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Article

Thermal Comfort Assessment in University Classrooms: A Discriminant Analysis for Categorizing Individuals According to Gender and Thermal Preferences

by
Iasmin Lourenço Niza
*,
Inaiele Mendes da Luz
and
Evandro Eduardo Broday
IEQ Lab, Federal University of Technology—Paraná (UTFPR), Rua Doutor Washington Subtil Chueire 330, Jardim Carvalho, Ponta Grossa 84017-220, Brazil
*
Author to whom correspondence should be addressed.
Atmosphere 2023, 14(9), 1325; https://doi.org/10.3390/atmos14091325
Submission received: 2 August 2023 / Revised: 18 August 2023 / Accepted: 21 August 2023 / Published: 23 August 2023
(This article belongs to the Special Issue Future-Proofing Buildings for Enhanced Indoor Air Quality and Thermal Comfort: An Opportunity for Resilient Tomorrow)
Browse Figures
Versions Notes

Abstract

:
The concern with the well-being of users in buildings has become increasingly essential, covering aspects related to health, energy efficiency, and productivity. The thermal environment evaluation in buildings has become more frequent due to the time people spend inside them. In this context, this study aimed to analyze thermal comfort in classrooms at a Brazilian University. During the autumn, 50 measurements were performed, resulting in 519 valid responses. The results of the linear regression analysis revealed that the thermal comfort range for females was 20.39–22.19 °C, while for males it was 19.47–22.56 °C. Through discriminant analysis, participants were classified based on their thermal sensation vote (TSV), predicted mean vote (PMV), and thermal preference votes (PREF), achieving a success rate of 76.1% for females and 81.6% for males in forming the groups, which demonstrates the effectiveness of discriminant functions in predicting thermal comfort for both groups. These results highlight the importance of considering gender differences in the search for thermal comfort conditions and providing guidelines that promote the well-being of occupants and the conscious use of energy. This implies adjusting the thermal conditions according to the specific needs of males and females in classrooms, always seeking to provide a suitable environment for activities, and considering energy efficiency and users’ productivity.

1. Introduction

Over the years, engineers and architects have become aware of the need to design more energy-efficient buildings. This implies reducing energy consumption and providing comfort indoors [1]. Considering that people spend about 90% of their time indoors, it is essential to ensure comfortable thermal conditions [2]. Several strategies are implemented to achieve this thermal comfort, including heating, ventilation, and air-conditioning systems [3], the application of thermal comfort and sustainability standards, and the inclusion of adaptability to individuals. These aspects are usually addressed in field research involving personal, environmental, interpersonal, and non-thermal factors [4]. To perform this analysis, it is important to include subjective responses from rating scales to describe individuals’ acceptability, comfort, and thermal sensation [5]. It is worth noting that due to the COVID-19 pandemic, the interest in ensuring healthier environments has become even more evident [6].
In this context, educational environments play a relevant role in people’s lives. They should value the well-being and performance of students throughout their academic stages, which require concentration and critical thinking [7]. However, environmental conditions can have an impact on these aspects. Educational levels range from kindergartens to universities [8], and research has focused on analyzing the relationship between thermal comfort and student satisfaction and productivity. Over the years, studies have been carried out in educational buildings, such as kindergartens in Slovenia and Korea [9,10], secondary schools in Portugal and Indonesia [11,12], elementary schools in Australia and Costa Rica [13,14], and universities in Ecuador, Malaysia, and Japan [15,16].
In addition to these studies, several statistical techniques have been used to investigate thermal comfort in classrooms. These approaches range from using factor analysis to examine whether the surrounding environment can influence math performance [17] to applying Bayesian statistical methods to improve building energy efficiency [18]. Logistic regression has also been used to identify acceptable air temperature limits in buildings with heating, ventilation, and air-conditioning (HVAC) systems [19]. Griffiths analysis was applied to measure the sensitivity of individuals to different temperatures [20] and clustering analysis to understand people’s predominant perception of the thermal environment [21].
Techniques such as linear regression [22] and discriminant analysis [23] have disclosed interactions between variables and categorized elements into independent groups. Lai and Chen [24] used linear regression to predict the distribution of thermal comfort based on subjective evaluations of thermal sensations. Maykot, Rupp, and Ghisi [25] determined thermal comfort temperatures for men and women in air-conditioned and mixed-mode offices. Gobo et al. [26] developed a thermal comfort model suitable for subtropical climates. Wu et al. [27] created an adaptive comfort model to evaluate the conditions of naturally ventilated residential buildings in China. In the study by Talukdar et al. [28], linear regression was applied to relate evaluations of thermal sensations to the operative internal temperature to estimate the neutral temperature. Singh and Chani [29] investigated naturally ventilated apartments to determine the corresponding temperatures and comfort range.
Niza and Broday [30] used discriminant analysis to categorize individuals based on their thermal sensations, obtaining an accuracy of over 96%. In addition, Wu, Li, and Qi [31] investigated the possibility of identifying an individual’s state of thermal comfort in the environment using electroencephalography (EEG) signals, achieving a discrimination rate of approximately 87.9%. Shan et al. [32] evaluated energy consumption in residential buildings based on thermophysical properties, achieving a classification rate of up to 97.9%. Gładyszewska-Fiedoruk and Sulewska [33] classified mental states in different thermal conditions using patterns of electroencephalogram (EEG) neural signals, optimizing the experience of individuals in buildings, where they achieved a classification rate of over 95% for both task and rest conditions. Neale, Kummert, and Bernier [34] used linear discriminant analysis to apply machine learning classification to predict building characteristics from electricity smart meter data.
In this context, the central aim of this research is to comprehensively investigate thermal comfort conditions in university classrooms, focusing on analyzing the differences in preferences and perceptions of thermal comfort between the female and male genders. The focus was on determining the thermal comfort temperatures for each gender based on the subjective responses collected from the participants and investigating how the participants distinguish themselves into groups based on thermal sensation votes (TSVs), predicted mean votes (PMVs), and thermal preference votes (PREF) using discriminant analysis. Although studies have been carried out at various levels of education to understand thermal comfort and its implications in classrooms, there is a lack of specific research into how thermal comfort preferences and perceptions may vary in university institutions. Most of the research has focused on younger age groups, such as kindergarten and elementary school, and little attention has been paid to higher education. Thus, the gap to be filled is understanding the differentiated thermal preferences of university students and how this can influence their satisfaction, academic performance, and well-being.

