Aggression in the workplace makes social distance difficult

The spread of new coronavirus (COVID-19) infections continues to increase. The practice of social distance attracts attention as a measure to prevent the spread of infection, but it is difficult for some occupations. Therefore, in previous studies, the scale of factors that determine social distance has been developed. However, it was not clear how to select the items among them, and it seemed to be somewhat arbitrary. In response to this trend, this paper extracted eight scales by performing exploratory factor analysis based on certain rules while eliminating arbitrariness as much as possible. They were Adverse Conditions, Leadership, Information Processing, Response to Aggression, Mechanical Movement, Autonomy, Communication with the Outside, and Horizontal Teamwork. Of these, Adverse Conditions, Response to Aggression, and Horizontal Teamwork had a positive correlation with Physical Proximity, and Information Processing, Mechanical Movement, Autonomy, and Communication with the Outside had a negative correlation with Physical Proximity. Furthermore, as a result of multiple regression analysis, it was shown that Response to Aggression, not the mere teamwork assumed in previous studies, had the greatest influence on Physical Proximity.


Introduction
The spread of new coronavirus  infections is increasing steadily. As of this writing, August 8, 2020, there are 19,382,107 infected people worldwide (Johns Hopkins University & Medicine, 2020). The recommended practice of preventing infection is the social distance, that is, maintaining the distance between people (World Health Organization, 2020). However, some jobs are easy and difficult to take social distance. Therefore, research to clarify the relationship between work characteristics and social distance is becoming active (Crowley & Doran, 2020;Dingel & Neiman, 2020;Hatayama et al., 2020;Koren & Pető, 2020). Such research can give great hints and significance to the new industrial structure in the era of with-corona. However, it does not mean that there is no problem at all, such as making people feel arbitrary about how to make the scale. Therefore, this paper uses 98 items recorded in the Work Context and Work Activities of O*NET to perform factor analysis while eliminating arbitrariness as much as possible. Then, after creating an independent variable from the extracted factors, a regression analysis using Physical Proximity as the dependent variable is performed. The purpose of this is to find the factors that influence the social distance (Physical Proximity as a proxy variable). At the same time, Koren & Pető (2020) 's Teamwork, Customer and Presence, and Dingel & Neiman (2020)'s Remote Working Index will be used as independent variables to verify whether these are useful as determinants of social distance.
Among them, the Social Distance Index developed by Koren & Pető (2020)

and the Remote Working
Index developed by Dingel & Neiman (2020) have 49 and 266 citations respectively (as of August 8, 2020, computed by Google Scholar). However, there is some arbitrariness in how to create the indicators. The former classifies 14 questionnaire items recorded in O*NET, an occupational information site in the United States, into these 3 categories, based on the hypothesis that three factors that influence social distance are Teamwork, Customer, and Presence. The latter also creates variables on the assumption that 17 items related to outdoor work etc. recorded in O*NET influence the executability of remote work. However, neither of them clearly shows the criteria for classification.
Probably they are classified by the authors' eyes.
However, there is no guarantee that the respondents to the questionnaire have responded as the researchers intended. For example, the variables created as Teamwork by Koren & Pető (2020) include items related to leadership. Perhaps there is a difference in the possibility of social distance between vertical and horizontal teams. In the first place, it is a problem that the correlation between Work Context -Physical Proximity, the items seemingly closest to the feasibility of social distance and remote work among the items recorded in O*NET, and each scale is not verified. Therefore, in this paper, to eliminate arbitrariness as much as possible, some factors common to various occupations will be extracted by performing exploratory factor analysis based on certain rules. And based on those factors, we will show the factors that determine Physical Proximity by performing multiple regression analysis using the constructed independent variables. At the same time, we will analyze Teamwork, Customer, Presence by Koren & Pető (2020), and the Remote Working Index by Dingel & Neiman (2020) as independent variables, and verify whether these are useful as determinants of social distance.

