# Effects of Dexterity Level and Hand Anthropometric Dimensions on Smartphone Users’ Satisfaction

Authors: N. Firat Ozkan; Fulya Gokalp-Yavuz
Journal: Mobile Information Systems
 (2015)

---

## Abstract

The usage of smartphones instead of simple mobile phones increases sharply in our era, especially among young people, because they do multiple tasks with single equipment. This study mainly focuses on smartphone satisfaction by combining hand measurements, smartphone users’ survey results, and hand dexterity levels of corresponding users acquired from Minnesota Manual Dexterity Test (MMDT). Structural Equation Modelling (SEM) is used as a statistical tool to discover the potential direct and indirect relations among user satisfaction, hand dimensions, and dexterity scores. Results indicates that thumb length, hand length, and dexterity level of the users have notable effects on users’ satisfaction with smartphones. Based on the results, a new approach that includes both gross motor skills and physical measurements is suggested to see hidden indirect relations with satisfaction.


---

## Body

## 1. Introduction

The increasing need for fast communication brings along the widespread use of the latest communication technologies. New forms of communication become mobile and they tend to coalesce into a single unit which is called smartphone. Numerous brands offer various smartphone models that have different technical features, physical designs, screen types, input devices, and so forth. People prefer different models of smartphones depending on their needs but it is quite hard to anticipate how they will be pleased with their smartphone. Smartphones have various features that are used in daily life such as standard phone calls, video phone calls, various instant messaging systems, advanced audio video recording technology, rapid Internet access, and various other features. Therefore, smartphone users have different expectations and purposes of using their devices. Their expectations and purposes of using affect their habits of the usage and the level of satisfaction. In the literature, there are numerous studies that have been conducted to measure user satisfaction and uncover information about the use of these devices.Balakrishnan and Yeow [1] investigate the relationship between hand dimensions and short message service (sms) satisfaction. They measured hand breadth, thumb length, and thumb circumference measurements of the participants and applied a questionnaire to measure sms satisfaction. As a result of the study, it is suggested that manufacturing customized mobile phones for people who have larger thumbs can increase customer satisfaction.Zulkefly and Baharudin [2] study the extent of mobile phone use amongst university students. They use several questionnaires to determine family and personal factors affecting purposes of using the mobile phone and its features using. Choi and Lee [3] focus on smartphone interface simplicity in their study. They conduct an online survey among smartphone users to evaluate their smartphone’s interface design in terms of simplicity. Park and Han [4] investigate the effects of touch key sizes and locations on one-thumb input on a mobile phone. They compare three different touch key sizes and twenty-five locations and use thumb length, thumb breadth, and hand length data of the participants. Lobo et al. [5] explain some guidelines which increase web usability of smartphones. Nitsche et al. [6] design an ergonomic user interface for a mobile search application by following a user centred design process which includes related questionnaires. They finalize the study with usability tests for their ergonomic user interface concept.Physical design of smartphones is also a crucial point for user satisfaction. Since smartphones may require use of two hands and different fingers depending on the activity, smartphone sizes, screen, and keyboard sizes have a critical importance for the ease of usage. Many researchers conduct studies about physical design and mobile phone sizes and hand anthropometrics.Jain and Pathmanathan [7] investigate keypad design satisfaction of mobile phone users using questionnaires, mobile phone dimensions, and 20 different hand measurements of the participants. Bradley et al. [8] conduct a survey on 362 people to examine user capabilities on mobile phone related tasks.According to most of the related studies’ results, usability of devices and anthropometric features of the users are considered as critical points for design. These are supporting points to clarify the relationship between user expectations and device attributes. However, previous studies do not take into account the human capabilities that may affect overall user satisfaction on mobile devices. Essentially, it is very crucial to know approximate manual dexterity level of the target market for designing more appropriate devices. Although user capability is considered as a component of user satisfaction in some recent studies, there is still a gap in terms of considering motor skills of the users. This study fills this gap through using Minnesota Manual Dexterity Test (MMDT) as a part of the user satisfaction research.Manual dexterity is a measurable characteristic and it is one of the indicators of human capabilities. Some tests are available to determine dexterity of one or two hands, but not both hands. Since smartphones may require use of both hands and several fingers, it is important to consider effect of user’s manual dexterity on their satisfaction of use. Since using the smartphone is not totally the same as using conventional mobile phones, it often requires use of both hands and fingers besides thumbs. On the other hand, smartphones offer much more features related with screen size and keyboard; because of that, their dimensions are bigger. At this point, manual dexterity level of users and choosing the most appropriate smartphone model must be emphasized in terms of user satisfaction. People should decide their smartphone model considering their aims of use, hand dimensions, and manual dexterity level. This study tries to emphasize the relationships between these three aspects and satisfaction level of smartphone users.In this study, dexterity level is considered as an indirect effect on the satisfaction, besides hand anthropometric dimensions that directly (or naturally) affect dexterity level. It is possible to use both direct and indirect effects with the help of Structural Equation Modelling (SEM) as an extension of Path Analysis (PA) [9] to determine variables influencing the outcome (satisfaction). SEM encompasses PA and both models use the same underlying idea of model fitting and testing [10]. However, SEM allows us to work with latent variables that are weighted values of some observed satisfaction indicators. Also, it takes into account measurement errors and allows using mediator in the model [11]. The reason why SEM is preferred in this study is that it contains latent variables, contrary to PA, and it takes into account the measurement error, especially for independent variables, contrary to classical regression models.The paper is structured as follows. Section2 describes methods including user hand/finger dimensions, satisfaction, and dexterity test. The characteristics of the data and statistical analysis, basically PA and SEM, are defined in Section 3. Section 4 describes model settings and comparisons. Sections 5 and 6 include SEM result diagrams, conclusions, and future work, respectively.


