2-Step Evaluator
28/01/2020
Introduction
There is continuous dialogue between the team members, and with the teacher, encouraging reflection and collaboration, and incorporating self, peer, and teacher formative assessment (Dochy et al., 1999). []
the educator is plagued with opportunity-cost and time-use choices (Burns, Gentry, & Wolfe, 1990) as well as effectiveness concerns [Gosen and Wasbush 2004]
Students assume that the focus of exams and assignments reflects the educational goals most valued by an instructor, and they direct their learning and studying accordingly (McKeachie & Svinicki, 2006).
Ideally, effective exams have four characteristics. They are:
Valid, (providing useful information about the concepts they were designed to test),
Reliable (allowing consistent measurement and discriminating between different levels of performance),
Recognizable (instruction has prepared students for the assessment), and
Realistic (concerning time and effort required to complete the assignment) (Svinicki, 1999)Literature review
Expertiental learning
Approaches to describe team work described by McGrath’s circumplex model
Teams have been investigated by many research disciplines. In consequence, multiple definitions of teams have been suggested since now. One widely established definition describes teams as a collection of individuals who are interdependent in their tasks and who share responsibility for outcomes (Stock, 2004). So, one key feature of a team is that members work together on a common project for which they all are accountable (Levi, 2015). In defining teams, the academic literature has sometimes discussed a distinction between teams and groups. Most definition of teamwork classify a team as a special type of group. Therefore, the group is considered as more inclusive term then team. For example, political parties and social organisation are seen as a group but not team. A team is not simply people who belong to the same group or who are co-acting in the same place. Team is a special type of group in which people work interdependently to accomplish a goal. This helps distinguish teams from work groups, whose members jointly do the same tasks but do not require integration and coordination to perform them (Levi, 2015). However, a different use of these terms is not yet widely shared (Cohen & Bailey, 1997) Therefore, in this document, the words “team” and “group” are used interchangeably.
As we said, individuals are interdependent in their task in a team. The McGrath’s circumplex model identifies four general groups’ task processes which are (1) to generate (2) to choose (3) to negotiate and (4) to execute. Each process is divided into two subtypes which represent eight basic activities that are (1) planning, (2) creating, (3) solving problems, (4) making decisions, (5) forming judgments, (6) resolving conflicts, (7) competing and (8) performing. The tasks in the upper four quadrants in the picture below are linked to cooperation interaction when tasks in the lower quadrants are related to conflict interaction. Then, tasks on the right side of the circle are related to behavioural tasks whereas those on the left are more conceptual. This schema can be a good framework for the teacher to identify the needs and / or tasks that the groups have developed to guide and guide them accordingly.
- Quadrant I – Generate is divided into Generating Plans and Generating Ideas. The former is related to the adjacent performance category in having an emphasis on action orientation. The latter, Generating Ideas is the locus for “creativity” tasks. It’s related to the adjacent intellective problem category in having an emphasis on cognitive matters.
- Quadrant II – Choose is also divided into two types: (3) Intellective tasks and (4) Decision-Making tasks. The former refers to tasks for which there is a demonstrable right answer, and the group task is to invent, select, compute that correct answer. The latter refers to tasks for which there is not a demonstrably correct answer, and for which the group’s task is to select, by some consensus, a preferred alternative.
- Quadrant Ill – Negotiate is more or less an extension of Quadrant II. The key word here is not solved, but resolved. There are also two types: Resolving Conflicts of Viewpoint and Resolving Conflicts of Interest. The first refers to cases where members of the group do not just have different preferences, but have different preference structures systematically. They may interpret information differently may give different weights to different dimensions, and/or may relate dimensions to preferences via different functional forms. The second is when member has opposing interests, of which at least one of them could corrupt the motivation to act on others, or at least give that impression.
