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Chapter 6 MODEL SPECIFICATIONS
6-1 Log-based User Behavior and Perception Data Analysis
We specify the following model to test our research hypotheses, and the linear regression model was used for estimation.
Learning comprehension (H1)
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿ℎ𝐿𝐿𝐿𝐿𝑒𝑒𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 = 𝛽𝛽0 + ∑2𝑗𝑗=1𝛽𝛽𝑗𝑗𝐺𝐺𝐿𝐿𝐿𝐿𝑙𝑙𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝐿𝐿𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 +
∑4 𝛽𝛽𝑗𝑗𝐹𝐹𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝑖𝑖
𝑗𝑗=3 + 𝛽𝛽5𝑇𝑇𝐿𝐿𝑒𝑒𝑇𝑇𝑖𝑖 + 𝛽𝛽6𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝑃𝑃𝑖𝑖 +
∑8𝑗𝑗=7𝛽𝛽𝑗𝑗𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝐿𝐿𝐿𝐿𝑖𝑖 + 𝛽𝛽9𝐺𝐺𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝑖𝑖 + 𝜀𝜀𝑖𝑖 (1)
Understanding of visualization (H2)
𝑈𝑈𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝑒𝑒𝑂𝑂𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝑈𝑈𝑈𝑈𝐿𝐿𝑒𝑒𝐸𝐸𝐿𝐿𝑙𝑙𝐿𝐿𝑈𝑈𝐿𝐿𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 = 𝛽𝛽0+ ∑2𝑗𝑗=1𝛽𝛽𝑗𝑗𝐺𝐺𝐿𝐿𝐿𝐿𝑙𝑙𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝐿𝐿𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 +
∑4 𝛽𝛽𝑗𝑗𝐹𝐹𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝑖𝑖
𝑗𝑗=3 + 𝛽𝛽5𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝑃𝑃𝑖𝑖 +
∑7𝑗𝑗=6𝛽𝛽𝑗𝑗𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝐿𝐿𝐿𝐿𝑖𝑖 + 𝛽𝛽8𝐺𝐺𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝑖𝑖 + 𝜀𝜀𝑖𝑖 (2)
Perceived learning (H3)
𝑃𝑃𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 = 𝛽𝛽0+ ∑2𝑗𝑗=1𝛽𝛽𝑗𝑗𝐺𝐺𝐿𝐿𝐿𝐿𝑙𝑙𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝐿𝐿𝑂𝑂𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖+ ∑4𝑗𝑗=3𝛽𝛽𝑗𝑗𝐹𝐹𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑂𝑂𝑖𝑖+
𝛽𝛽5𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝑃𝑃𝑖𝑖+ ∑7𝑗𝑗=6𝛽𝛽𝑗𝑗𝑃𝑃𝑃𝑃𝐿𝐿𝐿𝐿𝐸𝐸𝐸𝐸𝐿𝐿𝐸𝐸𝐿𝐿𝐿𝐿𝑖𝑖+ 𝛽𝛽8𝐺𝐺𝐿𝐿𝐿𝐿𝑃𝑃𝐿𝐿𝐿𝐿𝑖𝑖+ 𝜀𝜀𝑖𝑖 (3)
The equation (1) test how goal orientation impact the learning comprehension.
Also, it test the influences of the format of graph visualization and the type of learning tasks on the learning comprehension. The index i stands for each observation in our integrated collected data. The effects of dummy variable GoalOrientation on learning
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comprehension are denoted by the parameters 𝛽𝛽1𝐿𝐿𝐿𝐿𝑃𝑃𝛽𝛽2, which represents the difference level of the high degree observation and the low degree observation of the goal orientation, and the difference level of the high degree observation and the middle degree of the goal orientation. 𝛽𝛽3𝐿𝐿𝐿𝐿𝑃𝑃𝛽𝛽4 are coefficients for the effect of dummy variable Format on learning comprehension, which represents the difference level of the line format and the bar format, and the difference level of the radar format and the bar format. 𝛽𝛽5 reflects the effect of dummy variable Task on learning comprehension, which represents the difference level between search fact task and inference generation task on learning comprehension. 𝛽𝛽6, 𝛽𝛽7, 𝛽𝛽8, 𝛽𝛽9 are coefficients for the effect of control variable. 𝛽𝛽6 reflects the effect of dummy variable ProgrammingExperienced, which represents the difference level between the participants experienced in programming and the beginner. 𝛽𝛽7𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽8 are estimate of dummy variable ExamNumber, which represents the difference level of the exam 2, exam 3 and the exam 1 as the baseline. 𝛽𝛽9 is estimate of dummy variable Gender, which reflects the effect of difference level between the male and female. Finally the 𝜀𝜀𝑖𝑖 is the level-1 error term.
In sum, the coefficient estimates of GoalOrientation_Low is statistically significant at the level of 0.05 and Task_SearchFact is statistically significant at the level of 0.001. The results show that there is a significant difference between the high degree observation and the low degree observation of the goal orientation, which strongly support for H1c and support for H1a. However, the estimates of Format_Line and Format_Radar provide no statistical support for H1b. The estimated results for learning comprehension are summarized in Table 6.1. Also we have observed significant difference of control variables exam number 1 and exam number 2, which show that there are difference between the three exams. We discuss this in chapter 7.
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Table 6.1 Estimated results for learning comprehension.