## 2. Method

A multistage measurement process is designed to collect the data. The study is conducted with 36 participants. Firstly, each participant is asked to answer the questionnaire that includes questions about demographics, smartphone choices, habits, and satisfaction. Secondly, hand and finger dimensions of participants are measured. Finally, each participant performs the Minnesota Manual Dexterity Test.


### 2.1. Hand and Finger Dimensions

All hand and finger dimensions are measured for both right and left hands. However, not all of them are used in analysis part because there are high correlations between some of these measurements. Lafayette anthropometric tapes and small anthropometer are used for measuring the hand dimensions such as hand length, hand breadth, palm length, index finger length, index finger breadth, thumb length, and thumb breadth. Hand and finger dimensions (mm) are presented in Table1.Table 1
Hand and finger dimensions (mm).
Subjectnumber
Right handlength
Left handlength
Right handbreadth
Left handbreadth
Right palmlength
Left palm length
Right index finger length
Left index finger length
Right indexfinger breadth
Left indexfinger breadth
Right thumblength
Left thumblength
Right thumbbreadth
Left thumbbreadth
1
174
172
74
73
91
91
70
70
15
15
50
50
18
19
2
182
182
83
81
99
101
75
75
15
16
57
57
19
19
3
183
186
84
80
103
102
70
71
17
17
65
65
21
21
4
180
182
94
93
94
94
74
74
18
18
55
55
23
23
5
189
190
84
85
108
108
72
73
16
16
59
67
21
21
6
166
166
76
75
93
93
67
68
16
15
58
58
20
20
7
186
187
82
82
104
105
74
73
18
17
67
64
23
22
8
175
175
73
71
99
99
70
69
15
15
64
61
18
18
9
177
177
77
78
99
100
71
71
16
16
66
65
20
20
10
168
169
80
80
95
95
66
66
17
17
58
57
21
21
11
174
174
79
80
99
99
65
65
15
15
65
64
20
20
12
174
174
78
78
97
97
71
68
16
16
61
61
21
20
13
196
197
87
86
113
112
76
77
18
17
67
68
23
22
14
181
181
85
85
102
103
70
72
16
17
66
66
21
21
15
187
186
89
88
107
107
75
75
17
17
66
65
21
22
16
175
176
82
82
99
100
69
69
16
16
65
65
22
21
17
180
181
83
83
101
100
73
73
17
17
64
65
22
22
18
172
172
75
73
92
92
72
73
15
14
62
61
18
18
19
166
165
73
73
91
91
67
66
14
13
59
59
18
17
20
198
197
96
96
110
110
80
79
18
17
70
70
22
22
21
181
181
95
94
93
93
76
77
18
18
60
60
22
22
22
173
173
80
81
98
98
66
66
16
16
66
65
21
21
23
177
179
84
83
96
97
67
68
15
15
65
64
21
20
24
189
189
82
81
104
104
74
73
15
15
66
66
19
19
25
166
165
73
72
94
94
63
63
14
14
62
62
17
17
26
175
175
79
78
102
102
67
68
15
15
65
65
20
20
27
185
184
83
85
102
102
77
76
15
15
62
63
20
19
28
187
187
82
82
105
105
71
72
16
16
65
64
20
20
29
173
172
74
74
93
93
73
73
16
15
61
62
19
19
30
169
168
75
74
92
92
70
71
16
16
62
63
19
19
31
188
188
83
84
106
106
73
72
17
17
65
66
22
22
32
185
185
80
80
103
104
70
71
17
17
64
65
22
23
33
189
188
84
84
109
109
74
74
18
18
68
69
24
23
34
172
172
74
73
96
96
68
68
16
16
64
63
19
19
35
171
172
73
73
92
92
73
73
15
15
63
63
17
17
36
178
178
85
85
97
96
69
68
16
16
66
66
22
21