Method
Among questionnaire results for 968 occupations posted on the O*NET website (https://www.onetonline.org/), we use the 98 items recorded in Work Context and Work Activities which were used in the studies of Koren & Pető (2020), Dingel & Neiman (2020) and others. Importance and Level are recorded in Work Activities, but Importance is used in the current research following previous research. All items are in the format of making a number from 0 to 100 for frequency and importance. The criterion for factor extraction is eigenvalue 1 or more, and the factor load is calculated after performing varimax rotation by the main factor method. After that, items with a factor load of less than 0.4 and items with a factor load of 0.4 or more on a plurality of factors are excluded, and factor analysis is performed again using the same criteria. After that, this process is repeated until there are no items whose factor loads are less than 0.4 and items whose factor loads are 0.4 or more. Here, we follow the idea of Stevens (1992) who suggests using a cut-off of 0.4, irrespective of sample size, for interpretative purposes. After the factor structure is established, this paper presents a simple hypothesis that should be verified and performs a regression analysis using the variables consisting of each factor as the independent variable and Physical Proximity as the dependent variable to analyze the factors that influence social distance.
As a result of repeating the factor analysis 6 times by the above method, as shown in Table   1, eight factors consisting of 46 items were extracted. Note that the sentences listed are not the question text, but the content of the question text. Details of questions and options can be referred to on O*NET, so they are omitted in this article. However, to give an example, the question sentence corresponding to the content sentence at the top of the table, "Work Context -Very Hot or Cold Temperatures" is "How often does this job require working in very hot (above 90 F degrees) or very cold (below 32 F degrees) temperatures?", and the options are "Never", "Once a year or more but not every month", "Once a month or more but not every week", "Once a week or more but not every day", and "Every day". For each answer, 0 points, 25 points, 50 points, 75 points, and 100 points are assigned, and the average value is calculated for each occupation. Also, the Physical Proximity used as a dependent variable in the current research is selected from "I don't work near other people (beyond 100ft.)", "I work with others but not closely (e.g., private office)", "Slightly close (e.g., shared office)", "Moderately close (at arm's length)", and "Very close (near touching)" for the question sentence of "To what extent does this job require the worker to perform job tasks in close physical proximity to other people?" and is similarly assigned a value of 0 to 100 when totaling.
Based on the contents of the included items, the factors were named as Adverse Conditions, Leadership, Information Processing, Response to Aggression, Mechanical Movement, Autonomy, Communication with the Outside, and Horizontal Teamwork. By the way, Physical Proximity is not included in any of these variables because it loaded multiple factors in the first factor analysis. As indicated by the symbol (R) at the end of the sentence, four of Adverse Conditions overlap with Remote Working in Dingel & Neiman (2020). Also, as shown in (P), one of them overlaps with the Presence of Koren & Pető (2020). Similarly, three of the Leadership and one of Horizontal Teamwork overlap with Teamwork of Koren & Pető (2020) as shown in (T). One of Response to Aggression overlaps with the Presence of Koren & Pető (2020) as shown in (P). There were no duplicate items 4 with Customer of Koren & Pető (2020). Overall, 9 of 46 items, or 19.6%, overlapped with either or both of Dingel & Neiman (2020) and Koren & Pető (2020).  (Purvanova & Bono, 2009). In this regard, Horizontal Teamwork is an element that involves a more horizontal relationship, so it is considered that Physical Proximity is required compared to Leadership. This is because who takes the initiative depends on the tasks that change day by day. Also, when someone performs many tasks, adjustments are frequently made such that someone reduces the tasks. However, with the proper feedback and procedural justification from the boss, the adverse effects of role ambiguity can be significantly reduced (De Clercq & Belausteguigoitia, 2017;Jong, 2016). Therefore, it is expected that Response to Aggression has the greatest correlation with Physical Proximity. This is because collaboration with a person who is not good at emotional control is likely to induce an unexpected situation, so it is considered necessary to have him or her nearby and to cooperate with others around them. Previous studies have shown that maintaining physical proximity to students, for example, is most necessary for teachers to turn their negative consciousness into a positive one (den Brock et al., 2005). Therefore, the following hypothesis is derived.
H4: Response to Aggression has the strongest positive correlation with Physical Proximity. Table 2 is descriptive statistics. In addition to the above eight variables, Physical Proximity, the three variables of Teamwork, Customer, and Presence by Koren & Pető (2020) and Remote Working by Dingel & Neiman (2020) are listed with their values and correlations by the author's calculation. In general, 0.7 or more is considered to be an acceptable reliability coefficient (Cortina, 1993), but several researchers have accepted it as 0.6 or more (Taber, 2018;van Griethuijsen et al., 2015). According to the latter criterion, all eight variables are acceptable. However, according to the former criteria,