2. Materials and Methods

2.1. Research Information and Procedures for Obtaining the Variables

This research was conducted in the same environment and using the same database as the previous study by Bueno et al. [35]. A cluster analysis assessed the relationship between thermal dissatisfaction and productivity in university classrooms in southern Brazil. This region has a humid temperate climate (Cfb), moderately hot summers, mild winters, and predominantly rainy weather [36,37].
The campus in question houses several buildings for classrooms, laboratories, a university restaurant, and spaces for sports activities. The facilities are built with masonry materials and ceramic blocks [38], with an average area of approximately 65 m2 and a capacity for 42 students, as illustrated in Figure 1. All the analyzed classrooms have natural ventilation and similar dimensions.
Data collection was performed using 50 measurements, from 23 March to 14 June 2022, during the autumn. This period was chosen to collect data because this was the first semester in the university where presential classes took place since the COVID-19 pandemic started. During this period, 519 valid responses were obtained by employing questionnaires, which included information about environmental variables, personal variables, and thermal preferences. Measurements were taken during three periods of the day (morning, afternoon, and evening), and the number of participations was counted, not the total number of individuals.
Bueno et al. [35] collected the environmental variables using a device similar to the BABUC-A microclimate station manufactured by Brüel and Kjaer, as shown in Figure 2.
The microclimate station has built-in measurement sensors, ensuring high accuracy and resolution to guarantee reliable and detailed measurements. This enables real-time monitoring and access to data that have been recorded and stored over a period. The following values were obtained for the expanded uncertainties (coverage factor = 2, 95% probability) of the measured variables: dry and wet bulb temperature = ±0.2 °C; relative humidity RH = ±1%; globe temperature = ±0.03 °C.
Personal variables were obtained through a questionnaire that requested participants fill in information such as age, weight (in kg), height (in cm), gender (female/male), clothing used, the thermal sensation votes (TSVs) following the seven-point scale of ISO 7730 [40] (+3 hot, +2 warm, +1 slightly warm, 0 neutral, −1 slightly cool, −2 cool, −3 cold), and the thermal preference (PREF) described in ISO 10,551 [41] (+3 much warmer, +2 warmer, +1 a little warm, 0 neither warmer nor cooler, −1 slightly cooler, −2 cooler, −3 much cooler).
Clothing insulation was calculated for all participants according to ISO 9920 [42] and ASHRAE 55 [43]. For ambient temperature conditions, a minimum air velocity of 0.1 m/s was considered, as used by Wang et al. [44] and Fernández-Hernández et al. [45]. The metabolic rate adopted was 1.2 met, as established by ISO 8996 [46] for sedentary activities, corresponding to the activity performed by students in the classroom.
To obtain the PMV, calculations were performed using the thermal comfort tool developed by the Center for the Built Environment [47] of the University of Berkeley. To organize and tabulate the data obtained from the equipment, questionnaires and thermal comfort tools, MS Excel® spreadsheets were used. After obtaining the PMV and the data from the questionnaires, the statistical analysis was performed using the IBM SPSS Statistics software, version 23.

2.2. Development of Linear Regression Analysis in SPSS

For each completed measurement, the operative temperature (Top) was calculated as the simple average between the air temperature (ta) and mean radiant temperature (trm) following the method performed by Mičko et al. [48]. The mean PMV, TSV, and PREF were calculated for each gender, resulting in 95 mean values. Thus, it was possible to perform a simple linear regression analysis to obtain equations relating TSV and Top for males and females. This equation makes it feasible to obtain the comfort temperature for each gender. Furthermore, obtaining a comfort temperature range equivalent to a thermal comfort zone for each group becomes interesting. By replacing the TSV value of the equation with −0.5 and +0.5, it is possible to obtain, respectively, the lower and upper limits of a temperature range that meets category B, as presented in ISO 7730 [40]. In this category, the extremes of the comfort zone are about 10% of people feeling thermally dissatisfied, or 90% of people are thermally satisfied.