- Quadrant IV - Execute deals with overt, physical behaviour, with the execution of manual and psychomotor tasks. Again, there are two types: Contests and Performances. Contests are tasks for which the unit of focus, the group, is in competition with an opponent, an enemy, and performance results will be interpreted in terms of a winner and a loser, with payoffs in those terms as well. The Performance approach, the other adjacent task category, involve striving to meet standards of excellence/sufficiency, with payoffs tied to such standards rather than to “victory” over an opponent. Figure 5 : Model of group tasks - McGrath’s circumplex model
Source : (McGrath, 1984)
Of course, the McGrath’s tasks circumplex model of group tasks can be linked to team dynamic’s theory, especially with the upper part of the circle, linked to cooperation, and lower part, linked to conflict. Cartwright and Zander (1968) define group dynamics as the nature of groups; the laws of their development; and their relationships with people, other groups, and larger institutions. For the purpose of this note, group dynamics is defined as the interaction of the congregational team as it relates to its internal workings (Savage, 2016) and as the way team and individuals act and react to changing circumstances (Lewin, 1951). Therefore, the notion of team dynamics is close to the notion of the group development that is the change through time in the internal structures, processes, and culture of the group (Sarri & Galinsky, 1985). The literature on group development is plentiful and Smith (2001) made a literature review that divides group development models into three categories that are (1) linear progressive models (2) cyclical and pendular models, and (3) non-sequential or hybrid models. This model allows to better understand how team behave throughout the collaborative process. Figure 6 : Group Development Models
Source : (Mennecke et al., 1992)
• Linear progressive models are models that “imply that groups exhibit an increasing degree of maturity and performance over time” (Mennecke, Hoffer, & Wynne, 1992). The linear-progressive models are perhaps the best known and most widely cited type of developmental model. These models assume that groups develop in a definite linear fashion and that there is a “definite order of progression” from one phase or stage to another. Basiquement, quatre phases principales composent la vie et le développement d’une équipe. Mis dans un contexte académique, dans un premier temps, les étudiants vont chercher à se connaître et à trouver leur place au sein du groupe. Après l’orientation, une phase d’insatisfaction, qui peut notamment être liée à la prise de pouvoir, au sentiment d’incompétence des autres membres de l’équipe ou à un non-alignement lié aux objectifs à atteindre. Il est donc primordial que l’équipe ne reste pas dans cette phase négative et que les moyens adéquats soient mis en œuvre pour l’aider à résoudre les problèmes et divergences. Dès que la confiance est retrouvée, les responsabilités partagées et la motivation retrouvée, le groupe atteint une phase de maturité au cours de laquelle chacun participe de façon active à l’atteinte des objectifs.
Figure 7 : Collaborative process: Examples of linear progressive model
Source : (Lacoursiere, R. B., 1980)
Source (Tuckman & Jensen, 1977)
Cyclical and pendular models are defined as models that “imply a recurring sequence of events” (Mennecke et al., 1992). In this case, groups revisit stages and phases over and over or swing between issues again and again during the developmental process. The specific ordering of these stages is not as important to these models as was the case for the linear progressive models. The authors assume, however, that for a group to fully develop and mature, it must deal with the issues found in each of the developmental stages or phases. According to the theory, groups must constantly address similar issues and problems at multiple time periods and settings, for reasons ranging from changes in the external environment, to changes in group membership, to changes in the nature of the group task. Each cycle or swing serves to strengthen the group’s understanding of its present situation and its assigned task and to modify the group’s approach to dealing with those issues.
Figure 8 : Collaborative process: Example of cyclical model
Source : (Hare, 1976)
• Non-sequential models are models that “do not imply any specific sequence of events; rather, the events that occur are assumed to result from contingent factors that change the focus of the group’s activities” (Mennecke et al., 1992). Hybrid models tend to be models that combine several different models to form a new model. The hybrid models are grouped with the non-sequential models because they also do not propose a specific, ordered pattern of group development. For example, Gersick (1988) noticed that teams did not go through the universal stages of group development as prescribed by linear model and she created the punctuated equilibrium model (see Figure below). The model is based on two phases of inertial movement interrupted by a transition period. The first phase of inertial movement starts after the first meeting of the team. At the end of the first team meeting the team establishes a way of working that becomes a normal routine for the rest of the first phase. At the midpoint of the team’s lifespan, the team encounters a transition point. Team members feel the need to innovate because the old work routines are no longer valid to create a qualitative end product and meet the deadline. At this halfway point, the stage is set for the team to progress by dropping old work routines, adapting to new approaches and views on their work, and looking for new routines. In phase 2, the second phase of inertia, the team maintains this new and approved way of working until the end of the project. During the second phase of inertia the effort of the team is situated at a higher level of performance (Raes, 2015).