### 2.2. Dexterity Test

Minnesota Manual Dexterity (MMD) Test includes several test methods. Two of them used in this study are the placing test performed by single hand and the turning test performed by two hands. Dexterity scores are determined based on task completion duration [12]. Both placing and turning tests are performed two times. Total trial times are used to determine percentile scale value that is provided by Examiner’s Manual of the Minnesota Manual Dexterity Test. To obtain a composite score, the average of two percentile values is calculated. Analyses are implemented separately with placing, turning, and composite test scores.Before starting the MMD test, each participant is informed about the tasks of the test and they are allowed to get familiar with the test equipment. After they performed both placing and turning tests, completion time of each task is recorded. Dexterity scores are provided in Table2.Table 2
Minnesota Manual Dexterity Test results.
Subjectnumber
(1) Placingtest (sec)
(2) Placingtest (sec)
Placing total(sec)
Placing percentile scale
(1) Turning test (sec)
(2) Turningtest (sec)
Turningtotal (sec)
Turning percentile scale
1
67
63
130
25
67
54
121
1
2
60
58
118
60
52
48
100
40
3
57
49
106
95
40
35
75
99
4
68
61
129
25
50
49
99
50
5
54
54
108
90
55
48
103
31
6
63
56
119
60
61
45
106
20
7
58
54
112
85
49
45
94
69
8
65
55
120
60
56
44
100
40
9
66
54
120
60
58
44
102
31
10
63
58
121
60
64
51
115
3
11
66
61
127
31
60
58
118
2
12
58
59
117
69
63
50
113
3
13
69
66
135
10
53
50
103
31
14
67
61
128
31
52
48
100
40
15
60
58
118
60
56
55
111
10
16
59
56
115
80
48
45
93
75
17
60
56
116
75
49
48
97
60
18
69
63
132
20
47
46
93
75
19
64
58
122
50
52
46
98
50
20
56
49
105
95
55
52
107
20
21
63
60
123
50
58
56
114
5
22
67
65
132
20
57
52
109
15
23
69
62
131
20
40
41
81
97
24
57
53
110
90
55
50
105
25
25
67
70
137
5
49
46
95
60
26
61
56
117
69
59
51
110
10
27
64
60
124
40
58
53
111
10
28
66
64
130
25
63
48
111
10
29
60
53
113
85
51
46
97
60
30
68
64
132
20
51
50
101
40
31
63
60
123
50
57
50
107
20
32
70
62
132
20
54
50
104
31
33
60
55
115
80
49
48
97
60
34
71
65
136
10
58
47
105
25
35
60
57
117
69
60
54
114
5
36
70
60
130
25
53
46
99
50


### 2.3. User Satisfaction Questionnaire

1–5 Likert scale is used to measure satisfaction level of participants with their smartphones. Additionally, demographic information, the reasons for choosing their smartphones, daily usage preferences, usage habits, and satisfaction questions (Table3) are asked in the questionnaire. To make the data collection process easier and to have more reliable results, all the participants are asked for their voluntary consent.Table 3
Satisfaction questions and rotated component matrix (rotation converged in 3 iterations).
Question codes
Question explanations
Component
Physical
General
M15
I don’t have difficulty in holding my phone with one hand.
.628
M16
I don’t have difficulty in reaching keys with my thumbs.
.549
M17
I push neither incorrect nor multiple keys with my thumbs.
.630
M18
Even I need to be quick, I don’t make mistakes in my transactions.
.707
M19
I don’t feel strain in my hand, on my fingers or wrist while using my phone.
.707
M20
My phone’s keyboard and keys have appropriate dimensions to be used comfortably.
.637
M21
I am satisfied with my smartphone’s dimensions.
.913
M23
My phone’s physical design doesn’t cause any difficulty of use for me.
.857
M24
I am generally satisfied with my phone.
.937
M25
I like my smartphone.
.888
M26
I am disappointed on my smartphone.
.691
Extraction method: principal component analysis.
Rotation method: Varimax with Kaiser normalization.


## 2.1. Hand and Finger Dimensions

All hand and finger dimensions are measured for both right and left hands. However, not all of them are used in analysis part because there are high correlations between some of these measurements. Lafayette anthropometric tapes and small anthropometer are used for measuring the hand dimensions such as hand length, hand breadth, palm length, index finger length, index finger breadth, thumb length, and thumb breadth. Hand and finger dimensions (mm) are presented in Table1.Table 1
Hand and finger dimensions (mm).
Subjectnumber
Right handlength
Left handlength
Right handbreadth
Left handbreadth
Right palmlength
Left palm length
Right index finger length
Left index finger length
Right indexfinger breadth
Left indexfinger breadth
Right thumblength
Left thumblength
Right thumbbreadth
Left thumbbreadth
1
174
172
74
73
91
91
70
70
15
15
50
50
18
19
2
182
182
83
81
99
101
75
75
15
16
57
57
19
19
3
183
186
84
80
103
102
70
71
17
17
65
65
21
21
4
180
182
94
93
94
94
74
74
18
18
55
55
23
23
5
189
190
84
85
108
108
72
73
16
16
59
67
21
21
6
166
166
76
75
93
93
67
68
16
15
58
58
20
20
7
186
187
82
82
104
105
74
73
18
17
67
64
23
22
8
175
175
73
71
99
99
70
69
15
15
64
61
18
18
9
177
177
77
78
99
100
71
71
16
16
66
65
20
20
10
168
169
80
80
95
95
66
66
17
17
58
57
21
21
11
174
174
79
80
99
99
65
65
15
15
65
64
20
20
12
174
174
78
78
97
97
71
68
16
16
61
61
21
20
13
196
197
87
86
113
112
76
77
18
17
67
68
23
22
14
181
181
85
85
102
103
70
72
16
17
66
66
21
21
15
187
186
89
88
107
107
75
75
17
17
66
65
21
22
16
175
176
82
82
99
100
69
69
16
16
65
65
22
21
17
180
181
83
83
101
100
73
73
17
17
64
65
22
22
18
172
172
75
73
92
92
72
73
15
14
62
61
18
18
19
166
165
73
73
91
91
67
66
14
13
59
59
18
17
20
198
197
96
96
110
110
80
79
18
17
70
70
22
22
21
181
181
95
94
93
93
76
77
18
18
60
60
22
22
22
173
173
80
81
98
98
66
66
16
16
66
65
21
21
23
177
179
84
83
96
97
67
68
15
15
65
64
21
20
24
189
189
82
81
104
104
74
73
15
15
66
66
19
19
25
166
165
73
72
94
94
63
63
14
14
62
62
17
17
26
175
175
79
78
102
102
67
68
15
15
65
65
20
20
27
185
184
83
85
102
102
77
76
15
15
62
63
20
19
28
187
187
82
82
105
105
71
72
16
16
65
64
20
20
29
173
172
74
74
93
93
73
73
16
15
61
62
19
19
30
169
168
75
74
92
92
70
71
16
16
62
63
19
19
31
188
188
83
84
106
106
73
72
17
17
65
66
22
22
32
185
185
80
80
103
104
70
71
17
17
64
65
22
23
33
189
188
84
84
109
109
74
74
18
18
68
69
24
23
34
172
172
74
73
96
96
68
68
16
16
64
63
19
19
35
171
172
73
73
92
92
73
73
15
15
63
63
17
17
36
178
178
85
85
97
96
69
68
16
16
66
66
22
21