2.3. Development of Discriminant Analysis in SPSS

Canonical discriminant functions were developed to perform a statistical discriminant analysis to investigate how subjects discriminate against each other based on their thermal sensation, reality, and preference votes. In this study, the dependent variable was the thermal sensation votes (TSVs) reported by the participating students. After averaging the TSVs for each measurement, the non-integer values were categorized according to the seven-point scale of ISO 7730 [40], depicted in Figure 3. Therefore, five groups were formed for females and four for males to perform the discriminant analysis.
The measurements corresponded to students classified as slightly warm to group 1, neutral to group 0, slightly cool to group −1, cool to group −2, and cool to group −3. Next, Wilks’ Lambda test was used to test the hypotheses that the group means are equal or that there is a difference between them. The hypotheses tested were as follows:
H0: 
equality of the group means.
H1: 
at least one group mean is different.
Another test performed is Box’s M, which investigated whether the covariance matrices of the groups and their variables were homogeneous. The hypotheses tested were:
H0: 
the matrices are homogeneous.
H1: 
the matrices are not homogeneous.
The eigenvalues obtained provided information about the distinct groups within the discriminant functions. The more distant from one the eigenvalues are, the greater the variation between the groups, which explains the formation of the canonical discriminant functions [30]. According to Iacobucci et al. [49], the eigenvalues represent the variance present in the linear combination of the weights of the eigenvectors. Thus, the eigenvalues reflect the real factors in each discriminant function, contributing to their ability to distinguish between groups with significant similarities [50].
The relevance of these discriminant functions was evaluated using chi-square tests, which determine the separation of the observations into groups. All discriminant functions were tested together, revealing that the first function is always the most important for discrimination. Each independent variable (average predicted votes and thermal preference) has unstandardized coefficients used to formulate the discriminant functions. These coefficients helped to identify the coordinates of the centroids of the groups based on their averages, validating their characteristics and allowing the creation of canonical discriminant graphs to visualize the distance between the groups. In addition, a structural matrix was developed to understand how the variables influenced the formation of the discriminant function.

3. Results

3.1. Initial Measurement Results

Firstly, Table 1 shows the average values obtained throughout the 50 measurements regarding the environmental variables and the average PMV, TSV, and PREF.

3.2. Linear Regression Analysis

Excel spreadsheets were used to facilitate data entry in SPSS, so it was possible to start the linear regression analysis between the operative temperature (Top) and the thermal sensation votes (TSVs), obtaining the comfort temperature for female and male students in this classroom. Table 2 presents the means and standard deviations (SDs) for the variables that comprise this linear regression.
In Table 3, there is a summary of the linear regression model, presenting the quality of the model developed along with the R-value that represents the multiple correlation coefficient and the R square that characterizes the percentage of variation in one variable over the other, in this case being the operative temperature (Top) on the thermal sensation votes (TSVs). The Durbin–Watson test has verified the existence of autocorrelation in the residuals (the difference between the predicted value and the observed value). Thus, this obtained value should vary between 0 and 4; the closer to 0, the greater the autocorrelation [51]. In the ANOVA, the F test verified how the fit of the regression model occurs, being for the female gender (F = 18.605, p < 0.05) and male gender (F = 28.058, p < 0.05), confirming that the model fits the data well. In the part that refers to the coefficients, the first row of values provides the intercept of the graph (B = constant). The second row presents the value of the angular coefficient that refers to the slope of the line induced by the variable that appears in the table, which is the TSVs. The t-test investigates two hypotheses:
H0: 
coefficient of the constant is equal to zero (B = 0).
H1: 
coefficient of the constant is different from zero (B ≠ 0).
The p-value for this test is less than 0.05, so the alternative hypothesis is accepted, proving that the coefficients are non-zero and have a weight on the straight-line equation.
Briefly, Table 4 shows the results of the linear regression analysis between TSV and Top employing the equations obtained; the value of comfort temperature is obtained when the person is in thermal neutrality (zero is inserted in the equation). A comfort temperature of 21.29 °C for female and 21.02 °C for male was found; furthermore, a comfort temperature range (thermal comfort zone) was obtained according to category B of ISO 7730 [40], replacing the TSV of the equation by −0.5 and +0.5, being the lower and upper limits for this temperature range.
The comfort temperature range for females and males varies between 1.8 °C and 3.09 °C, respectively. For both cases, the values of the coefficient of determination were closer. Furthermore, it is important to note that the identified comfort temperature ranges apply specifically to the inhabitants of that region, considering its climatic conditions, or to areas with similar characteristics. This is related to the concept of “adaptive comfort”, where people gradually adjust to environmental conditions over time. Figure 4 shows the histogram that proves the normality of the data, following a normal distribution for both groups; thus, this distribution shows the good adequacy of the data in modeling the probability distribution of the comfort temperature. In the histogram, the female group is represented by purple and the male group by blue.
Figure 5 shows the relationship between operative temperature (Top) and thermal sensation votes (TSVs), showing a coefficient of determination (R2) of 0.297 for the female group and 0.374 for the male group; thus, Pearson’s correlation is considered weak due to the coefficient being R2 < 0.3 [52] and moderate for R2 ≥ 0.3 [53].