Figure 9 : Collaborative process: The punctuated equilibrium model
Source : Gersick (1988)
Thus, the literature shows that there are divergent opinions on how a team’s life develops and evolves over time. Regardless of the model, however, everyone agrees that a team’s life is dynamic, changes over time and contains moments of fragility. Therefore, in order to support the teacher in his or her role as a facilitator of interactions between group members, a tool for monitoring the dynamics of the team is proposed. This tool, which complements the teacher’s expertise, goes beyond the primary observation and understanding of students by allowing them to know how students evaluate their own dynamics, in terms of coordination. The tool is based on common ground theory. The notion of common ground is defined as a collection of mutual knowledge, mutual beliefs, and mutual assumptions (Clark, 1996) and as well-known to influence the performance of project teams (Aral, Brynjolfsson, & Van Alstyne, 2008). Common ground is inevitable in communication (Kecskes & Zhang, 2009) and is specifically an important process in design tasks because of the domain and cultural differences of co-designers (Détienne, 2006). But common ground isn’t just there, ready to be exploited and should be established by each person interacting together (Clark, 1996). Then, more common ground is activated, shared and created between people and better people are supposed to understand each other and achieved the desired effect (Kecskes & Zhang, 2009). This approach makes it possible to counteract the difficulty of diagnosing in which phase of development a team is situated in its development cycle, particularly that of Lacoursiere (1980) and allows an objective longitudinal analysis throughout the project.
Notice: Our main hypothesis is that conversation is the main mechanism for mediating between individuals, particularly in terms of how they understand each other’s intentions. From then, in the light of the different development models presented above, if the teacher can monitor the level of alignment in the groups, then the latter will be able to diagnose, or even anticipate, the phases of dissatisfaction, tension and/or transition within the teams and accompany them consciously. In other words, the tool supports the teacher in his or her role as a facilitator and guarantor of interaction between group members.
Assessing teams in experiental learning projects.
How to address 3 challenges
Should we assess the team performance?
To some degree, the group product will be codified in an artifact (e.g., group report, dialogue, diagram, etc.), but the individual experience of that CL event will be transposed to future CL events. Hence, even if group-level interaction is considered as the engine for CL, the individual level cannot be dismissed." [Strijbos 2010: 4] * –> Hypothesis to test: The individual performance is more relevant than the group performance
The individual performance is less relevant than the group performance *
How should we assess a group and a team
To measure transactivity, that is, “the extent to which students refer and build on each others’ contributions [68], [76] reflected in collaborative dialogue or individual products, or the extent to which students transform a shared artifact (e.g., a group report)” [Strijbos 2010]
How should assess if students want to work like a team
students have multiple goals and motivations in the context of CL [84], [90]. Hijzen et al. [84], for example, found that mastery goals (“I want to learn new things”) and social responsibility goals (“I want help my peers”) prevail in effective CL groups. Furthermore, belongingness goals (e.g., “I want my peers to like me”) were more important than mastery goals in ineffective CL groups, whereas the opposite was observed for effective groups. Finally, students in effective CL groups were more aware of their goals compared to students in ineffective groups [84]. [Strijbos 2010]
A recent paper has proposed an effcient way to assess team performance.
Methodology
Testable propositions associated to our artefact
P0: The individual performance does not have a statistically significant effect on the group performance.
Prelminary data analysis
Loading dataset with scores
The scores dataset contains 66 rows. An example of the first three lines is shown below.
