Estimation of digraph costs for keyboard layout optimization

International Journal of Industrial Ergonomics 48 (2015) 127e138

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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon

Estimation of digraph costs for keyboard layout optimization _ ¸ eri*, Mahmut Eks¸iog lu Ali Is _ aziçi University, 34342 Istanbul, Ergonomics Laboratory, Department of Industrial Engineering, Bog Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 September 2014 Received in revised form 16 April 2015 Accepted 22 April 2015 Available online 20 May 2015

The main aim of this study was to estimate the digraph costs (interkey-stroke times) based on the digraph (two consecutive keys) tapping rates for the optimization of keyboard layouts considering the touch typing principles. The study also investigated the effects of column, row, hand and period on digraph-tapping rate. For the purpose, a laboratory experiment was performed with seven subjects using a conventional keyboard. Digraph-tapping rates of a total of 241 same hand digraphs were recorded for a duration of 2-min. The interkey-stroke times were calculated as the digraph costs for the same hand digraphs using the estimated mean digraph-tapping rates. The different hand digraph costs were calculated based on the same hand digraph costs and the results of a previous study. The results indicated significant column, row, hand and period effect on the digraph-tapping rate. Using the digraph costs and the digraph frequencies of the considered language in a quadratic assignment problem, an optimal touch typing keyboard layout can be developed to satisfy all but one of Dvorak's touch typing criteria. As an application, an optimal keyboard layout, called Turkish I-layout, is developed for Turkish language. The comparison results between I and existing Turkish F and Q layouts showed that the Ilayout is superior both according to the results of the optimization and Dvorak's criteria. Relevance to industry: Optimal and ergonomic keyboard layouts improve typing performance and reduce the likelihood of upper extremity disorders. The digraph-tapping rates estimated through this study are essential for the development of such layouts. © 2015 Elsevier B.V. All rights reserved.

Keywords: Digraph-tapping rate Keyboard layout optimization Touch typing Quadratic assignment problem Dvorak's criteria Interkey-stroke time

1. Introduction

1.1. Basics of touch typing

Despite considerable advancements in science and technology in recent decades, today keyboards are still in use as the main text entry devices. Number of researchers tried to optimize the layouts of keyboards over the years; however, with some shortcomings. In this study, a new approach to optimize the keyboard layouts for touch typing was proposed. First, touch typing principles were examined and keyboard optimization approaches were covered briefly. Following that, digraph-tapping rates were estimated and the effects of some factors on digraph-tapping rates were investigated through an experimental study. Finally, using the experimentally determined digraph-tapping rates, digraph costs were quantified and then used in a quadratic assignment problem for the optimization of the keyboard layout for a selected language.

In touch typing, typists type by using the muscle memory without looking at the keys. All the eight fingers are placed on the home row initially; the left hand on the keys “2, 5, 8 and 11” which correspond to “A, S, D and F” in Q layout with the thumb on the space bar; while the right hand on the keys “20, 23, 26 and 29” which correspond to “J, K and L” in Q layout and again with the thumb on the space bar (Fig. 1). Each finger has its assigned keys and the finger returns to its standard position after pressing any of these keys if it is not already on the home row or the finger is not in preparation of another key press. Touch typing is a very rapid process which includes the parallel movement of fingers. For instance, world champion typists can type at very high speeds up to 200 words per min; and an average professional typist types 60 words per min, which corresponds to five keystrokes per sec (200 ms per keystroke). These interkey stroke times are relatively small compared to the typical choice reaction times. For instance, a study by Salthouse (1984) stated that median interkey interval in touch typing is 177 ms while the median interkey interval for the same subjects in a two-alternative

* Corresponding author. Tel.: þ90 212 866 3300. _ ¸ eri). E-mail address: [email protected] (A. Is http://dx.doi.org/10.1016/j.ergon.2015.04.006 0169-8141/© 2015 Elsevier B.V. All rights reserved.

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Fig. 1. Key positions, columns and rows on a conventional keyboard.

serial choice reaction time task is 560 ms. This and similar studies from the literature showed that touch typing is not comprised of serial movements of fingers; instead, the movements of different fingers are parallel and overlap in time (Salthouse, 1986). That is, as a keystroke being performed by a finger, the other fingers are simultaneously in preparation of their movements for the next keystrokes. The span that shows how far in advance of the current keystroke the typist is prepared for the next keystrokes is called as the replacement span and it is highly correlated with the skill of the typist. For professional typists, replacement span is approximately three characters in advance of the current keystroke (Salthouse and Saults, 1985). Typists are generally 30e60 ms faster when the preceding keystroke is done by the opposite hand than when the preceding keystroke is done by the same hand. This phenomenon was observed by many researchers (e.g., Dvorak et al., 1936; Terzuolo and Viviani, 1980; Gentner, 1981, 1983; Rumelhart and Norman, 1982). This is because when two successive keystrokes are pressed by the same hand, there is little opportunity for the preparation of the next keystroke; and furthermore, if the same finger is used for the successive keystrokes, there is no opportunity at all for the preparation. However, when two successive keystrokes are pressed by the fingers of the alternating hands, as the preceding key is being struck by one of the fingers, the other finger can simultaneously begin its movement toward the next key. Salthouse (1984) divided the digraphs in four categories and showed the differing performances of each category. He calculated the interkey-stroke times of each digraph category using the professional touch typists (Table 1). As can be seen from the table, the category of the fingers of two different hands takes less time than the others while the category of the one finger non-double takes the longest time. The same categorization was used in nearly all of the studies for interkey-stroke times such as Gentner (1983) and Heath and Willcox (1990). However, Hiraga et al. (1980) tried to drive a regression formula for all the digraph combinations based on the data on time intervals between keystrokes.