3.3. Discriminant Analysis

At first, the data referring to TSV, PREF, and PMV for both genders were organized in Excel and then submitted to SPSS to obtain the descriptive statistics of these variables, with their respective means and standard deviations (Table 5).
For this discriminant analysis, the independent variables were the traditional PMV model and the students’ thermal preference for classrooms; thus, it was possible to form the discriminant functions responsible for classifying the observations, of each gender, into groups that represent the thermal sensation votes. Table 6 shows the number of observations in each group for both genders.
Table 7 contains the Wilks’ Lambda tests, where all p-values were less than 0.05, meaning that the variables accepted the alternative hypothesis (H1) and indicated that at least one group means is different.
In Table 8, the results of Box’s M test are presented. For the female group, the p-value was not significant (p > 0.05), showing that the covariance matrices are homogeneous; thus, H0 is accepted. The male group’s p-value was significant (p < 0.05), indicating that the covariance matrices are not homogeneous. Thus, H1 is accepted. The homogeneity assumption of the covariance matrices was met only for the female group. Still, this did not occur for the male group, but it is important to note that the sample sizes may influence this occurrence.
The eigenvalues corresponding to the female (98.8% and 1.2%) and male (93.4% and 6.6%) groups are contained in Table 9, in which the first discriminant function is the one that collaborates to express the differences that exist between the groups.
The results of the function tests are contained in Table 10, in which the first discriminant function will always be significant due to the Chi-square value, which is responsible for the separations into groups. For both genders, the second discriminant function presented values higher than the acceptable significance level of 0.05, being 0.630 for females and 0.206 for males, showing that these variables are not statistically significant for discrimination into groups.

3.4. Discriminant Functions

For male and female genders, the discriminant functions of the independent variables (PMV and PREF) were elaborated on and are shown in Table 11. From these, the students in the classrooms were classified according to their group thermal sensations, and these results helped to gain a better view of how the groups are formed.
In Table 12, the structure matrix contains all the variables that comprise the discriminant functions; those accompanied by asterisks are the most important and describe the highest correlations.
The coordinates of the centroids of each group (female and male) of thermal sensation symbolize the levels of the remoteness of the groups and the particularities of their components (individuals) (Table 13).
Figure 6 comprises the centroids of each group in the canonical discriminant functions. It is reproduced through scatter plots that make it possible to observe how the data behaved (1 slightly warm, 0 neutral, −1 slightly cool, −2 cool, −3 cold).
In the results, the success rate of the classification of the individuals was provided and calculated automatically by the software: 76.1% for the female group and 81.6% for the male group. These values showed a high probability of being correct in the classification and the effectiveness in forming canonical discriminant functions that verify the existence of differences in the thermal comfort of people based on their gender and thermal preference.

4. Discussion

4.1. General Aspects of the Research

This research assessed thermal comfort conditions in university classrooms, exploring statistical techniques to understand and anticipate these conditions. To achieve this goal, linear regression analysis was used to estimate the ideal comfort temperatures. In addition, it was possible to understand how different variables influence the participants’ perception of thermal comfort by developing discriminant functions.
According to Maroco [54], linear regression seeks to model the relationship between variables employing a straight line; this relationship can be of functional dependence and be used to predict the value of a variable. This research analyzed the relationship between the operative temperature and the thermal sensation votes under their magnitudes. From the modeling, equations were obtained that allowed us to calculate and predict the optimal comfort temperature for both genders in classrooms according to the comfort range established by ISO 7730 [40].
With the canonical discriminant functions, it was verified that thermal preference was the most prominent independent variable in forming these functions, representing the existing differences between the observations of the groups concerning the thermal sensation votes (dependent variable). Moreover, the thermal reality calculated by the PMVs did not significantly contribute to the formation of the functions, demonstrating that the users of the classrooms were thermally dissatisfied and preferred that the conditions of the environment be optimized. The accuracy of these functions was significant according to their thermal characteristics, and these discriminations can be used later for a more rigorous analysis.
In line with the purpose of this research, Torriani et al. [55] state that there are diverse thermal comfort expectations in educational environments, especially considering that adaptive capacities are less pronounced at earlier educational stages, such as elementary and high school. Therefore, it is understood that the more advanced a person’s educational stage, the greater their adaptive capacity in terms of clothing selection, window operations, and other actions. In addition, it is worth noting that temperature and comfort preference variations will also change throughout the different educational stages.
In this research, the environment under analysis is naturally ventilated. Faheem, Bhandari, and Tadepalli [56] emphasize that the same applies to Tiruchirappalli, India. They point out that implementing adaptive controls is essential to improve the internal environment. Additionally, Singh et al. [57] point out that significant energy consumption in buildings has become a global concern, mainly due to global warming and climate change. In this sense, specific adaptive comfort guidelines have become viable options in projects seeking to reduce energy consumption without jeopardizing occupants’ thermal comfort and indoor environmental quality (IEQ). This results in the planning of buildings focused on occupants and sustainability.
Another essential aspect is the provision of guidance to indoor users to promote well-being and the conscious use of energy. This type of measure was not commonly applied in the past, as evidenced by the research conducted by Run, Cévaër, and Dubé [58] in France. This research investigated a university building constructed in the late 1960s when energy issues were not considered particularly relevant. However, today the scenario differs substantially due to the advent of solutions that allow for the modernization of the building and its systems. In addition, simulations and even renovations have been introduced. However, such actions do not automatically guarantee an improvement in IEQ. Jain et al. [59] also highlight the importance of considering, at the planning stage, the continuous purpose of the building over time, including the maintenance and operation of building systems. According to Verma et al. [60], these aspects could be enriched by analyzing occupant behavior and measuring and simulating factors related to IEQ. These elements can promote individuals’ well-being, comfort, and health.