Estimate Std. Error t value Pr(>|t|)
Constant 0.75939 0.054018 14.031 < 2e-16 ***
Goal orientation (Low) -0.088151 0.036983 -2.384 0.0181 **
Goal orientation (Middle) -0.031032 0.034210 -0.907 0.3655
Format (Line) -0.002351 0.032971 -0.071 0.9432
Format (Radar) -0.037530 0.032971 -1.138 0.2564
Task (SearchFact) 0.128123 0.026909 4.761 3.76e-06 ***
Programming-experienced
(Experienced) -0.053657 0.033959 -1.580 0.1157
Exam number (2) 0.163285 0.032971 4.952 1.59e-06 ***
Exam number (3) 0.147371 0.032971 4.470 1.33e-05 ***
Gender (Female) 0.025574 0.027578 0.927 0.3549
* Significance (Sig.) at 0.1 level, ** Sig. at 0.05 level, *** Sig. at 0.01 level.
The equation (2) test how goal orientation impact the understanding of visualization. Also, it test the influences of the format of graph visualization on the understanding of visualization. The index i stands for each observation in our integrated collected data. The effects of dummy variable GoalOrientation on learning comprehension are denoted by the parameters 𝛽𝛽1 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽2, which represents the difference level of the high degree observation and the low degree observation of the goal orientation, and the difference level of the high degree observation and the middle degree of the goal orientation. 𝛽𝛽3 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽4 are coefficients for the effect of dummy variable Format on learning comprehension, which represents the difference level of the line format and the bar format, and the difference level of the radar format and the bar format. 𝛽𝛽 , 𝛽𝛽 , 𝛽𝛽 , 𝛽𝛽 are coefficients for the effect of control variable. 𝛽𝛽
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reflects the effect of dummy variable ProgrammingExperienced, which represents the difference level between the participants experienced in programming and the beginner.
𝛽𝛽6 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽7 are estimate of dummy variable ExamNumber, which represents the difference level of the exam 2, exam 3 and the exam 1 as the baseline. 𝛽𝛽8 is estimate of dummy variable Gender, which reflects the effect of difference level between the male and female. Finally the 𝜀𝜀𝑖𝑖 is the level-1 error term.
In sum, the coefficient estimates of Format_Line and Format_Radar are statistically significant at the level of 0.01. The results show that there is a difference between three formats on the understanding of visualization, which fairly strong support for H2b. However, the estimates of GoalOrientation_Low and GoalOrientation_Middle provide no statistical support for H2a. The estimated results for understanding of visualization are summarized in Table 6.2.
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Table 6.2 Estimated results for understanding of visualization.
Estimate Std. Error t value Pr(>|t|)
Constant 0.71088 0.06361 11.176 < 2e-16 ***
Goal orientation (Low) -0.05556 0.04497 -1.235 0.21815 Goal orientation (Middle) -0.04556 0.04160 -1.095 0.27473
Format (Line) -0.12367 0.04009 -3.085 0.00233 ***
Format (Radar) -0.11703 0.04009 -2.919 0.00392 ***
Programming-experienced
(Experienced) 0.12021 0.04129 2.911 0.00402 ***
Exam number (2) -0.03795 0.04009 -0.947 0.34499
Exam number (3) -0.05902 0.04009 -1.472 0.14259
Gender (Female) -0.08599 0.03353 -2.564 0.01109 *
* Significance (Sig.) at 0.1 level, ** Sig. at 0.05 level, *** Sig. at 0.01 level.
The equation (3) test how goal orientation impact the perceived learning. Also, it test the influences of the format of graph visualization on the perceived learning. The index i stands for each observation in our integrated collected data. The effects of dummy variable GoalOrientation on learning comprehension are denoted by the parameters 𝛽𝛽1 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽2, which represents the difference level of the high degree observation and the low degree observation of the goal orientation, and the difference level of the high degree observation and the middle degree of the goal orientation.
𝛽𝛽3 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽4 are coefficients for the effect of dummy variable Format on learning comprehension, which represents the difference level of the line format and the bar format, and the difference level of the radar format and the bar format. 𝛽𝛽5, 𝛽𝛽6, 𝛽𝛽7, 𝛽𝛽8 are coefficients for the effect of control variable. 𝛽𝛽5 reflects the effect of dummy variable ProgrammingExperienced, which represents the difference level between the
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立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
participants experienced in programming and the beginner. 𝛽𝛽6 𝐿𝐿𝐿𝐿𝑃𝑃 𝛽𝛽7 are estimate of dummy variable ExamNumber, which represents the difference level of the exam 2, exam 3 and the exam 1 as the baseline. 𝛽𝛽8 is estimate of dummy variable Gender, which reflects the effect of difference level between the male and female. Finally the 𝜀𝜀𝑖𝑖 is the level-1 error term.
In sum, the coefficient estimates of GoalOrientation_Low is statistically significant at the level of 0.001. The results show strong support for H3a. However, the estimates of Format_Line and Format_Radar provide no statistical support for H3b.
The estimated results for perceived learning are summarized in Table 6.3.
Table 6.3 Estimated results for perceived learning.
Estimate Std. Error t value Pr(>|t|)
Constant 3.96456 0.20965 18.910 < 2e-16 ***
Goal orientation (Low) -0.56790 0.14821 -3.832 0.000172 ***
Goal orientation (Middle) -0.14607 0.13709 -1.065 0.287977
Format (Line) 0.01183 0.13213 0.090 0.928735
Format (Radar) -0.04473 0.13213 -0.339 0.735313
Programming-experienced
(Experienced) -0.16053 0.13609 -1.180 0.239610
Exam number (2) 0.06898 0.13213 0.522 0.602247
Exam number (3) -0.07677 0.13213 -0.581 0.561914
Gender (Female) 0.16727 0.11052 1.514 0.131764
* Significance (Sig.) at 0.1 level, ** Sig. at 0.05 level, *** Sig. at 0.01 level.