1.2. Keyboard layout optimization Varying methods have been used for keyboard layout optimization in the previous studies. Most of the earlier keyboard layouts were developed using some heuristic rules while later studies used assignment formulations, multi objective functions and metaheuristic optimization algorithms. With the use of optimization techniques, keyboard layout design has embarked on a new era. Some well-defined mathematical approaches can be found in the literature for solving the keyboard layout optimization problem (e.g., Eggers et al., 2003; Yin and Su, 2011). Eggers et al. (2003) used six criteria and combined them in an aggregating function for the multi objective optimization of keyboard layouts. On the other hand, they did not use valid digraph cost parameters, instead relied on subjective opinions of a few experts in determining the values of the parameters. Yin and Su (2011) decreased the number of criteria from six to two but used the same parameter values like Eggers et al. (2003). There are several studies that used QAP model in single finger lu and keyboard layouts such as virtual keyboards (e.g., Eks¸iog Soydal, 2010; Us¸s¸ak, 2004; Dell'Amico et al., 2009; Li et al., 2006). In these studies, distance matrix of the QAP model was mostly taken as the distance between the keys since in that case interkeystroke time is highly correlated with the distance between the keys. However, in a touch typing keyboard layout, there is either no or very small correlation between the interkey-stroke time and the

Table 1 Means and standard deviations of median interkey-stroke times for the four digraph categories (Salthouse, 1984). Digraph Categories

Median (msec)

The fingers of two different hands (e.g., “ep” in Q layout) Two fingers of the same hand (e.g., “ac” in Q layout) One finger non-double (e.g., “ed” in Q layout) One finger double (e.g., “ee” in Q layout)

144 185 221 168

x (s) (46) (51) (42) (22)

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distance between the keys. This is because of the characteristics of the touch typing. As explained earlier, interkey-stroke time between two keys located on the two edges of the keyboard can be smaller than the interkey-stroke times of the adjacent keys. This is because a digraph having its letters on the opposite sides of the keyboard is executed by alternating hand fingers while a digraph with adjacent letters is pressed by the same or adjacent fingers. Below is a summary of the QAP model and its usage in keyboard layout optimization. 1.2.1. Quadratic assignment problem (QAP) for keyboard layout optimization Pollatschek et al. (1976) were the first in application of QAP for the optimization of keyboard layouts. The QAP model is very useful to design a single finger keyboard such as virtual keyboards. It was also used to create physical keyboard layouts by some researchers (e.g., Light and Anderson, 1993; Malas et al., 2008). For the QAP formulation of the keyboard layout optimization problem, the flow between the letters can be taken as the frequencies of the digraphs (pairs of letters) in the considered language. However, there are different opinions for the distance matrix in the literature; though most studies used time intervals between specific key locations during touch typing. However, touch typing is a highly skilled task that involves parallel finger movements of both hands, so calculating a distance matrix is not easy. There are studies, though not complete, that calculate the time intervals between key positions or specific finger movements. Kinkead (1975), Hiraga et al. (1980) and Heath and Willcox (1990) are the most important studies in this area. 1.2.2. Dvorak et al.'s criteria The book by Dvorak et al. (1936) defined eleven criteria for the design and evaluation of keyboard layouts. These criteria, listed below, were formed based on the principles of touch typing and provided the guidelines of optimal keyboard layout designs: (i) Deviation from the balance of hand and finger loads should be as low as possible. (ii) Percentage of tapping with the same fingers should be as low as possible. (iii) Percentage of tapping that includes top row should be as low as possible. (iv) Percentage of tapping that includes bottom row should be as low as possible. (v) Percentage of tapping in the home row should be as high as possible. (vi) Percentage of tapping by alternating hands should be as high as possible. (vii) Percentage of hurdles with the same finger should be as low as possible. (viii) Percentage of hurdles with adjacent fingers should be as low as possible. (ix) Percentage of hurdles with remote fingers should be as low as possible. (x) Percentage of reach with the same finger should be as low as possible. (xi) Percentage of reach with adjacent fingers should be as low as possible. In summary, the distribution of typing load among fingers; tapping with the same, adjacent or remote fingers; tapping in the home, bottom or top rows; tapping with the same hand or alternating hands; hurdles and reaches all play an important role in the speed of touch typing.

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As explained by Dvorak et al. (1936), a hurdle is defined as a movement of fingers over two rows; i.e., from top row to bottom row or vice versa; and a reach was defined as a movement of fingers over one row; e.g., from top to home, from home to bottom, etc. Although it is known which category is better than the other for faster typing (e.g., hurdles with the same finger are worse than hurdles with the remote fingers; and hurdles are worse than reaches), there are not enough studies to quantify these information objectively. For instance, Salthouse (1984) quantified the interkey stroke times (digraph costs) for four categories of digraphs as mentioned previously (Table 1). However, there are n2 (n: the number of keys on the keyboard layout) digraph costs that need to be quantified objectively. To estimate these digraph costs through the evaluation of the finger movements while typing digraphs is a difficult task. It is because the number of degrees of freedom of a hand movement is high and multiple solutions are possible for a key stroke (Saltzman, 1979) since each of eight fingers has three joints and bones of a finger are controlled by two tendons, and each tendon controlled by muscles located in the forearm.

1.3. Rationale and objectives As the literature review indicates, there are some well-defined mathematical approaches in the literature for solving the keyboard layout optimization problem. However, these models did not use valid digraph cost parameters. Most of them relied on subjective opinions of a few experts instead of determining the parameter values experimentally. As seen from the Dvorak et al.'s (1936) criteria, the distribution of typing load among fingers, tapping with the same, adjacent or remote fingers, tapping in the home, bottom or top rows, tapping with the same hand or alternating hands, hurdles and reaches play an important role in the speed of touch typing. Though it is known which category is better than the other, there are no studies that quantified these satisfactorily by objective methods. This study aimed to address some of the aforementioned shortcomings. For the purpose, the utilization of a single parameter, the digraph cost, was introduced for the quantification of all the criteria of Dvorak et al. (1936) except the first criterion (deviation from the balance of hand and finger loads). This first criterion is not related to digraphs and cannot be handled with a QAP model. Based on the rationale above, this study had the following primary objectives: (i) estimate the digraph-tapping rates for a keyboard layout with up to 32 keys; (ii) investigate the effects of digraph, column, row, hand and period factors on digraph tapping rate (such information could serve scientists who work on finger kinematics, anatomy, etc.); (iii) estimate the digraphs costs based on the tapping rates for the purpose of keyboard layout optimization; and (iv) develop an optimal keyboard layout for a language using the estimated digraph costs and digraph frequencies. The secondary objective of the study was to investigate the relationship between digraph-tapping load and EMG related fatigue indices. The fatigue results would be used as a weight factor in digraph cost estimations.

2. Methods The study consisted of two parts: In the first part, an experimental study was carried out to accomplish the first three and the secondary objectives; and in the second part, the optimization of a keyboard layout was performed using the some of the results of the first part to accomplish the fourth objective of the study.