4.2. Specific Aspects of the Research

Based on the results obtained, it was found that this study did not reveal statistically significant differences between the female and male genders. This lack of differentiation can be attributed to the comfort temperature range, which varies between 1.8 °C and 3.09 °C for females and males, respectively. It is important to note that this variation results from various factors, such as local conditions, climate, and even the type of environment investigated. This phenomenon is similar to that observed in the study conducted by Yang et al. [61], which indicated that women tend to feel less comfortable in cold temperatures due to their lower metabolic rate and skin temperature. At the same time, men report less comfort in hot environments.
As for the linear regression analysis, the coefficients of determination (R2) were 0.297 for the female group and 0.374 for the male group. As Talukdar et al. [28] pointed out, the literature suggests that these relatively low values are due to the more prominent discomfort tendencies in naturally ventilated environments. Additionally, the p-value was considered significant (p < 0.001). In agreement with this study, Maykot, Rupp, and Ghisi [25] also carried out research in southern Brazil, specifically in Florianópolis, which shares similar climatic characteristics to the city of Ponta Grossa, both classified as temperate climates according to the Köppen–Geiger climate classification [62]. For these conditions, in the autumn, comfort temperatures were estimated at 24.8 °C for women and 25.2 °C for men, higher than the approximate values of 21.29 °C for the female group and 21.02 °C for the male group found in the present study. This discrepancy can be attributed to differences in climatic patterns, cooling methodologies, or even the method of obtaining the comfort temperature.
Only three variables were used to develop the canonical discriminant functions: TSV (dependent variable), PMV, and PREF (independent variables). This approach resulted in a classification success rate of 76.1% for the female group and 81.6% for the male group in the discriminant functions. Neale, Kummert, and Bernier [34] emphasize that the accuracy of classification in discriminant analysis is directly related to the variables used in the development of the model; therefore, the greater the number of variables used in the model, the greater the power of discrimination between groups. As a point of comparison, the accuracy rates in the studies by Wu, Li, and Qi [31] and Gladyszewska-Fiedoruk and Sulewska [33] were 87.9% and 88.52%, respectively. These results are similar to the findings of this study, demonstrating the effectiveness of the discriminant functions developed.
Based on the analyses carried out, evidence was found indicating the existence of an ideal temperature range for thermal comfort. The discriminant functions revealed that thermal preference was the most relevant variable in forming these functions, representing the differences between the groups regarding thermal sensation votes. On the other hand, the thermal reality calculated by the PMV did not significantly contribute to the formation of these functions.

4.3. Study Limitations

We identified some limitations of this study that may have influenced the results obtained. One of them concerns the limited number of observations per group, which may have impacted the analysis and, consequently, the accuracy of the results. It would be beneficial to perform a more significant number of measurements to obtain a more solid analysis and a better approximation of reality. On the other hand, data collection was restricted to autumn only, which may have limited the understanding of user behavior throughout the year. It is recommended to expand the measurements to the other seasons to obtain a more comprehensive view and increase the accuracy of the results.
Another limitation highlighted by Soto-Muñoz et al. [63] was also found in this research, which is the decrease in the number of responses throughout the questionnaire application. The researchers relied on the availability of the volunteer participants; however, a change in engagement was observed throughout the study. Furthermore, Parkinson et al. [64] pointed out that a binary approach to addressing gender is not comprehensive enough as gender is not limited to male and female categories. Future research should include other gender identities in the questionnaires to avoid possible errors arising from name-based gender estimation.
According to Hair, Anderson, and Black [65], discriminant analysis is sensitive to the ratio between the number of predictor variables and the sample size, recommending a ratio of 20 observations per predictor variable. This study used two predictor variables: thermal preference (PREF) and the PMV, so having at least 40 observations would be desirable.

