = 577.70, P = 0.026). The overall perceptual tendency toward proportion follows a distinctly nonlinear form when aggregating across participants, as illustrated in Figure 8.

Figure 8.

Polynomial regression analysis: participants’ preference versus ratio.

Overall, the results show that a cubic polynomial regression effectively describes how mouse aspect ratio relates to gender-specific aesthetic preferences. Although both the female (R² = 97.41%, P = 0.204) and male models (R² = 95.36%, P = 0.272) fit well, neither reached statistical significance, likely due to the small sample size. In both groups, the cubic term provided most of the explanatory power, suggesting a nonlinear response to proportion. In contrast, the combined model was both highly accurate and statistically significant (R² = 99.91%, P = 0.038), with the cubic term emerging as the key predictor. These findings indicate that participants judge mouse proportions through a nonlinear pattern, with both genders showing a higher preference at ratios around 1.50–1.62. Future studies should increase sample size and include additional design variables to improve generalizability and explore sources of gender differences.

This study also found no significant correlation between whether a mouse conformed to the golden ratio (approximately 1.62) and its popularity, suggesting that the golden ratio does not inherently produce the expected aesthetic appeal in product design.

Apply machine learning in a prediction system

This study collected user aesthetic preference data for mouse designs to serve as the basis for developing a prediction system. Machine learning is a key tool for analyzing IoT data for descriptive, predictive, and adaptive purposes.³⁰ Accordingly, I employed a decision tree-based machine learning approach as the prediction system, implemented in Minitab, with mouse aspect ratio and user preference as the input variables. The results showed that the highest preference range was the mouse aspect ratio = 1.44–1.56, and the mouse ratio in this range was the most acceptable. Exceeding 1.66 or falling below 1.44 would significantly reduce the preference. Currently used as a design benchmark for the appearance ratio of new mice, this CART analysis can be used to predict the possible preference values of new products. Future applications can be used in the field of product design.

Figure 9.

CART regression tree analysis of mouse ratio and preference.

According to the results of the mouse aspect ratio and user preference survey, the preference degree can be divided into five intervals: when the mouse ratio is lower than 1.44 (T1 interval), the preference mean is Male = 0.05, Female = 0.10, All participants = 0.08, indicating that this interval is narrow and generally not favored; when the ratio is between 1.44 and 1.56 (T2 interval), the preference mean is Male = 0.59, Female = 0.39, All participants = 0.46, representing the user's favorite ratio range with the highest aesthetic appeal; when the ratio is between 1.56 and 1.66 (T3 interval), the preference mean is Male = 0.24, Female = 0.31, All participants = 0.28, showing a slight drop but still within the acceptable range; when the ratio is between 1.66 and 1.74 (T4 interval), the preference mean is Male = 0.08, Female = 0.08, All participants = 0.08, indicating a wide ratio that is not favored; and when the ratio exceeds 1.74 (T5 interval), the preference mean is Male = 0.03, Female = 0.13, All participants = 0.09, showing that an overly wide ratio also reduces preference. For mouse design, it is recommended to control the aspect ratio between 1.44 and 1.56, shown in Figure 9.

Application of the ratio prediction system in mouse design

This study integrated the decision tree and regression analysis methods. The optimal ratio for the decision tree is 1.44 to 1.56, and the optimal ratio for the regression analysis is 1.5 to 1.62. After integration, the optimized interval is 1.5 to 1.56, which is used as the reference data for the final prediction system.

In summary, this study proposes a preliminary model for a mouse appearance design prediction system based on the interaction between gender differences and design ratio preferences. Future developments could integrate more design attributes (such as color, curvature, and weight distribution) and user characteristics (such as age, human factors, and usage habits) to create a multidimensional design prediction system, enabling a more accurate alignment of product design with target user groups.

Conclusion

This investigation explored the perception of golden ratio proportions in computer mice from both absolute and relative judgment perspectives across five different mouse models. Participants generally failed to reliably identify the golden ratio mouse, regardless of judgment types. Several factors may have contributed to this outcome. First, the contour design of mice, often featuring large-radius corners, may mislead users into misjudging the actual length-to-width ratio. Mice with sharper, more rectangular edges were more likely to be perceived as conforming to the golden ratio, even when they did not. Second, the numerical proximity of ratios (e.g., 1.62 vs. 1.7) may make it difficult for participants to perceive meaningful differences. Third, as a three-dimensional product, the mouse is presented in 2D imagery, whether in a flat or perspective view, which may limit perceptual accuracy and contribute to recognition difficulties. Lastly, the study found no evidence to suggest that a golden ratio design enhances aesthetic preference. Thus, designers should not overly rely on the golden ratio as a determinant of user appeal in product design. Based on the results, if I develop a ratio prediction system for mouse design in the future, a mouse design with an aspect ratio of 1.5 to 1.56 can serve as an essential reference for preference prediction.

Footnotes

ORCID iD

Chih-Ping Chen

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Ministry of Science and Technology, Taiwan (Grant Number NSTC 114-2410-H-130-019-MY2).

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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