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2.1. Digraph-tapping rate experiment In this first part of the study, a digraph-tapping experiment was performed to accomplish the first, second, third and secondary objectives of the study. 2.1.1. Participants Seven participants (4 males and 3 females) who are between 19 and 28 were recruited from the university population. A selfreported survey tool was administered to determine the health status of the participants. All the participants were in good health both physically and mentally and had no records of upper-extremity, neck, or shoulder disorders or pain. The participants signed an informed consent form after a full explanation about the study procedures prior to the experiments. All the participants were right handed and all used computers at least ten times per week for a total of at least 8 h per week. This study was approved by the Institutional Review Board aziçi University. for Research with Human Subjects at Bog 2.1.2. Experimental set up A computer workstation similar to the one that typists typically use served as the experimental set up. In this workstation, each subject performed the task on a windows-based personal computer with a standard keyboard of conventional geometry. The workstation was equipped with a fully adjustable seat and a footrest. To allow maximum personal comfort and standardize the posture, the guidelines provided by ANSI/HFES 100-2007 standard “Human Factors Engineering of Computer Workstations” were followed and among the three reference sitting postures (recline, upright and decline), upright sitting posture was adapted. In the adapted posture, the participant's torso and neck were approximately vertical and in line (between 90 and 105 to the horizontal). Shoulder, elbow and wrist joints were in neutral posture with forearm supported. The thighs were approximately horizontal and lower legs were about vertical. Then all subjects were asked to adjust the height of the seat and the backrest inclination based on personal preference, and then it was checked and made sure that postural angles of the subjects while typing were within the range suggested in ANSI/HFES 100-2007. The temperature of the room was kept in the range of 22e24  C during the experiments using an air conditioner. As an attempt to quantify the fatigue of forearm muscles during digraph tapping activities, electromyogram signals of flexor digitorum superficialis (FDS) muscle were recorded using single differential surface electrodes (Delsys® DE-2.1). The placement of the electrodes was made according to the technical notes from the manufacturer (Delsys, 2011). The raw EMG data at a sampling rate of 1000 Hz were filtered with two filters: a band pass filter in the range of 20e450 Hz and a band stop filter between 49 and 51 Hz to eliminate the noises in the signal. The band pass filter was the recommendation of the manufacturer (Luca, 2008) while the band stop filter was put to eliminate the noise from the electrical devices which operate around 50 Hz in Turkey. 2.1.3. Study protocol The experimental task consisted of performing a two-minute digraph-tapping task with maximum volitional speed on a

conventional keyboard for each of the digraph pairs. Each participant repeated the experiment for a total of 241 digraphs. Of these 105 were left hand key and 136 were right hand key combinations. Left hand key combinations were the binary combinations of keys from key 1 to key 15 for which left hand was responsible in touch typing; and right hand key combinations were the binary combinations of keys from key 16 to key 32 for which right hand was responsible in touch typing (Fig. 1). Due to the setup of the experiment, it was not possible to detect the differences of the hit direction. Hence, digraphi,j and digraphj,i are treated as the same digraph in all the experiments and analysis. No alternating hand digraph-tapping rate was measured because the experimental procedure used in this study was not appropriate for measuring them accurately. If we would use the procedure and set up of this study for alternating hand digraph-tapping rates, the fingers of each hand would be just hanging over the corresponding key and tapping, which would not be realistic to obtain the accurate digraph cost scores. Instead, they were calculated based on the same hand digraph results and Salthouse (1984) study. A two-minute tapping duration was determined based on the results of the pilot study. The results indicated that the tapping rate becomes nearly steady for all the digraphs after a certain period. Two-minute was chosen as the duration long enough to differentiate the taping rates of the digraphs. The experiment was conducted using the touch typing principles; that is, the keys in each of the combinations were pressed with the assigned fingers. For instance; for the key combination of 23 and 31, a subject pressed key 23 with the right middle finger and key 31 with the right little finger consecutively (key23, key31, key23, key31, …). The subjects typed the digraphs using a special program written in Java. This program divided each of the two minutes into four consecutive 30-sec periods and calculated the number of correct taps and errors per 30-sec period. Prior to actual tests, a short explanation regarding the task and experimental procedure was given to each participant. Then, each participant practiced the tapping task until he/she felt comfortable to perform the actual tests. Actual tests were done in groups of nine combinations. All 241 digraph combinations were randomized such that within each group, a subject performed 5 right hand and 4 left hand key combinations. These combinations were performed in a way that left or right hand combinations always followed one another. In addition, subjects were allowed to rest at least 15 min between the groups. For a given day, at most 4 groups of trials (9*4 ¼ 36 combinations) were performed in order to avoid overall fatigue of upper extremities and whole body. For each subject, the average total time for the experiment, excluding the resting times, was about eight hours. Overall, it took about 60 workdays to complete the experiment. 2.1.4. Statistical methods A randomized complete block design was used with the subjects serving as blocks to remove the variability between subjects from the experimental error. Table 2 presents the response and independent variables. The response variable was the digraph tapping rate per 30-sec (i.e., number of key strokes per 30 s):

Digraph tapping rate per 30 sec ¼ Net number of correct key strokes per 30 sec ¼ ðnumber of correct keystrokes per 30 secÞ ­ ðnumber of errors per 30 secÞ ¼ ðtotal number of keystrokes per 30 secÞ ­ 2ðnumber of errors per 30 secÞ

(1)

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Table 2 Experimental variables. Variable type

Variable

Response Independent

Digraph tapping rate (# of key strokes) per 30 s Digraph Period Hand Column

Row

Levels 241 same hand digraph levels (105 left hand, 136 right hand digraphs) 1, 2, 3, 4 Right, Left C1eC1, C1eC2, C1eC3, C1eC4, C1eC5, C1eC6, C1eC7, C2eC2, C2eC3, C2eC4, C2eC5, C2eC6, C2eC7, C3eC3, C3eC4, C3eC5, C3eC6, C3eC7, C4eC4, C4eC5, C4eC6, C4eC7, C5eC5, C5eC6, C5eC7, C6eC6, C6eC7 BottomeBottom, TopeBottom, TopeTop, TopeHome, HomeeBottom, HomeeHome

As may be noticed, the number of errors was subtracted two times from the total number of key presses. This was done because, in general, when a typist makes an error, he/she also presses backspace to correct the error. In other words, each error increases total number of keystrokes by 1. This needs to be subtracted from the total since it takes time to correct an error. The independent variables were digraph, period, hand, column and row factors. Period factor was selected to investigate the effect of tapping-duration on the response. As explained previously, each digraph-tapping test lasted two minutes. Each test was divided into four 30-sec periods. Hand factor was selected to see if there was a difference in the response between left and right hands. The column factor was chosen mostly to understand how different fingers interact with each other and the finger kinematics. Since each finger has its own column(s) in touch typing, the indicated column number(s) also shows the finger that presses the associated digraph. Each column was given a name as shown in Fig. 1. Each digraph was expressed using the column numbers it belonged to (Table 2). For instance, digraph24,30 has a column level of “C3eC6” since key 24 is in column 3 and key 30 is in column 6 (Fig. 1). Columns were not separated as left and right hands, since ‘hand’ was another factor in the analysis. The row factor was selected to understand the movement between rows. A conventional keyboard has three rows: top, home and bottom rows (Fig. 1). Each digraph was expressed by the row(s) they belonged to (Table 2). For instance, digraph24,30 (Fig. 1) has a row level of “topebottom” since key 24 is in bottom row and key 30 is in top row. The effect of hit direction on the response was not considered. Hence, it was assumed, for instance, stroking key 7 after key 12 had the same digraph-tapping rate as stroking key 12 after key 7. However, hit direction can have an effect on tapping rate (Eggers et al., 2003). Stroking from little finger towards index finger (outside-in) is better than stroking from index finger towards little finger (inside-out). To accomplish the first objective, descriptive statistics (mean and standard deviation) of the digraph-tapping rate were performed. To accomplish the second objective, an analysis of variance (ANOVA) was used after verifying the underlying assumptions (normality, equal variance, and independency). For multiple comparisons, Tukey's tests were performed. For all the inferential statistical analyses, a p value <0.05 was used to indicate significance. Minitab software was used for all these analyses.