4.4. Future Trends

Among the main future research trends is the application of machine learning (ML) to optimize the performance of comfort predictions and the combination of parameters [62,66]. In addition, it is essential to analyze the relationship between students’ economic vulnerability and its impacts on comfort temperature [67] and to investigate the implications of building orientations on occupants’ indoor conditions [68]. Another relevant point is the development of dynamic and complex models that connect occupants to the thermal environment to understand their productivity [63].
It is also necessary to investigate the impact of shading strategies and morphology on optimizing energy efficiency [69] and assessing climate change’s implications. Another essential aspect is the attention paid to energy consumption during the design phase [70]. In this way, possible problems can be mitigated even before construction begins, leading to various financial, sustainable, and thermal benefits. In addition, it is important to include new parameters that influence people’s perception of the environment, such as air quality, noise levels, and lighting. Therefore, studies that address and combine these parameters are becoming increasingly pertinent, and it is also important to incorporate physiological considerations [71] and even atmospheric pressure, which is rarely considered [72].
Similarly, it is essential to perform predictive analyses relating learning variables with environmental variables to discover favorable classroom conditions [73]. Furthermore, it is necessary to investigate how indoor environmental quality (IEQ) refers to class size, thermoregulatory indicators, and the thermophysical properties of building materials in educational buildings [74].
Since the onset of the COVID-19 pandemic, other needs must be prioritized in the built environment. Thapa et al. [75] report that in addition to the impacts on the economy, health, and lifestyle, overall comfort has been reduced, affecting the psychological well-being of individuals. In this sense, Rus et al. [76] highlight the importance of adapting the IEQ of educational buildings to medical protocols, providing better conditions of comfort and safety, reducing energy consumption, and improving learning ability, concentration, and performance. Finally, it is crucial to establish connections between thermal comfort and the Sustainable Development Goals (SDGs) to make spaces safer, more sustainable, inclusive, and resilient [77], contributing to people’s well-being and mitigating the challenges affecting both natural ecosystems and society in general [63].

5. Conclusions

Promoting thermal comfort can bring numerous advantages to building occupants, especially regarding productivity, energy efficiency, health, and well-being. A linear regression analysis revealed that the comfort temperature for people in thermal neutrality resulted in approximately 21.3 °C for women and 21 °C for men. In addition, a thermal comfort range was obtained based on ISO 7730 category B. By replacing the TSVs (thermal sensation votes) in the equation by −0.5 and +0.5, a comfortable temperature range was obtained between 20.39 °C and 22.19 °C for women and between 19.47 °C and 22.56 °C for men, so that the comfort temperature range varies from 1.8 °C to 3.09 °C for females and males, respectively, with no statistically significant differences. It is crucial to mention that these comfort temperature ranges are specific to the region’s inhabitants, considering their unique climatic conditions or areas with similar characteristics. In short, this is related to the concept of “adaptive comfort”, in which people gradually adapt to their environment over time.
Through discriminant analysis, it was found that the first canonical function was the most relevant in discriminating between the groups. The structure matrix revealed that the PREF variable had the highest correlation and was the most influential factor in determining the first discriminant function. However, the PMVs did not contribute significantly to the discriminant functions. The classification results showed a high success rate of 76.1% for the female group and 81.6% for the male group, indicating the relevance of the discriminant functions and how gender and thermal preference influence thermal comfort. Given the predictive capabilities of the equations formed, these findings may facilitate further studies in similar educational settings.
The measurements obtained 46 and 49 observations for the female and male groups, respectively. However, it is essential to note that variations in group size can impact the estimation of the discriminant functions and the classification of the observations. The groups showed significant variations, with most observations classified as neutral concerning thermal sensation. In some cases, extremes occurred on the TSV scale, where responses were considered “hot” and “cold” in the questionnaire. In summary, understanding and meeting the thermal needs of occupants is fundamental to creating healthy, productive, and efficient indoor environments. The application of the results of this study can contribute to the design of more sustainable and comfortable buildings, promoting the well-being and quality of life of those that use them.
In a broader context, the findings in this research may have implications for the physical conditions of the learning environment and student satisfaction, academic performance, and general well-being. A thermally comfortable environment impacts how students perceive their learning experience and can positively influence their engagement and academic performance. Furthermore, when considering well-being, comfortable environments contribute to students’ mental and physical health, promoting an environment conducive to concentration and learning.