## 2.2. Dexterity Test

Minnesota Manual Dexterity (MMD) Test includes several test methods. Two of them used in this study are the placing test performed by single hand and the turning test performed by two hands. Dexterity scores are determined based on task completion duration [12]. Both placing and turning tests are performed two times. Total trial times are used to determine percentile scale value that is provided by Examiner’s Manual of the Minnesota Manual Dexterity Test. To obtain a composite score, the average of two percentile values is calculated. Analyses are implemented separately with placing, turning, and composite test scores.Before starting the MMD test, each participant is informed about the tasks of the test and they are allowed to get familiar with the test equipment. After they performed both placing and turning tests, completion time of each task is recorded. Dexterity scores are provided in Table2.Table 2
Minnesota Manual Dexterity Test results.
Subjectnumber
(1) Placingtest (sec)
(2) Placingtest (sec)
Placing total(sec)
Placing percentile scale
(1) Turning test (sec)
(2) Turningtest (sec)
Turningtotal (sec)
Turning percentile scale
1
67
63
130
25
67
54
121
1
2
60
58
118
60
52
48
100
40
3
57
49
106
95
40
35
75
99
4
68
61
129
25
50
49
99
50
5
54
54
108
90
55
48
103
31
6
63
56
119
60
61
45
106
20
7
58
54
112
85
49
45
94
69
8
65
55
120
60
56
44
100
40
9
66
54
120
60
58
44
102
31
10
63
58
121
60
64
51
115
3
11
66
61
127
31
60
58
118
2
12
58
59
117
69
63
50
113
3
13
69
66
135
10
53
50
103
31
14
67
61
128
31
52
48
100
40
15
60
58
118
60
56
55
111
10
16
59
56
115
80
48
45
93
75
17
60
56
116
75
49
48
97
60
18
69
63
132
20
47
46
93
75
19
64
58
122
50
52
46
98
50
20
56
49
105
95
55
52
107
20
21
63
60
123
50
58
56
114
5
22
67
65
132
20
57
52
109
15
23
69
62
131
20
40
41
81
97
24
57
53
110
90
55
50
105
25
25
67
70
137
5
49
46
95
60
26
61
56
117
69
59
51
110
10
27
64
60
124
40
58
53
111
10
28
66
64
130
25
63
48
111
10
29
60
53
113
85
51
46
97
60
30
68
64
132
20
51
50
101
40
31
63
60
123
50
57
50
107
20
32
70
62
132
20
54
50
104
31
33
60
55
115
80
49
48
97
60
34
71
65
136
10
58
47
105
25
35
60
57
117
69
60
54
114
5
36
70
60
130
25
53
46
99
50


## 2.3. User Satisfaction Questionnaire

1–5 Likert scale is used to measure satisfaction level of participants with their smartphones. Additionally, demographic information, the reasons for choosing their smartphones, daily usage preferences, usage habits, and satisfaction questions (Table3) are asked in the questionnaire. To make the data collection process easier and to have more reliable results, all the participants are asked for their voluntary consent.Table 3
Satisfaction questions and rotated component matrix (rotation converged in 3 iterations).
Question codes
Question explanations
Component
Physical
General
M15
I don’t have difficulty in holding my phone with one hand.
.628
M16
I don’t have difficulty in reaching keys with my thumbs.
.549
M17
I push neither incorrect nor multiple keys with my thumbs.
.630
M18
Even I need to be quick, I don’t make mistakes in my transactions.
.707
M19
I don’t feel strain in my hand, on my fingers or wrist while using my phone.
.707
M20
My phone’s keyboard and keys have appropriate dimensions to be used comfortably.
.637
M21
I am satisfied with my smartphone’s dimensions.
.913
M23
My phone’s physical design doesn’t cause any difficulty of use for me.
.857
M24
I am generally satisfied with my phone.
.937
M25
I like my smartphone.
.888
M26
I am disappointed on my smartphone.
.691
Extraction method: principal component analysis.
Rotation method: Varimax with Kaiser normalization.