2.1.5. Calculation of digraph costs The third objective of the study was the calculation of digraph costs of both the same and alternating hands. In the experiment discussed above, only the same hand digraph-tapping rates were investigated. So the same hand digraph costs were estimated from these data; while the alternating hand digraph costs were

estimated using the same hand digraph costs and the data obtained from the study by Salthouse (1984). The procedures used for both cases are described below. Calculation of the same hand digraph costs: The digraph cost for each of the 241 same hand digraphs were expressed in msec as the average time it took to press one key after another in the digraph. That is, the digraph cost of digraphij was the time lag from key i to key j (interkey-stroke time between key i and j as expressed in eq. (2)). To do that, the mean values of the response variable (# of key strokes for 30 s) stratified by digraph levels (Table 3) were converted to the mean interkey-stroke times (msec) using the following formula:

Digraph cost ¼ Interkey Stroke Time mean # of keystrokes in 30 sec 1 sec * Þ1 ¼ð 30 sec 1000 millisec Average time ðmillisecÞ ¼ Keystroke (2) Calculation of the alternating hand digraph costs: There are n1*n2 alternating hand digraphs (n1: number of keys assigned to the left hand; and n2: number of keys assigned to the right hand). The present study considered all of these 255 digraphs (n1 ¼ 15 and n2 ¼ 17). Though almost in all of the keyboard optimization models all the alternating hand digraphs were treated as the same erroneously, in this study a new approach was suggested to calculate the alternating hand digraph costs based on the same hand digraph costs and the study by Salthouse (1984). Details are provided below. The average same hand digraph cost calculated from the digraph experiment of the present study was 190 ms, and the value obtained from the Salthouse's (1984) study was 193 s. For the normalization of both groups of digraphs, all the same hand digraph costs (except the same finger doubles) were multiplied by 1.016 to move their average from 190 ms to 193 ms. No multiplication factor was used for the same finger doubles since the average of these digraphs, 168 ms, was the same in the study by Salthouse (1984). First of all, it was assumed that in order to press two keys by alternating hands, a typist moves his/her fingers from the standard key position to the position of the key. This assumption is true if the typist's replacement span is one character. Although, as explained earlier, the replacement span of the professional typists is approximately three characters, this assumption would provide a way to approximate alternating hand digraph costs, which are otherwise hard to quantify. Digraph costs for these digraphs were calculated using the average costs of two digraphs from the standard (home row) positions to the individual keys. For instance, to calculate the cost of digraph4,18 (interkey-stroke time between key 4 and 18; refer to Fig. 1), the digraph costs for digraph4,5 (key 4 was the key in the digraph, key 5 was the standard position of the associated finger of

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Table 3 Descriptive statistics of the digraph-tapping rate per 30-sec for the 241 same hand digraphs. Digraph

x

s

Min

Max

20e23 20e25 20e26 20e22 18e25 18e27 20e27 16e25 18e26 18e24 21e24 19e25 16e26 21e27 19e26 20e30 18e22 18e23 20e31 17e22 16e22 19e28 21e23 19e30 21e31 8e14 17e30 21e26 4e10 20e28 17e23 7e14 6e11 19e22 17e27 17e29 18e30 9e12 6e15 16e30 8e11 7e10 7e13 20e24 5e11 21e22 9e15 4e13 8e15 17e25 19e31 5e12 16e28 17e31 5e13 19e23 8e12 4e14 4e11 18e29 21e32 20e29 5e14 5e15 16e23 19e32 6e14 17e32 17e26 17e28 21e25 7e11 1e13 16e31

228.3 223.5 223.1 222.6 222.1 220.1 219.4 219.0 218.7 218.2 217.9 216.1 216.1 214.6 213.6 213.0 211.7 211.6 211.5 211.1 210.3 210.0 209.9 209.9 209.6 208.5 208.2 208.0 207.6 207.2 207.0 206.8 206.6 206.3 205.8 205.6 205.5 205.2 205.1 204.8 204.7 204.5 204.3 204.0 203.5 203.4 203.4 203.4 203.3 203.1 203.1 202.9 202.8 202.4 201.8 201.7 201.3 200.9 200.8 200.7 200.1 199.2 199.1 198.9 198.2 197.4 197.3 197.2 196.9 196.8 196.0 195.8 195.8 195.6

32.1 34.0 38.9 32.2 43.4 29.5 32.4 32.8 30.7 36.3 36.1 36.6 39.6 45.4 33.9 45.6 29.4 31.0 32.0 41.7 36.9 27.5 41.4 30.6 33.8 29.4 34.4 33.6 29.6 40.8 26.5 22.5 30.2 31.4 39.2 35.6 44.6 27.7 27.9 33.9 28.1 30.7 34.8 33.6 22.7 40.3 31.4 26.8 28.7 28.8 25.9 23.3 35.7 36.1 23.2 33.5 33.5 30.4 31.6 39.6 39.4 27.1 38.8 26.3 30.2 30.2 27.2 33.6 42.5 26.0 38.4 40.0 32.2 30.4

180 145 137 167 153 159 170 162 168 137 158 139 134 133 146 127 148 141 145 136 132 163 125 159 146 163 137 156 163 130 157 155 175 150 132 141 142 141 150 132 172 135 127 143 172 128 142 142 152 149 158 168 133 125 169 140 152 125 145 136 134 146 124 154 147 130 122 139 118 140 127 119 154 147

297 289 280 278 294 283 285 291 300 282 271 288 291 286 276 287 267 270 258 272 265 265 283 290 282 276 271 282 259 267 253 251 274 270 277 271 286 257 281 283 261 257 283 278 254 273 278 263 254 258 259 253 269 273 253 260 257 265 260 274 272 243 276 248 255 234 247 280 252 235 257 259 263 248