Author Contributions

Conceptualization, I.L.N., I.M.d.L. and E.E.B.; methodology, I.L.N., I.M.d.L. and E.E.B.; software, I.L.N. and I.M.d.L.; validation, E.E.B.; formal analysis, E.E.B.; investigation, I.L.N. and I.M.d.L.; resources, I.L.N. and I.M.d.L.; writing—original draft preparation, I.L.N. and I.M.d.L.; writing—review and editing, I.L.N., I.M.d.L. and E.E.B.; visualization, I.L.N., I.M.d.L. and E.E.B.; supervision, E.E.B.; project administration, E.E.B.; funding acquisition, I.L.N., I.M.d.L. and E.E.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior” (CAPES)—financing code 001 and “Conselho Nacional de Desenvolvimento Científico e Tecnológico” (CNPq).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Figure 1. Classroom analyzed in the research.
Figure 1. Classroom analyzed in the research.
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Figure 2. Microclimatic station [39].
Figure 2. Microclimatic station [39].
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Figure 3. Classification of TSVs into groups.
Figure 3. Classification of TSVs into groups.
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Figure 4. (a) Representation of data normality by histogram for females; (b) representation of the normality of the data by histogram for males.
Figure 4. (a) Representation of data normality by histogram for females; (b) representation of the normality of the data by histogram for males.
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Figure 5. (a) Linear regression analysis between TSV and Top for females; (b) linear regression analysis between TSV and Top for males.
Figure 5. (a) Linear regression analysis between TSV and Top for females; (b) linear regression analysis between TSV and Top for males.
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Figure 6. (a) Centroids of the female group with the canonical discriminant functions.; (b) centroids of the male group with the canonical discriminant functions.
Figure 6. (a) Centroids of the female group with the canonical discriminant functions.; (b) centroids of the male group with the canonical discriminant functions.
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Table 1. Values of the variables per measurement.
Table 1. Values of the variables per measurement.
MeasurementTaTrmHRMean PMVMean TSVMean PREF
122.1022.7766.02−0.3739−0.38890.2778
223.2923.6073.690.00110.0000−0.1667
324.9325.1070.690.17770.2727−0.7273
423.6624.4371.910.05710.0000−0.2857
522.0622.0979.97−0.3675−0.18750.1875
623.4224.2170.960.03310.0769−0.2308
724.3624.7067.99−0.11001.0000−1.0000
823.5023.3670.34−0.29000.1000−0.2000
922.0122.5668.99−0.31530.1333−0.3333
1022.9423.4964.26−0.2242−0.50000.5000
1122.1822.5177.25−0.1747−0.20000.2000
1221.6421.9676.23−0.5430−0.80000.2000
1321.7121.9175.75−0.4900−0.06670.0667
1427.3927.7447.650.63580.7500−1.0000
1522.5422.6977.61−0.1553−0.0667−0.2000
1622.7222.8579.07−0.01000.10000.0000
1720.9821.6755.97−0.3742−0.83330.7500
1820.6621.2857.45−0.4156−0.22220.5556
1921.7721.9563.96−0.20110.1111−0.5556
2019.8319.9864.82−0.6600−0.33330.1667
2120.3320.1368.89−0.56000.50001.5000
2220.2420.4871.19−0.80860.00000.5714
2320.9121.1771.78−0.3576−0.64710.4706
2419.7520.1156.07−0.7376−0.35290.2353
2518.6618.8845.62−0.6150−1.00000.5000
2617.4917.9438.34−1.1525−1.50001.2500
2714.6115.0461.20−1.4186−1.71431.8571
2814.7914.8553.32−1.5675−1.00001.2500
2916.3916.7269.92−1.5050−0.50001.0000
3018.1818.1570.58−0.7880−0.20000.0000
3117.9418.4271.73−0.9092−0.25000.2500
3219.1019.3368.24−0.86290.00000.0000
3319.8920.6070.76−0.5172−0.66670.5000
3420.5521.0354.08−1.0200−0.20000.4000
3519.6820.0573.02−0.4870−0.20000.0000
3620.1220.8670.61−0.37300.10000.1000
3720.0520.5270.37−0.5444−0.11110.2222
3819.0319.9771.51−0.6758−0.57691.0385
3916.8818.1579.75−1.2940−0.80001.2000
4019.5819.8267.25−0.3479−1.14291.0000
4116.1816.6888.03−0.9450−1.33331.5000
4217.8118.1783.00−0.8633−1.66672.0000
4318.8118.9175.89−0.45000.00000.0000
4419.5319.5773.00−0.79200.3000−0.1500
4518.5618.8380.81−0.79000.33330.3333
4619.1219.4282.48−0.7550−0.66670.8333
4719.3319.6873.49−0.7785−0.23080.3077
4819.0019.5276.60−0.57910.09090.0000
4916.2216.0661.70−1.1700−0.25000.5000
5014.6914.9466.48−1.9343−1.28571.2857
Table 2. Descriptive statistics for genders.
Table 2. Descriptive statistics for genders.
FemaleMale
MeanSDMeanSD