The first column shows the anonymized unique identifier (UID) of each student, associated to a group numer and the class. The other columns show the attendance score, the score of the MidTerm evaluation, the result of the part of the final exam done individually (Exa01)) and the part of the exam done in group (Exa02).
| UID | Class | Group | Attendance | MidTerm | Exa01 | Exa02 |
|---|---|---|---|---|---|---|
| 23 | 2 | 8 | 5.5 | 5.68 | 10.00 | 8.33 |
| 37 | 2 | 16 | 5.5 | 4.45 | 8.79 | 10.00 |
| 25 | 1 | 14 | 5.4 | 5.88 | 10.00 | 9.79 |
| 8 | 2 | 8 | 5.2 | 5.68 | 6.40 | 7.98 |
| 44 | 2 | 8 | 5.4 | 5.06 | 9.05 | 8.98 |
Descriptive statistics
The previous figure shows, not only the groups, but the individual performances. However, the individual dots are not very informative because within the group the dots are the same color. Since columns can separate the groups from each other, I would save the color code of the dots to individuals. That would reveal if the individual change in performance between the two measurements is systematic (everybody goes to same direction) or random (some improve the results, some get lower results).
Linear regressions
Model 01: The result of the group performance is a function of the individual performance
With start by rejecting the null hypothesis H0, which states that there is no causal effect between the first exam (done individually) and the second exam (done in group).
We scale the results, in order to properly compare the coefficients. Hence, Exa01 and Exa02 shift from a scale of [0:10] to a normal distribution [-3;+3]. Moreover, we look for outliers with a large residual.
Accordingly, we identify and remove the outlier in the row 43 (a student who attended the exam, but did not do it).
The performance of the first exam (Exa01) positively effects the score of the second exam (Exa02), with a coefficient of 0.22. The value of p = 0.08 shows that the relationship between the two variables is statistically significant.
Nonetheless, the Adjusted R2 = 0.03 suggests that the explanatory power of this model is farily low.
The analysis of the residuals in the appendix does not indicate any problem.
Model 02: Each group has fixed effect, which overseeds the individual performance
| Variable | Model.01 | Model.02 |
|---|---|---|
| Intercept | 0.00 ( 1.00 ) | -1.59 ( 0.00 ) |
| Scale (Exa01) | 0.22 ( 0.08 ) | 0.06 ( 0.42 ) |
| G02 | 1.23 ( 0.00 ) * | |
| G03 | 2.17 ( 0.00 ) * | |
| G04 | 1.43 ( 0.00 ) * | |
| G05 | 2.02 ( 0.00 ) * | |
| G06 | 2.15 ( 0.00 ) * | |
| G07 | 1.78 ( 0.00 ) * | |
| G08 | 1.63 ( 0.00 ) * | |
| G09 | -0.46 ( 0.24 ) | |
| G10 | 1.11 ( 0.01 ) * | |
| G11 | 1.87 ( 0.00 ) * | |
| G12 | 2.01 ( 0.00 ) * | |
| G13 | 0.65 ( 0.09 ) | |
| G14 | 2.20 ( 0.00 ) * | |
| G15 | 2.79 ( 0.00 ) * | |
| G16 | 2.51 ( 0.00 ) * | |
| Adj R2 | 0.03 | 0.71 |
The Adjusted R2 of the new model (0.71) is very good.
The coefficient of the first Exam (0.06) if not statistically significant (p = 0.42).
Model 03: Decision tree
Linear Predictions for Exa02 of 30% of the total sample
The benchmark is the model done with the linear regression and the fixed effects.