Table 3 (continued ) Digraph

x

s

Min

Max

2e14 16e32 6e12 8e10 3e11 2e10 21e29 3e15 3e12 18e31 9e14 5e10 16e29 19e27 6e13 1e14 21e28 1e10 3e13 8e13 19e29 7e12 3e10 20e32 1e11 3e14 2e11 4e12 2e15 2e13 2e12 18e32 9e11 7e15 24e27 4e15 18e28 21e30 23e26 22e32 4e7 5e8 23e27 23e29 5e9 6e9 24e26 1e12 16e27 6e10 19e20 24e31 22e25 23e25 17e19 22e26 17e24 20e21 18e20 5e7 23e30 3e9 16e19 4e8 2e7 18e21 1e15 17e18 17e20 3e8 23e31 16e17 22e31 23e24 1e7 18e19

195.3 193.8 193.8 193.0 191.1 190.9 190.6 190.6 190.2 190.0 189.9 189.9 189.2 189.1 188.3 187.5 186.9 186.3 186.0 185.8 184.9 184.8 184.2 184.1 183.5 183.5 183.0 182.4 182.1 181.6 180.8 180.3 179.6 177.4 174.1 173.9 172.6 172.4 170.8 168.8 167.6 166.6 166.5 166.4 165.8 165.6 165.3 164.9 163.7 163.3 162.2 162.0 161.5 161.4 160.0 159.7 159.2 158.6 157.8 156.9 156.9 156.8 155.4 155.3 155.1 153.9 152.5 152.2 151.2 151.2 150.4 150.3 149.8 149.5 149.3 147.4

27.2 37.6 22.9 29.4 32.4 27.7 36.6 26.3 28.2 34.9 31.3 32.0 37.6 38.1 28.5 20.7 32.2 24.3 21.1 45.3 32.6 42.9 22.8 31.9 40.7 28.3 33.4 41.0 24.5 27.5 24.5 33.1 32.1 40.0 22.0 38.7 31.7 33.0 23.3 22.6 29.3 33.1 27.9 32.8 38.3 27.5 22.4 45.7 41.2 37.6 18.8 21.5 27.0 22.9 11.2 28.9 38.1 15.4 15.9 25.6 19.1 32.9 16.1 34.8 33.8 13.2 44.8 12.9 22.1 28.8 24.7 15.3 26.0 18.3 36.0 16.2

138 115 162 156 130 156 135 140 144 145 134 120 137 126 142 131 126 129 132 107 143 111 157 120 120 128 115 127 142 117 143 129 120 119 134 97 113 120 123 129 117 102 113 123 112 112 115 94 104 95 124 129 113 126 137 106 117 133 123 113 127 97 130 87 101 132 91 118 106 111 106 119 108 113 106 121

254 260 239 251 266 273 249 243 257 248 262 244 257 274 239 216 242 262 243 272 263 255 244 254 248 261 252 261 214 231 232 266 253 250 209 236 222 250 209 210 224 224 207 229 224 222 194 237 226 244 191 203 198 211 177 214 236 187 178 213 195 207 195 204 237 174 226 177 184 204 199 175 185 195 218 176

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Table 3 (continued )

Digraph

x

s

Min

Max

Digraph

x

s

22e23 2e9 22e27 22e29 2e8 19e24 26e27 25e26 23e28 22e28 24e32 23e32 16e20 6e7 19e21 6e8 17e21 16e18 13e14 11e12 1e4 16e24 24e25 31e32 10e11 24e29 14e15 16e21 22e24 12e14 25e30 27e31 29e30 11e14 25e29 30e31 1e8 22e30 4e9 26e31 7e8 12e15 11e13 28e30 3e6 28e29 3e7 8e9 26e30 2e4 2e5 25e27 26e29 9e10 29e31 10e14 3e5 30e32 4e5 10e13 11e15 25e28 26e28 13e15 25e32 5e6 1e5 9e13 10e12 12e13 7e9 29e32 27e30 1e2 1e9 2e6

147.1 146.9 146.6 146.6 146.2 145.5 145.1 145.0 144.7 144.6 144.0 142.9 142.2 142.1 142.0 140.6 139.8 139.7 137.6 137.4 135.7 135.3 135.1 134.9 134.9 134.7 134.1 134.1 133.9 133.9 133.2 132.8 132.7 132.4 132.3 131.9 131.9 131.3 131.3 131.2 130.8 130.1 129.7 129.5 129.4 128.4 127.6 127.6 127.6 127.5 127.0 127.0 127.0 126.5 126.2 126.0 124.6 124.6 124.5 121.4 120.1 119.7 119.7 119.6 119.3 119.0 118.3 116.8 116.5 116.4 115.7 115.6 115.1 114.7 114.5 114.3

18.7 30.4 30.3 24.8 33.5 32.1 20.6 17.6 24.9 36.5 32.5 18.0 18.0 31.0 18.8 30.5 20.8 16.6 15.4 13.1 30.6 27.7 23.3 16.2 13.6 20.9 17.8 15.2 17.5 11.9 21.5 29.9 15.6 9.3 26.5 22.8 30.6 21.6 33.6 16.4 15.0 8.2 14.5 17.1 30.1 23.5 25.8 15.2 23.2 33.0 27.8 20.5 26.7 30.4 18.4 7.5 29.3 17.9 11.9 11.7 9.8 11.8 26.5 11.7 12.8 13.4 19.4 22.9 16.8 10.4 12.9 27.0 19.4 14.7 37.8 17.7

115 91 105 108 87 114 112 122 103 94 107 110 105 87 111 77 105 103 109 116 85 92 85 104 101 93 89 103 99 111 83 95 103 119 96 103 86 105 93 101 97 116 103 109 77 92 76 97 86 74 69 100 89 93 99 112 76 94 105 103 102 95 87 103 89 91 92 83 83 93 97 75 88 92 76 71

171 196 211 216 203 212 192 186 189 216 218 176 169 207 188 213 187 166 167 175 184 196 171 165 159 167 161 158 160 154 167 198 166 151 197 170 187 196 216 160 158 146 152 171 207 172 179 163 162 205 175 170 173 200 163 137 178 166 143 145 137 141 185 140 145 145 164 165 139 134 151 165 165 149 188 141

24e30 24e28 2e3 26e32 28e31 10e15 27e32 25e31 3e4 27e29 28e32 4e6 1e6 1e3 27e28

113.8 113.4 112.4 111.5 111.4 110.2 109.0 108.6 105.6 105.5 104.9 103.0 93.6 84.3 82.4