Top20.48572.745920.23362.6779
TSV−0.44660.8272−0.25440.5300
Table 3. Model summary, ANOVA, and coefficients.
Table 3. Model summary, ANOVA, and coefficients.
Model Summary (Female)Model Summary (Male)
RR squaredRR squared
0.5450.2970.6110.374
ANOVA (female)ANOVA (male)
ModelSum of squaredf *Mean squareF *p-valueModelSum of squaredf *Mean
square		F *p-value
Regression100.841100.84018.605<0.001Regression128.6811128.68128.058<0.001
Residual238.48445.420 Residual215.557474.586
Total339.3245 Total344.23848
Coefficients (female)Coefficients (male)
Non-standardized coefficientsStandardized coefficients Non-standardized coefficientsStandardized coefficients
ModelBStandard errorBetatp-valueModelBStandard errorBetatp-value
Coefficient21.2940.391 54.45 Coefficient21.0200.34 61.817<0.001
TSV1.8100.4200.545 <0.001TSV3.0890.5830.6115.297<0.001
* F = F-statistic; df = degree of freedom.
Table 4. Results of the linear regression analysis.
Table 4. Results of the linear regression analysis.
GroupEquationCoefficient of DeterminationComfort
Temperature (°C)		Comfort Temperature
Range (°C)
FemaleTop = 21.29 + 1.81TSVR2 = 0.29721.2920.39–22.19
MaleTop = 21.02 + 3.09TSVR2 = 0.37421.0219.47–22.56
Table 5. Descriptive statistics.
Table 5. Descriptive statistics.
FemaleMale
VariablesMeanSDMeanSD
TSV−0.44660.8272−0.25440.5300
PMV−0.41020.4853−0.65420.4998
PREF0.39290.91340.27190.7030
Table 6. Number of observations of the groups.
Table 6. Number of observations of the groups.
FemaleTSV−3−2−101
N2215225
MaleTSV−2−101
N210343
Table 7. Test for equality of means.
Table 7. Test for equality of means.
FemaleWilks’ LambdaF *df1 *df2 *p-ValueMaleWilks’ LambdaF *df1 *df2 *p-Value
PMV0.7733.0174410.029PMV0.6498.129345<0.001
PREF0.24232.030441<0.001PREF0.51214.302345<0.001
* F = F-statistic; df = degree of freedom.
Table 8. Box’s M test.
Table 8. Box’s M test.
Box’s M (Female)9.723Box’s M (Male)33.940
FApproach.1.410FApproach.4.233
df16 df16
df21039.940 df2212.380
p-value0.207 p-value<0.001
Table 9. Eigenvalues.
Table 9. Eigenvalues.
Function (Female)Eigenvalues% of Variance% CumulativeCanonical Correlation
13.391 a98.898.80.879
20.43 a1.2100.00.202
Function (Male)Eigenvalues% of Variance% CumulativeCanonical Correlation
11.035 a93.493.40.713
20.073 a6.6100.00.260
a. The first two canonical discriminant functions were used in the analysis.
Table 10. Wilks lambda and chi-square.
Table 10. Wilks lambda and chi-square.
Function Test (Female)Wilks’ LambdaChi-Squaredf *p-Value
1 to 20.21863.1368<0.001
20.9591.73030.630
Function Test (Male)Wilks’ LambdaChi-Squaredf *p-Value
1 to 20.45835.1406<0.001
20.9323.15720.206
* df = degree of freedom.
Table 11. Discriminant functions.
Table 11. Discriminant functions.
GenderDiscriminant Functions
FemaleZ1 = −1.061 − 0.631 PMV + 2.041 PREF
Z2 = 0.652 + 2.146 PMV + 0.582 PREF
MaleZ1 = −0.939 − 0.790 PMV + 1.551 PREF
Z2 = 1.283 + 2.589 PMV + 1.512 PREF
Table 12. Structure matrix.
Table 12. Structure matrix.
Function (Female)Function (Male)
1212
PREF0.959 *0.2820.956 *0.292
PMV−0.2740.962 *−0.6980.716 *
* Highest absolute correlation between each variable and any discriminant function.
Table 13. Centroids of the groups.
Table 13. Centroids of the groups.
Function (Female) Function (Male)
TSV12TSV12
−35.344−0.442−22.9630.039
−20.417−0.613−11.366−0.028
−11.1990.1910−0.536−0.083
0−0.610−0.0111−0.4511.004
1−3.220−0.102
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Niza, I.L.; da Luz, I.M.; Broday, E.E. Thermal Comfort Assessment in University Classrooms: A Discriminant Analysis for Categorizing Individuals According to Gender and Thermal Preferences. Atmosphere 2023, 14, 1325. https://doi.org/10.3390/atmos14091325

AMA Style

Niza IL, da Luz IM, Broday EE. Thermal Comfort Assessment in University Classrooms: A Discriminant Analysis for Categorizing Individuals According to Gender and Thermal Preferences. Atmosphere. 2023; 14(9):1325. https://doi.org/10.3390/atmos14091325

Chicago/Turabian Style

Niza, Iasmin Lourenço, Inaiele Mendes da Luz, and Evandro Eduardo Broday. 2023. "Thermal Comfort Assessment in University Classrooms: A Discriminant Analysis for Categorizing Individuals According to Gender and Thermal Preferences" Atmosphere 14, no. 9: 1325. https://doi.org/10.3390/atmos14091325

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