## 3. Statistical Analysis

### 3.1. Data

The survey is conducted with 36 participants, the average age is 23 ranging between 19 and 34, and half of the participants are female. The main characteristics of the data are as follows: the average monthly income is 1007 (±796) TL (Turkish Lira), while the average family income is 4000 (±2153) TL. 83% of them are right-handed. The smartphones are used mostly for phone calls and instant messaging programs such asWhatsapp, Tango, with 39% and 25%, respectively. The brand and the price of the smartphone are two most popular answers, with 39% and 27%, respectively, to the question of “What is the most important feature for you while buying a smartphone?” The dimension of the smartphone is generally the second or the third option for the participants while buying a smartphone.The objectives of smartphone usage and the satisfaction questions are asked with 5 Likert points withdefinitely dissatisfied to highly satisfied scale in the survey. Cronbach’s Alpha for the reliability of these items is 0.849. The average scores of satisfaction questions are mostly higher than 4 and this shows that participants are satisfied with their smartphones. However, the participants state that “it is possible to do some mistakes if they need to act faster,” which is one of the indicators of physical dissatisfaction. The average score for the related question is 2.67, that is, the lowest score among all satisfaction scores. The average scores obtained from the answers of questions M16, M17, M19, and M20 (descriptions are placed in Table 3) are lower than 4, as well.Data collection part also includes hand/finger measurements and Minnesota Manual Dexterity Test results mentioned in Sections2.1 and 2.2, respectively. The raw data and/or related information can be obtained from the author via e-mail.


### 3.2. Analysis

By usingt-test, it is concluded that there is no significant difference between right and left hand measurements with 5% confidence level. The analysis part proceeds with factor analysis. Participants answer several questions about their satisfaction in physical and general sense, and it is observed that the scores are split into two groups (Table 3). The first one is the physical satisfaction component, and the second one is the general satisfaction component. The final rotated component matrix of factor analysis is located at Table 3.In the analysis part, it is aimed at keeping the number of variables limited, because of the sample size constraint. Additionally, since variables are highly correlated, two indicators for each factor are preferred. One is the physical satisfaction (F1) composed of M16 and M17, and the other one is the phone size-general satisfaction (F2) composed of M21 and M24. We implemented structural equational model (SEM) with two different types of indicators of satisfaction.


### 3.3. Path Analysis and Structural Equation Modelling

Path Analysis (PA), introduced by Wright [9], is a statistical tool to indicate direct and indirect relations between variables. The correlations among variables influencing the outcome are used to write structural equations in Wright’s analysis. Blau and Duncan [13] introduce PA into social scientific research. The extensive research on PA is developed by Blau and Duncan [13] in the bookThe American Occupational Structure. In their path models, they utilize occupational and educational outcomes in a sample of male adults and parents of them. In 1970s, PA gains its popularity among sociology, psychology, political science, economics, ecology, and other methods.It is widely known that regression and correlation analysis are used to show relations between variables, but they are not quite enough to explain direct and indirect effects together. Pedhazur [14] emphasizes that “PA is intended not to discover causes but to shed light on the tenability of the causal models a researcher formulates based on knowledge and theoretical considerations” (p. 769).Equations in Structural Equation Modelling (SEM) are known to beregression-like, because it is possible to use error terms which may not be independent of the other predictors like in regression models [15]. Maruyama [16] states that “Regression for prediction does not provide logic consistent with SEM approaches. The set of uses of regression in which the particular predictors and their regression weights are of interest, called regression for explanation, define why SEM techniques are so valuable” (p. 21).Path diagram and path coefficients are two main tools for PA and also for SEM. Path diagram is the visual representation of the total effects of explanatory variables, and it consists of observed variables (rectangles) and latent variables (circles) connected by single-headed and double-headed arrows. It is mandatory to use double-headed arrows between exogenous variables which are assumed to have the variance explained by causes outside of the model. Conversely, endogenous variables’ variances are assumed to be explained by exogenous variables and other endogenous variables.Figure1 depicts an example of a PA model. Variables 1 and 2 are exogenous variables, while variables 3 and 4 are endogenous variables. “a” and “b” are residuals and they are not correlated. The arrows are drawn from the variables assumed as causes to variables assumed as effects [14, 17]. Path coefficient located on the diagram is shown by pij with “i” subscript indicating the effect and “j” indicating the cause. r12 shows the correlation between exogenous variables. As it is seen in Figure 1, all variables are observed (not latent) in PA.Figure 1
PA diagram example.Figure2 depicts an example of a SEM model. There are 4 observed variables denoted by I1–I4 that receive two paths going to them (the one from latent variable and the other one from their residual terms) and two latent variables denoted by F1 and F2. ei (i=1,…,4) is error term and it is possible to use correlations among errors for SEM, although it is not mandatory. The same as in the path diagram, the curved two-way arrows show the correlation between variables.Figure 2
SEM diagram example.Model definition equations are main tools of SEM to see the relationship between observed and unobserved variables. Following Figure2, the equations are written as follows:(1)I1=λ1F1+e1,I2=λ2F1+e2,I3=λ3F2+e3,I4=λ4F2+e4,where λi, i=1,…,4, denotes the factor loadings estimated based on the observed data and ei, i=1,…,4, denotes residual terms. Detailed implementations for variances and covariance are found in related text books such as [10, 16, 18] among others. It is essential for SEM to use a computational program because of its burden mathematical complexity. We used AMOS [19] to implement our analysis. Programming languages such as AMOS use iteration for implementations, and it is crucial to check whether these minimization routines with iterations converge or not.