18.5 20.3 10.2 13.8 24.3 11.4 14.7 16.6 16.8 26.9 21.4 12.9 24.5 14.9 25.1

Min

Max

81 78 92 91 75 97 80 84 79 59 77 80 63 57 45

153 169 130 137 152 142 139 137 133 155 141 124 167 116 123

the left hand) and digraph18,20 (key 18 was the key in the digraph, key 20 was the standard position of the associated finger of the right hand) were averaged. This average was used as a raw cost for digraph4,18. If the key was also the key in the standard (home row) position of the same hand, then for the one hand digraph cost, the lu associated single finger-tapping rate was used (refer to Eks¸iog _ ¸ eri, 2015). and Is It is well known that two hand digraphs are faster. Salthouse (1984) revealed that the average interkey-time for two hand digraphs is 144 ms while the average interkey-stroke time for the same hand digraphs is 193 ms (Table 1). To obtain the final cost score (or interkey-stroke time), the raw cost was multiplied by 0.746 (~144/193). The equation to calculate the alternating hand digraph costs (AH Digraph cost for keys i and j) is provided below:

AH Digraph costi;j ¼

DCi;s þ DCj;s *0:746 2

(3)

where, DCi,s and DCj,s are digraph costs of associated right and left hand fingers from the standard position to the individual key, respectively.

2.2. Application of the digraph costs for the optimization of a keyboard layout In this second part of the study, the estimated digraph-cost data were used for the optimization of a keyboard layout of a selected language. This would accomplish the fourth objective of the study. For that purpose, Quadratic Assignment Problem (QAP) approach was used. The details of the approach are presented below. Given a set of keys and letters, the digraph frequency matrix of letters of the considered language (as flow matrix) and the digraph cost matrix between the keyboard keys (as the distance matrix), the QAP formulation of a keyboard layout optimization that minimizes the total distance (distances  flows) can be formulated as follows:

Table 4 ANOVA results. SOV

DF

Seq SS

Adj SS

Adj MS

F

p

Subjects (block) Column Row Hand Period Error Total

6 26 5 1 3 6662 6703

2,510,937 7,055,561 541,721 168,311 81,334 3,789,370 14,147,232

2,500,151 6,943,678 527,251 168,155 81,334 3,789,370

416,692 267,065 105,450 168,155 27,111 569

732.58 469.52 185.39 295.63 47.66

<0.01 <0.01 <0.01 <0.01 <0.01

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The selected language for the keyboard layout optimization was Turkish language. For the application of the digraph costs to Turkish language, the optimization model above was run using the experimentally determined digraph-cost matrix (distance matrix) and the digraph frequency matrix of Turkish language (which was calculated based on Turkish National Corpus by Aksan et al., 2012) to develop an optimal keyboard layout for Turkish. The best solution was obtained using a hybrid genetic algorithm developed by Misevicius (2004) for the solution of QAP. This algorithm was proven to solve QAP models very effectively and efficiently.

Table 5 ANOVA model coefficients and post hoc analysis. Term Constant Column 2-4 1-4 2-6 2-3 1-3 1-6 1-5 2-7 2-5 1-7 3-4 3-7 2-2 3-5 1-1 3-6 3-3 1-2 4-4 6-6 6-7 4-5 4-6 5-6 5-5 4-7 5-7 Row Bottom - Bottom Home - Home Top – Top Top - Home Home - Bottom Top - Bottom Hand Right Left Period Period 1 Period 2 Period 3 Period 4 *

Coef. 155.25

SE coef. 0.47

t 332.94

p 0.00

49.76 49.12 44.43 44.22 42.06 40.04 36.30 36.20 35.60 32.95 4.65 -5.64 -7.90 -9.50 -10.56 -15.34 -15.54 -17.04 -22.37 -30.81 -33.54 -34.83 -35.61 -39.13 -39.58 -43.31 -54.63

1.12 1.11 1.83 1.12 1.12 1.83 1.21 2.57 1.21 2.58 1.11 2.55 1.83 1.22 1.83 1.84 1.83 1.11 1.83 4.38 3.12 1.22 1.84 2.23 2.23 2.55

44.63 44.13 24.23 39.52 37.46 21.90 30.02 14.10 29.39 12.76 4.17 -2.21 -4.31 -7.80 -5.76 -8.32 -8.48 -15.31 -12.21 -7.03 -10.76 -28.66 -19.37 -17.56 -17.73 -16.97

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A A ABCD AB BCD BCDE DE BCDE E CDE F FG G G GH GHI GHI HI IJ IJK JK K K K K KL L

7.74 6.15 4.18 0.61 0.03 -18.71

1.00 0.82 0.76 0.57 0.63

7.77 7.47 5.51 1.07 0.04

0.00 0.00 0.00 0.28 0.97

A A A

5.64 -5.63 5.91 -0.98 -1.94 -2.99

*Grouping

3. Results and discussion 3.1. Digraph tapping rates For the first objective of the study, a descriptive statistical analysis of the collected digraph-tapping rate data was performed, and the tapping rates of all 241 digraphs were estimated (Table 3). Digraph-tapping rate changes dramatically across the digraph types. The range is between 82 and 228 taps per 30 s. The difference is nearly three times between the slowest and the fastest digraphs. From this result it can be concluded that the assignment of letter pairs on the correct digraph keys on the keyboard can have a high impact on the typing speed. 3.2. Factor effects on digraph tapping rates

B B C A

0.33

-17.19

0.00

0.51 0.50 0.50

11.71 -1.95 -3.85

0.00 0.05 0.00

B A B B B

Means that do not share a letter are significantly different.

X

min Total Distance ¼

DFik *Costjl *xij *xkl

(4)

i;k2LETTERS;j;l2KEYS

subject to P xij ¼ 1 ci2LETTERS j2KEYS P xij ¼ 1 cj2KEYS i2LETTERS

xij is binary

ci2LETTERS; j2KEYS

where: KEYS: the set of all keyboard keys LETTERS: the set of all letters in the considered language DFik: the digraph frequencies of letters i and k in the considered language Costjl: the digraph costs (the interkey-stroke times between the keys j and l). The digraph frequencies are the frequencies of the letter pairs that can be calculated using the corpus of the considered language or from other sources (e.g.; Turkish National Corpus by Aksan et al., 2012). The digraph-cost is the interkey-stroke time for a given digraph (time lag for pressing one letter after another).