The table below shows the ID of the random sample (30% of the total sample), the predicted values and the values after being rounded (round digit = 1)
| Prediction | Rounded.prediction | Actual.value | |
|---|---|---|---|
| 4 | 8.502988 | 9 | 8 |
| 6 | 7.305241 | 7 | 7 |
| 17 | 9.542940 | 10 | 9 |
| 19 | 8.158100 | 8 | 8 |
| 23 | 9.742626 | 10 | 10 |
| 25 | 7.536924 | 8 | 10 |
| 26 | 9.736988 | 10 | 10 |
| 29 | 8.562452 | 9 | 9 |
| 33 | 9.148554 | 9 | 10 |
| 34 | 8.108414 | 8 | 6 |
| 36 | 8.887092 | 9 | 10 |
| 39 | 6.114692 | 6 | 6 |
| 41 | 8.808722 | 9 | 9 |
| 42 | 9.612940 | 10 | 8 |
| 47 | 7.660850 | 8 | 8 |
| 48 | 7.037369 | 7 | 7 |
| 49 | 7.869861 | 8 | 9 |
| 57 | 8.308565 | 8 | 8 |
| 64 | 8.465886 | 8 | 9 |
| 65 | 9.501057 | 10 | 10 |
The confusion matrix allows to assess the performance of the predictions
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 3 0 1 1 0
## 7 0 2 0 0 0
## 9 2 0 2 1 0
## 10 1 0 2 3 0
## 6 1 0 0 0 1
##
## Overall Statistics
##
## Accuracy : 0.55
## 95% CI : (0.3153, 0.7694)
## No Information Rate : 0.35
## P-Value [Acc > NIR] : 0.05317
##
## Kappa : 0.4079
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.4286 1.0 0.40 0.6000 1.0000
## Specificity 0.8462 1.0 0.80 0.8000 0.9474
## Pos Pred Value 0.6000 1.0 0.40 0.5000 0.5000
## Neg Pred Value 0.7333 1.0 0.80 0.8571 1.0000
## Precision 0.6000 1.0 0.40 0.5000 0.5000
## Recall 0.4286 1.0 0.40 0.6000 1.0000
## F1 0.5000 1.0 0.40 0.5455 0.6667
## Prevalence 0.3500 0.1 0.25 0.2500 0.0500
## Detection Rate 0.1500 0.1 0.10 0.1500 0.0500
## Detection Prevalence 0.2500 0.1 0.25 0.3000 0.1000
## Balanced Accuracy 0.6374 1.0 0.60 0.7000 0.9737As a reminder, here is the model that uses only Exa01 to predict Exa02
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 3 0 2 0 0
## 7 0 0 2 0 0
## 9 2 0 2 1 0
## 10 2 0 3 1 0
## 6 1 0 1 0 0
##
## Overall Statistics
##
## Accuracy : 0.3
## 95% CI : (0.1189, 0.5428)
## No Information Rate : 0.5
## P-Value [Acc > NIR] : 0.9793
##
## Kappa : 0.0604
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.3750 NA 0.2000 0.5000 NA
## Specificity 0.8333 0.9 0.7000 0.7222 0.9
## Pos Pred Value 0.6000 NA 0.4000 0.1667 NA
## Neg Pred Value 0.6667 NA 0.4667 0.9286 NA
## Precision 0.6000 0.0 0.4000 0.1667 0.0
## Recall 0.3750 NA 0.2000 0.5000 NA
## F1 0.4615 NA 0.2667 0.2500 NA
## Prevalence 0.4000 0.0 0.5000 0.1000 0.0
## Detection Rate 0.1500 0.0 0.1000 0.0500 0.0
## Detection Prevalence 0.2500 0.1 0.2500 0.3000 0.1
## Balanced Accuracy 0.6042 NA 0.4500 0.6111 NA| Prediction | Rounded.prediction | Actual.value | |
|---|---|---|---|
| 4 | 8.253276 | 8 | 8 |
| 6 | 9.058106 | 9 | 7 |
| 17 | 9.518510 | 10 | 9 |
| 19 | 8.787486 | 9 | 8 |
| 23 | 9.514996 | 10 | 10 |
| 25 | 8.664477 | 9 | 10 |
| 26 | 8.305994 | 8 | 10 |
| 29 | 8.323567 | 8 | 9 |
| 33 | 8.734768 | 9 | 10 |
| 34 | 8.706652 | 9 | 6 |
| 36 | 7.824502 | 8 | 10 |
| 39 | 8.161898 | 8 | 6 |
| 41 | 8.724225 | 9 | 9 |
| 42 | 9.005388 | 9 | 8 |
| 47 | 8.302480 | 8 | 8 |
| 48 | 8.622303 | 9 | 7 |
| 49 | 7.866677 | 8 | 9 |
| 57 | 7.936968 | 8 | 8 |
| 64 | 8.966728 | 9 | 9 |
| 65 | 8.601216 | 9 | 10 |
The added value of midterm and attendance for linear models
To comparison, here is the model that uses attendances and midterm to predict Exa02.