## 3.1. Data

The survey is conducted with 36 participants, the average age is 23 ranging between 19 and 34, and half of the participants are female. The main characteristics of the data are as follows: the average monthly income is 1007 (±796) TL (Turkish Lira), while the average family income is 4000 (±2153) TL. 83% of them are right-handed. The smartphones are used mostly for phone calls and instant messaging programs such asWhatsapp, Tango, with 39% and 25%, respectively. The brand and the price of the smartphone are two most popular answers, with 39% and 27%, respectively, to the question of “What is the most important feature for you while buying a smartphone?” The dimension of the smartphone is generally the second or the third option for the participants while buying a smartphone.The objectives of smartphone usage and the satisfaction questions are asked with 5 Likert points withdefinitely dissatisfied to highly satisfied scale in the survey. Cronbach’s Alpha for the reliability of these items is 0.849. The average scores of satisfaction questions are mostly higher than 4 and this shows that participants are satisfied with their smartphones. However, the participants state that “it is possible to do some mistakes if they need to act faster,” which is one of the indicators of physical dissatisfaction. The average score for the related question is 2.67, that is, the lowest score among all satisfaction scores. The average scores obtained from the answers of questions M16, M17, M19, and M20 (descriptions are placed in Table 3) are lower than 4, as well.Data collection part also includes hand/finger measurements and Minnesota Manual Dexterity Test results mentioned in Sections2.1 and 2.2, respectively. The raw data and/or related information can be obtained from the author via e-mail.


## 3.2. Analysis

By usingt-test, it is concluded that there is no significant difference between right and left hand measurements with 5% confidence level. The analysis part proceeds with factor analysis. Participants answer several questions about their satisfaction in physical and general sense, and it is observed that the scores are split into two groups (Table 3). The first one is the physical satisfaction component, and the second one is the general satisfaction component. The final rotated component matrix of factor analysis is located at Table 3.In the analysis part, it is aimed at keeping the number of variables limited, because of the sample size constraint. Additionally, since variables are highly correlated, two indicators for each factor are preferred. One is the physical satisfaction (F1) composed of M16 and M17, and the other one is the phone size-general satisfaction (F2) composed of M21 and M24. We implemented structural equational model (SEM) with two different types of indicators of satisfaction.


## 3.3. Path Analysis and Structural Equation Modelling

Path Analysis (PA), introduced by Wright [9], is a statistical tool to indicate direct and indirect relations between variables. The correlations among variables influencing the outcome are used to write structural equations in Wright’s analysis. Blau and Duncan [13] introduce PA into social scientific research. The extensive research on PA is developed by Blau and Duncan [13] in the bookThe American Occupational Structure. In their path models, they utilize occupational and educational outcomes in a sample of male adults and parents of them. In 1970s, PA gains its popularity among sociology, psychology, political science, economics, ecology, and other methods.It is widely known that regression and correlation analysis are used to show relations between variables, but they are not quite enough to explain direct and indirect effects together. Pedhazur [14] emphasizes that “PA is intended not to discover causes but to shed light on the tenability of the causal models a researcher formulates based on knowledge and theoretical considerations” (p. 769).Equations in Structural Equation Modelling (SEM) are known to beregression-like, because it is possible to use error terms which may not be independent of the other predictors like in regression models [15]. Maruyama [16] states that “Regression for prediction does not provide logic consistent with SEM approaches. The set of uses of regression in which the particular predictors and their regression weights are of interest, called regression for explanation, define why SEM techniques are so valuable” (p. 21).Path diagram and path coefficients are two main tools for PA and also for SEM. Path diagram is the visual representation of the total effects of explanatory variables, and it consists of observed variables (rectangles) and latent variables (circles) connected by single-headed and double-headed arrows. It is mandatory to use double-headed arrows between exogenous variables which are assumed to have the variance explained by causes outside of the model. Conversely, endogenous variables’ variances are assumed to be explained by exogenous variables and other endogenous variables.Figure1 depicts an example of a PA model. Variables 1 and 2 are exogenous variables, while variables 3 and 4 are endogenous variables. “a” and “b” are residuals and they are not correlated. The arrows are drawn from the variables assumed as causes to variables assumed as effects [14, 17]. Path coefficient located on the diagram is shown by pij with “i” subscript indicating the effect and “j” indicating the cause. r12 shows the correlation between exogenous variables. As it is seen in Figure 1, all variables are observed (not latent) in PA.Figure 1
PA diagram example.Figure2 depicts an example of a SEM model. There are 4 observed variables denoted by I1–I4 that receive two paths going to them (the one from latent variable and the other one from their residual terms) and two latent variables denoted by F1 and F2. ei (i=1,…,4) is error term and it is possible to use correlations among errors for SEM, although it is not mandatory. The same as in the path diagram, the curved two-way arrows show the correlation between variables.Figure 2
SEM diagram example.Model definition equations are main tools of SEM to see the relationship between observed and unobserved variables. Following Figure2, the equations are written as follows:(1)I1=λ1F1+e1,I2=λ2F1+e2,I3=λ3F2+e3,I4=λ4F2+e4,where λi, i=1,…,4, denotes the factor loadings estimated based on the observed data and ei, i=1,…,4, denotes residual terms. Detailed implementations for variances and covariance are found in related text books such as [10, 16, 18] among others. It is essential for SEM to use a computational program because of its burden mathematical complexity. We used AMOS [19] to implement our analysis. Programming languages such as AMOS use iteration for implementations, and it is crucial to check whether these minimization routines with iterations converge or not.