For the second objective of the study, an ANOVA was performed to determine the effects of the independent variables on the response variable. In the ANOVA, the interaction effects were found insignificant, thus they were omitted. Therefore, in the calculation of the sum of squares, only significant main effects were considered. The statistical result table of the ANOVA is shown in Table 4, and ANOVA model coefficients with Tukey's multiple comparison tests with 95% confidence are presented in Table 5. The results indicated significant column, row, hand and period effects on the response. When the factors were ranked according to their explanatory power, column factor had the highest explanatory power and subject factor, which was blocked, had the second. Other factors although significant, did not have high explanatory power as the column or subject factor. The details of the analyses and comparisons are given in the following sub-sections. The main effects plots of the factors are shown in Fig. 2. In all of these graphs, the y-axis was converted into interkey-stroke times by dividing 30,000 ms (30 s) to the response (# of keystrokes/30 s), so the smaller the y value the faster the digraph typing speed is. Column effect. Column factor was the most important factor (had the highest explanatory power) on the response. As seen in Fig. 2 and Table 5, columns that included index finger (column 1 and column 2) had the least interkey-stroke times unless only the index finger was used in the digraph (e.g., column level 1e2). The digraphs that were pressed with the same finger such as 1e1, 1e2, 2e2, 3e3, 4e4, 5e5, 5e6, 5e7 had high interkey-stroke times. Other comparisons for the fingers and columns can be made from the same graph. Row effect. It was faster and easier to type if both of the keys in the digraph were on the same row (Fig. 2 and Table 5). However, when there was an excessive row hopping (e.g., from top row to bottom row (hurdle) or from top row to home row (reach)), the interkey stroke times significantly increased to a very high level. According to the post hoc analysis (see Table 5), the difference between tapping in the same row and a reach, and also between a reach and a hurdle was significant. Hand effect. Right hand was significantly faster than left hand (Fig. 2 and Table 5). Right hand fingers on average typed 0.38 taps

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per second faster than left hand fingers. However, it should be noted here that all the participants were right-handed. Period effect. There was a significant decrease between the first and all other periods (Fig. 2 and Table 5). However, there was no statistically significant difference between second, third and fourth periods. So it can be concluded that, subjects started with a high speed but could not sustain that speed after the first 30 s period. During and after the second period, their speed was decreased to a level that they could sustain for at least 5 min as observed in the pilot studies. 3.3. The digraph costs The third and the main objective of the study was to quantify the digraph costs. The cost values were calculated based on the mean values of the digraph tapping rates presented in Table 3. 3.3.1. The same hand digraph costs The final digraph costs which are ready to be used in the optimization are depicted in Table 6. Now let's illustrate the calculation of the same hand digraph cost of a digraph from Table 3 (see Section 2.1.5). The digraph cost, say, for digraph20,23 (or digraph23,20) is calculated as 133 ms, by dividing the 30,000 ms by 228 (from Table 3) and multiplying with 1.016 for normalization [(30,000/ 228)*1.016 ¼ 131 ms]. That is, pressing key 20 before or after key 23 takes 133 ms. The rest of the 241 same hand digraph costs can be calculated as described. As one may expect, the harder to stroke the keys of a digraph the higher the interkey-stroke time. 3.3.2. The alternating hand digraph costs Let's illustrate the calculation of the alternating hand digraph costs from the same hand digraph costs (see Section 2.1.5) by an

135

example. To calculate the digraph cost, say, for digraph4,18 (or digraph18,4), the digraph costs of digraph4,5 and digraph18,20 obtained from Table 6 are averaged and then multiplied by 0.746 (ie; [((245þ188)/2)*0.746] ¼ 162 ms). That is, the digraph cost of digraph4,18 (or digraph18,4) is 162 ms. The whole digraph cost matrix (i.e., the interkey-stroke time matrix) is shown in Table 6. The table is symmetrical along diagonal, since it was assumed that hit direction does not affect the response. So, for instance, interkey-stroke time of, say, digraph2,1 is the same as digarph1,2. EMG Results: To accomplish the secondary objective of the study, EMG analysis results of the forearm muscles were examined. However, the results did not indicate significant median frequency shift to lower values at the end of 2-min digraph typing test period. However, when the subjects were asked about their fatigue, they responded with some level of fatigue varying according to the digraph types. Tomatis et al. (2009) also found similar results regarding to median frequency in a similar typing experiment. These results supported the results in Kumar and Mital (1996) who stated highly dynamic tasks which require low force exertion level like typing may not be suitable to capture fatigue through EMG. Hence, EMG results were not considered as a weight factor in the calculation of digraph cost scores.

3.4. An application of the digraph costs for the development of a keyboard layout To accomplish the fourth objective of the study, the optimization model explained in Section 2.2 was run for Turkish Language using the digraph matrix of Turkish language and universal digraph costs. The obtained best solution, which is called Turkish

Fig. 2. Main effect plots for column, row, period and hand factors.

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Table 6 The digraph cost matrix: The values correspond to the interkey-stroke times in msec.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

196 266 357 225 258 325 204 231 263 164 166 186 155 163 196 179 174 169 169 156 171 176 156 175 178 158 177 186 163 185 189 196

196 271 239 240 267 196 208 208 160 166 169 167 156 168 153 148 143 143 129 145 150 129 149 151 132 151 160 137 159 163 170

196 289 245 236 237 201 194 165 160 161 164 167 160 181 176 171 171 157 173 178 157 177 179 160 179 188 164 187 191 198

181 245 296 182 196 229 147 150 167 149 152 175 171 166 162 162 148 163 169 148 167 170 150 169 178 155 177 182 188

181 256 194 183 184 161 149 150 151 153 153 147 142 138 138 124 139 145 124 144 146 126 145 154 131 153 158 164

181 214 215 184 185 147 157 162 154 148 175 170 166 166 152 167 173 152 172 174 154 173 182 159 181 186 192

170 232 263 149 155 166 149 147 171 166 162 157 157 143 158 164 143 163 165 145 164 173 150 172 177 184

170 239 157 149 151 164 146 150 143 138 134 134 120 135 141 120 140 142 122 141 150 127 149 154 160

170 234 170 150 248 161 149 169 164 159 159 145 161 166 145 165 167 148 167 176 153 175 179 186

169 226 257 251 240 276 164 159 154 154 141 156 162 141 160 163 143 162 171 148 170 175 181

169 221 235 231 254 142 138 133 133 119 135 140 119 139 141 122 141 150 126 149 153 160

169 262 228 235 162 157 153 153 139 154 160 139 159 161 141 160 169 146 168 173 179

169 221 255 167 163 158 158 144 159 165 144 164 166 146 165 175 151 173 178 185

169 228 166 161 156 156 142 158 163 142 162 164 145 164 173 150 172 176 183

169 174 170 165 165 151 166 172 151 171 173 153 172 182 158 181 185 192

151 203 216 196 213 226 145 153 220 139 142 185 149 160 148 155 157

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

151 200 191 201 218 144 147 188 149 153 148 154 148 146 150 155

151 207 188 198 144 144 140 137 139 138 176 152 148 161 167

151 188 213 147 151 204 141 142 162 145 164 145 149 154

151 192 137 133 149 136 138 139 147 152 143 144 165

151 149 145 140 155 145 142 164 160 175 145 151

151 207 227 189 191 208 209 206 226 197 181

151 204 188 179 183 206 183 194 201 213

151 226 185 175 268 220 265 188 205

157 210 239 253 231 225 276 254

157 208 251 240 235 229 273

157 362 293 265 230 279

170 233 236 271 291

170 230 242 260

170 230 245

170 226

170

I-layout is shown in Fig. 3. This layout corresponds to a penalty score (objective function value) of 141 ms. On the other hand, the penalty scores for Turkish Q layout and Turkish F layout correspond to the penalty scores of 170 ms and 149 ms, respectively.