Analysis and result
Mechanical Movement and Horizontal Teamwork are unacceptable. Therefore, for Mechanical Movement, we prepared a 3-item version without Work Context-Time Pressure, and for Horizontal Teamwork, we prepared a 3-item version with Work Context-Coordinate or Lead Others, dropped in the first factor analysis because it was the same factor as the other two items but loaded on other factors, added. After confirming that the reliability coefficients of these variables were 0.7 or more, they were used for the following analysis alternatively (The result is omitted because it did not make a big difference).
Looking at the magnitude of the correlation coefficient, all except for the two categories of Leadership and Mechanical Movement show a statistically significant correlation with Physical Proximity at the 5% level. However, the values exceeding 0.1, which is the standard value for "small" by Cohen (1988) This is probably because, as described at the beginning, items that represent horizontal teamwork and items that represent vertical teamwork are mixed in the variable.   The first column of Table 4  Leadership showed no significant correlation in either single regression or multiple regression.
Looking at the results of the three items of Koren & Pető (2020) from the second column of the Proximity, so it can be interpreted as a problem of multicollinearity. This indicates that some caution is required when using the three items of Koren & Pető (2020). By the way, 14 variables that compose the three variables of Koren & Pető (2020) were simply averaged and subtracted from 100 to create one variable Social Distance Index (α=0.727, mean value = 50.753, standard deviation = 9.085) following the way of Crowley & Doran (2020), and examined the relationship with Physical Proximity.
Therefore, in the third column, the results of a regression analysis performed on a variable group in which Customer and Remote Working whose adjusted R-squared for single regression exceed 0.13, the "medium" level (Cohen, 1988), are added to the first column model are shown experimentally.
In addition to Customer and Remote Working, four of the five variables shown in the first column, except for the Mechanical Movement, are significant. However, the magnitude of the partial correlation coefficient is different between the first and third columns, and it seems that there is a problem of multicollinearity. This is understandable considering that many of the items that make up Customer and Remote Working were the ones excluded during the exploratory factor analysis due to the load on multiple factors. Despite this problem, the fact that the variables in the first column including Response to Aggression became significant even after controlling the impact of Customer and Remote Working indicates the robustness of the model in the first column. For reference, the adjusted R-squared for all the three models in Table 4, 0.319, 0.293, and 0.491, exceed 0.26, the "large" level (Cohen, 1988). Among them, the value of the mixed model in the third column is the highest.
Therefore, although it is worrisome that the distortion of the partial correlation coefficient impairs the accuracy of the influence of individual variables, the mixed model in the third column is considered to be useful for predicting the feasibility of social distances more accurately by taking into account differences in customer contact and outdoor activities.   Aggression was shown to be the most important factor affecting Physical Proximity.
In parallel, we verified the relationship between the three variables shown by Koren & Pető (2020) and Physical Proximity and found that the correlation of Customer is significantly larger than that of Teamwork and Presence. It was also shown that the problem of multicollinearity occurred and the Teamwork coefficient was reversed when the three variables are applied to the regression equation at the same time, and it became clear that some caution is required in use. On the other hand, the variables that combine the three variables of Koren & Pető (2020) into one, or the Remote Working Index of Dingel & Neiman (2020) showed a significant correlation with Physical Proximity, avoiding the problem of multicollinearity. However, their adjusted R-squared were below 0.2, which leaves dissatisfaction with the model's explanatory power. In an attempt, we added the Customer of Koren & Pető (2020), which represents the contact with the customer, and the Remote Working of Dingel & Neiman (2020), which represents the small amount of outdoor activity, to our multiple regression model consisting of five variables. As a result, although the partial regression coefficient was distorted due to the problem of multicollinearity, it was significant in four of five variables including Response to Aggression in addition to Customer and Remote Working. This result shows that the model presented in this paper is significant even when the variables in the previous study are controlled. At the same time, it suggests that this mixed model can be used with higher accuracy when predicting the possibility of social distance in the workplace.
In the model shown in this paper, in addition to Response to Aggression, Horizontal