## 4. Model Setting and Comparisons

Before finalizing the model setting, a set of plausible models are tried. Maruyama’s quote [16] “attempting to impose a single path analytic solution to interpret makes no sense” (p. 18) is a common view in PA and SEM literatures. Also, using too many unknowns in a SEM model leads to not having an unequally solvable model. So, it is not preferable to add all variables existing in the study while building the model. There is also one thing to be kept in mind while determining the number of variables which is the sample size, which is recommended to be more than ten times the number of free parameters [20, 21].In this study, it is not so easy to increase the sample size because of the expense of data collection process. Additionally, since there are high correlations between satisfaction indicators, two main indicators for satisfaction for both latent variables are used.F1 shows the physical satisfaction indicator, while F2 shows the phone size-general satisfaction for the rest of the study. Also, placing percentile scores (PPS) and turning percentile scores (TPS) are added separately as mediators to the models, since placing task is completed with single hand, while turning test is completed with both hands. This discrimination makes using left hand measurements for left-handed participants and right hand measurements for right-handed participants important, even though we did not find any statistical differences between the measurements of hand sizes.According to satisfaction indicators and turning/placing percentile scores, four different models are implemented (Table4). In Models 1 and 2, physical satisfaction (F1) is taken as latent variable. The mediator of Model 1 is TPS, while the mediator of Model 2 is PPS. In Models 3 and 4, phone size-general satisfaction (F2) is taken as latent variable. The mediator of Model 3 is TPS, while the mediator of Model 4 is PPS. Also, each model is built in two different versions. The first one (A) omits mediator and correlations of errors as in classical regression model and the second one (B) is named as default model that includes both mediator and correlations. Each model includes hand length and thumb length of participants as exogenous variables (Table 4).Table 4
Model comparisons.
Main models
Model 1
Model 2
Model 3
Model 4
Model versions
A (∗)
B
A (∗)
B
A (+)
B
A (+)
B
Chi-square
8.937
0.5
8.937
0.172
41.578
5.716
41.578
2.903
Degrees of freedom
3
2
3
2
3
2
3
2
Probability level
0.03
0.779
0.3
0.918
0
0.057
0
0.234
RMSEA
0.238
0
0.238
0
0.606
0.230
0.606
0.114
AIC
22.937
26.5
22.937
26.172
55.578
31.716
55.578
28.903
A: without mediator and correlations of errors.
B: default model (with mediator and correlations of errors).
(∗) Without mediator, the first cases of Model 1 and Model 2 are the same models. (+) Without mediator, the first cases of Model 3 and Model 4 are the same models.The first and the base model (Model 1-A, Table4) does not include mediator or any covariance between independent variables and errors. The Chi-square test value of this model fit is 8.937 and probability value of the Chi-square test is 0.03 with 3 degrees of freedom (Table 4). An insignificant result at a 0.05 threshold is expected for a good model fit [22]. Therefore, in the base model, since p value is smaller than the 0.05 level, the null hypothesis is rejected that model fits the data. Contrary to classical methodology in statistics analysis in which it is aimed at rejecting the null hypothesis (usually alternative hypothesis reflects the difference or change), SEM usually concerns not rejecting the null hypothesis, since it shows the model fits the data well [10].Another absolute fit statistic is root mean square error of approximation (RMSEA) which is sensitive to the estimated number of parameters in the model [23]. Hooper et al. [24] report that it is taken as “one of the most informative fit indices” [25] (p. 54) because of its sensitivity property. Revisiting Model 1-A, RMSEA value (0.238) is not counted as good for expected well-fitted data since the model with a RMSEA greater than 0.1 would not be preferable [26]. Another fit index which takes into account both the measure of fit and model complexity is Akaike information criterion (AIC) [27] that is reported in the model comparisons table (AIC = 22.937 for the first model).One of the main benefits of SEM is that it allows researchers to work with indirect effects of variables in addition to direct variables. These indirect effects show the effects between two variables that are mediated by one or more intervening variables (mediators) [10]. In the default version of Model 1 (B) with two degrees of freedom, the null hypothesis is not rejected that model fits the data well (p value: 0.779). Also, RMSEA value is acceptable.It is noteworthy that Chi-square values and RMSEA get smaller values for all models with mediators. Additionally, SEM with mediators provides better results for general satisfaction indicator which is considered in Model 3 and Model 4. It is observed that, including a mediator to the models withF1 is not as effected as F2. It is an inevitable result because physical satisfaction is directly affected more by both hand and thump lengths than the general satisfaction. This emphasizes the importance of mediator effect in indirect types of relations in SEM structures.