These penalty scores in msec can be thought as the average interkey-stroke time of the given layout in Turkish language. Flayout, developed in 1950s specifically for Turkish language, was the only keyboard layout alternative to Q-layout for Turkish

Fig. 3. Turkish I-layout.

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Table 7 Comparisons of the Turkish I, F and Q layouts according to the criteria defined by Dvorak et al. (1936). The criteria marked with an * indicate that the larger the better while all the others indicate the smaller the better. Keyboard Percentage of Layout tapping with the same fingers

Percentage of tapping that includes top row

Percentage of *Percentage of tapping that tapping in the includes home row bottom row

* Percentage of Percentage of Percentage of Percentage of Percentage of Percentage of hurdles with reach with the reach with hurdles with hurdles with tapping by adjacent fingers the same finger adjacent fingers remote fingers same finger alternating hands

I F Q

34.24 60.11 75.32

33.48 21.35 36.57

84.93 80.38 48.62

2.37 6.18 9.68

41.75 31.12 18.84

0.03 1.10 2.60

0.50 0.34 4.53

0.14 0.07 2.20

1.67 4.28 5.69

3.26 4.38 5.61

The bold numbers show the best layout in the corresponding criterion.

language so far. It was based partly on Dvorak's criteria. The results of this study indicated that the developed Turkish I-layout performs better in terms of minimizing digraph penalty score. In addition, a comparison was made among the three layouts with respect to the criteria by Dvorak et al. (1936). The results are depicted in Table 7. It can be seen that I-layout is better than F layout in 7 of 10 criteria and better than Q-layout in all 10 criteria. This comparison shows the capability of the empirically calculated digraph cost scores for satisfying the Dvorak's criteria automatically when used in a QAP model. 3.5. Limitations of the study and suggestions for future studies There are some limitations and assumptions related to the methodology of the study. The parameters used to estimate the digraph penalties were based on the experiments performed using a conventional keyboard. Although we strongly believe that the methodology proposed by this study is applicable to alternative keyboard geometry such as split keyboard, yet this needs to be verified. The digraph experiment was performed using the touch typing principles. Hence, the optimization results and proposed layout is valid for the touch typists. If typist does not type according to the touch typing principles, then the proposed keyboard layouts may not have the same effect on the typing speed and ergonomics of typing. To design a keyboard layout for a different typing method; for instance, two- or four-finger typing, the digraph experiment should be repeated according to the principles of the corresponding typing method. Another limitation was that, in the digraph experiment, because of the experimental setup and procedure it was impossible to consider hit direction. When calculating the digraph penalty scores for the alternating hands, it was assumed that in order to press two keys on different hands, typist should move the fingers from the standard key position to the position of the key. This assumption is true if the typist's replacement span is one character. However, as explained in the text, the replacement span of the professional typists is approximately three characters. Optimization of a keyboard layout with the calculated digraph costs automatically satisfies 10 of 11 criteria of Dvorak et al. (1936). However, deviation from the balance of hand and finger loads criterion cannot be handled with digraph costs since it is related with the monographs. As a future study, experimental validation studies on the typing speed and comfort can be performed to validate the methodology and the digraph costs. Although the limitations, it is believed that the developed methodology and estimated digraph costs will contribute to the development of better keyboard layouts and thus improving typing performance and reducing risks of cumulative trauma disorders of hand and wrist.

4. Conclusions The main aims of this research were to determine the digraph costs for touch typing based on digraph-tapping rates and investigate the effects of various factors on the digraph-tapping rate. The results showed that digraph tapping rate varies with respect to column, row, hand and period factors. The column factor was found to be the most important factor affecting the digraph-tapping rate. The results suggested the importance of these factors in developing optimal keyboard layouts. The study also introduced a systematic approach for developing ergonomic and optimal keyboard layouts for the languages having 32 letters or less. It is expected that the developed layouts will reduce fatigue, and improve typing performance and comfort for touch typists. In contrary to the previous keyboard layout optimization studies, in this study, digraph cost scores were estimated empirically. These are essential and normative values that can be used together with digraph frequency matrix of the corresponding language to obtain an optimal keyboard layout using the QAP model. This was shown with an application to Turkish language. The obtained Turkish I-layout performed better than the Turkish Q and F layouts with respect to the results of the optimization and Dvorak's criteria. In almost all of the keyboard optimization models, all the digraphs pressed with alternating hands were treated as the same within their group. However, in the current study these digraphs were treated differently using the same hand digraph tapping data. Although there was an assumption for this approach, this is new to the literature. It is believed that the developed methodology and estimated digraph costs will contribute to the better keyboard layout development for various languages to improve typing performance and reduce the risks of upper extremity disorders. Acknowledgments This research was supported by the Scientific and Technological _ Research Council of Turkey (TÜBITAK) Grant 111M530 awarded to lu. Mahmut Eks¸iog References Aksan, Y., Aksan, M., Koltuksuz, A., Sezer, T., Mersinli, Ü., Demirhan, U.U., € S., Yıldız, I., _ 2012. Construction of the Turkish NaYılmazer, H., Atasoy, G., Oz, tional Corpus (TNC). In: Proceedings of the Eight International Conference on _ Language Resources and Evaluation (LREC 2012), Istanbul, Turkey. Dell'Amico, M., Díaz Díaz, J.C., Iori, M., Montanari, R., 2009. The single-finger keyboard layout problem. Comput. Oper. Res. 36, 3002e3012. Delsys, 2011. Technical Note-101 EMG Sensor Placement. http://www.delsys.com/ Attachments_pdf/TN101%20-20EMG%20Sensor%20Placement-web.pdf. Dvorak, A., Merrick, N.L., Dealey, W.L., Ford, G.C., 1936. Typewriting Behavior. American Book Company, New York. Eggers, J., Feillet, D., Kehl, S., Wagner, M.O., Yannou, B., 2003. Optimization of the keyboard arrangement problem using an ant colony algorithm. Eur. J. Oper. Res. 148 (3), 672e686.

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