Implication
In the study by Koren & Pető (2020), a model was constructed assuming that one of the three factors that influence social distance is Teamwork. However, the results of this paper show that Response to Aggression has a greater influence on Physical Proximity than on Horizontal Teamwork. This means that while some horizontal teamwork is possible even in the virtual world (Krumm et al., 2016;Painter et al., 2016), it is difficult to respond remotely and on the spot when dealing with people who bring confrontation such as getting angry or offensive. It means that it is necessary to face and deal with them directly. Unfortunately, it seems unlikely that science and technology will replace aggressive human contact. For instance, in the field of robot development, it has been pointed out that it is the most difficult task to operate in an unstructured environment that assumes contact with humans (Mori, 2020).
In this paper, to eliminate arbitrariness as much as possible, we have shown a model for determining physical proximity by executing exploratory factor analysis based on certain rules, extracting eight factors, and performing multiple regression analysis. The types of jobs that are hard to avoid Physical Proximity because of the response to aggression include teachers of elementary/middle school and special education, therapists, technicians, nurses, employees of restaurants and entertainment facilities, travel/postal service clerks, flight/transportation attendants, etc. For such occupations, it may not be easy to secure a social distance by replacing them with remote work, so it is necessary to devise and implement protective measures that can suppress infection even when they are close to people. However, in reality, people whose emotions cannot be suppressed exist in many workplaces not limited to these occupations in the process of contacting customers. For example, the results of an interview survey show that nurses suffer most from aggression from colleagues rather than from patients (Farrell, 1997). Therefore, the results of this paper suggest that the existence of such people may make Physical Proximity, which would otherwise be avoided by remote work, inevitable. Learning how to control own emotions well (Denson et al., 2011), and building a mechanism of reciprocity by increasing the social capital to suppress selfish thinking (Kokubun, 2020;Kokubun et al., 2020), etc. are also considered to be successful in the practice of social distance. At the same time, it should be noted that member aggression often results from mistreatment in the organization. For example, previous studies report that perceived injustice (Beugré, 2005) or unfair treatment of bosses (Neuman and Baron, 1998) increases employee aggression.
Therefore, management ingenuity such as devising a method of giving reasonable feedback to the employees should also lead to increasing the possibility of social distance.

Limitation
This paper exploratively extracted the factors that are the variables used in regression analysis, using the average values by the occupation of the attitude survey data recorded in the US occupation information site, O*NET. Therefore, if the primary data before being aggregated by occupation can be obtained and the results of this paper can be verified, its significance will be great. Besides, Physical Proximity used as the dependent variable of the analysis is a variable based on the questionnaire survey results and may differ from the actual proximity. It is also significant to verify the analytical model in this paper after measuring the actual proximity using GPS location information, etc.

Conclusion
The spread of new coronavirus (COVID-19) infections continues to increase. The practice of social distance attracts attention as a measure to prevent the spread of infection, but it is difficult for some occupations. Therefore, in previous studies, the scale of factors that determine social distance has been developed. However, it was not clear how to select the items among them, and it seemed to be somewhat arbitrary. In response to this trend, this paper extracted eight scales by performing exploratory factor analysis based on certain rules while eliminating arbitrariness as much as possible.