## 5. SEM Diagrams

The SEM diagrams of default version of four models (Model 1-B, Model 2-B, Model 3-B, and Model 4-B) with mediators and their comparisons are detailed in this section. The first theoretical model (Figure3) depicts a mediated model, in which turning percentile scale modifies the effects of hand length and thumb length on F1 which is a physical satisfaction indicator. It is pointed that hand and thumb lengths have direct effects, as well as having indirect effect on satisfaction. Hand length has a direct and positive (positive means that when hand lengths get bigger, physical satisfaction gets higher) effect on satisfaction with 0.97 standardized regression coefficient. See Figures 3, 4, 5, and 6.Figure 3
SEM diagram of Model 1-B.Figure 4
SEM diagram of Model 2-B.Figure 5
SEM diagram of Model 3-B.Figure 6
SEM diagram of Model 4-B.In Figures3, 4, 5, and 6, the correlations between exogenous variables are specified with double-headed arrows. Since the same exogenous variables are used for each model, the correlations (r12=0.45) are all the same. The numbers on one-headed arrows indicate standardized regression coefficients. It is observed that the direct effect of hand and thumb lengths on physical satisfaction indicator is observed, in addition to the indirect effect which is the product of the path coefficients. For example, in Model 4-B (Figure 6), the direct effect of hand length on general satisfaction (F2) is 0.61, while the indirect effect of hand length is 0.26×0.55=0.143.


## 6. Conclusion and Future Work

Smartphones are one of the most popular devices that are being used in daily life and requiring intensive human-machine interaction. Most of the consumers make their smartphone choices based on a few criteria. Usually, some technical features of smartphones and attractive appearance are being considered. This study attracts attention to the relationship between human attributes and satisfaction level of smartphones. Besides anthropometric dimensions, dexterity levels of participants are taken into account as a new approach and possible effects on smartphone satisfaction are inspected. Since motor skills of users are considered for the first time in this study, relevant findings provide a new viewpoint for smartphone satisfaction studies.One of the main aims of this study is to investigate the satisfaction factors while selecting and using smartphones. For that purpose, first, hand anthropometric measurements of the participants were collected and then a multistage experimental study was conducted. Minnesota Manual Dexterity Test was utilized to make participants perform one-hand and two-hand dexterity tasks. A survey was conducted to assess satisfaction measurements. Based on survey results, it was possible to group the response under two main factors (physical satisfaction and general satisfaction). The factors in concern were hand anthropometric measurements and manual dexterity levels. Therefore, effects of these factors were investigated through detailed statistical analyses.Another aim of this study is to assess the effects of placing percentile scale and turning percentile scale as mediators. Therefore, SEM is used as a statistical tool that is an extension of multiple regression models. After finalizing data collection, several models were implemented with two different types of indicators of satisfaction, which were determined with factor analysis, for different types of dexterity test results. Measured variables were selected as exogenous variables, while two variables were selected to generate latent variables for two different satisfaction indicators. Even though the direct effects of hand and thumb lengths were smaller on general satisfaction than physical satisfaction, it was possible to obtain the indirect effects of these lengths on general satisfaction with the help of SEM.SEM indicates that standardized regression coefficients (Figures3, 4, 5, and 6) between hand/thumb lengths and physical satisfaction (F1) are higher than general satisfaction (F2), since F1 includes direct physical satisfaction questions that are “I do not have difficulty in reaching keys with my thumbs” and “I push neither incorrect nor multiple keys with my thumbs.” Additionally, there is a negative relation between thumb length and satisfaction for each model; users with longer thumbs are less satisfied physically with their smartphones than the users with shorter thumbs. This result may bring an idea for smartphone practitioners and manufacturers to produce the new generation smartphones with varied key sizes. As it is known that there is a difference between male and female thumb sizes, key sizes may be specified for genders.As a conclusion, it can be stated that dexterity level and hand anthropometrics of the users affect smartphone satisfaction either directly or latently. Analyses results indicate a critical importance of considering user attributes regarding dexterity and hand anthropometrics for both designers and consumers in the smartphone market.Creating a more personal preference profile for users is an ongoing and natural extension of this study. Finding scientific evidence related to user-based factors for smartphone preferences would assist designers to invest more user friendly devices for their clients, especially in our era in which smartphones are tremendously popular and the sector of them are competitive indeed for designers and manufacturers. Future studies may consider different age groups. Further, other mobile devices used in daily life that require human-machine interaction may be studied. On the other hand, it is being planned developing a smartphone application to measure dexterity levels of potential users which will be applied prior to buying decision to help estimate prospective satisfaction level of them on the relevant smartphone.



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*Source: 649374-2015-10-28.xml*