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 2 0 3 0 0
## 7 1 0 0 1 0
## 9 1 0 4 0 0
## 10 3 0 3 0 0
## 6 1 0 1 0 0
##
## Overall Statistics
##
## Accuracy : 0.3
## 95% CI : (0.1189, 0.5428)
## No Information Rate : 0.55
## P-Value [Acc > NIR] : 0.9936
##
## Kappa : 0.0635
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.2500 NA 0.3636 0.0000 NA
## Specificity 0.7500 0.9 0.8889 0.6842 0.9
## Pos Pred Value 0.4000 NA 0.8000 0.0000 NA
## Neg Pred Value 0.6000 NA 0.5333 0.9286 NA
## Precision 0.4000 0.0 0.8000 0.0000 0.0
## Recall 0.2500 NA 0.3636 0.0000 NA
## F1 0.3077 NA 0.5000 NaN NA
## Prevalence 0.4000 0.0 0.5500 0.0500 0.0
## Detection Rate 0.1000 0.0 0.2000 0.0000 0.0
## Detection Prevalence 0.2500 0.1 0.2500 0.3000 0.1
## Balanced Accuracy 0.5000 NA 0.6263 0.3421 NAIn this case, the group effect does not add value to the model that uses attendances and midterm to predict Exa02.
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 4 0 0 1 0
## 7 1 1 0 0 0
## 9 2 0 3 0 0
## 10 1 0 3 2 0
## 6 1 0 0 0 1
##
## Overall Statistics
##
## Accuracy : 0.55
## 95% CI : (0.3153, 0.7694)
## No Information Rate : 0.45
## P-Value [Acc > NIR] : 0.2493
##
## Kappa : 0.4059
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.4444 1.0000 0.5000 0.6667 1.0000
## Specificity 0.9091 0.9474 0.8571 0.7647 0.9474
## Pos Pred Value 0.8000 0.5000 0.6000 0.3333 0.5000
## Neg Pred Value 0.6667 1.0000 0.8000 0.9286 1.0000
## Precision 0.8000 0.5000 0.6000 0.3333 0.5000
## Recall 0.4444 1.0000 0.5000 0.6667 1.0000
## F1 0.5714 0.6667 0.5455 0.4444 0.6667
## Prevalence 0.4500 0.0500 0.3000 0.1500 0.0500
## Detection Rate 0.2000 0.0500 0.1500 0.1000 0.0500
## Detection Prevalence 0.2500 0.1000 0.2500 0.3000 0.1000
## Balanced Accuracy 0.6768 0.9737 0.6786 0.7157 0.9737Moving beyond linear models: Decision trees
The decision tree that uses Attendance, midterm and Exa01 to predict Exa02 shows some interesting features.
As expected, if attendance is low, the score is low.
Surprinsingly, if the midterm exam is high, Exa02 is fairly low; this could be due to the fact that students who care most about passing the course do not put additional effort if the midterm exam is high enough.
Also, high Exa01 leads to lower Exa02; this could be an indication that stundents who care about individual performance do not perform well in a team.
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 0 2 3 0 0
## 7 0 1 1 0 0
## 9 0 1 4 0 0
## 10 0 2 4 0 0
## 6 0 1 1 0 0
##
## Overall Statistics
##
## Accuracy : 0.25
## 95% CI : (0.0866, 0.491)
## No Information Rate : 0.65
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.0654
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity NA 0.1429 0.3077 NA NA
## Specificity 0.75 0.9231 0.8571 0.7 0.9
## Pos Pred Value NA 0.5000 0.8000 NA NA
## Neg Pred Value NA 0.6667 0.4000 NA NA
## Precision 0.00 0.5000 0.8000 0.0 0.0
## Recall NA 0.1429 0.3077 NA NA
## F1 NA 0.2222 0.4444 NA NA
## Prevalence 0.00 0.3500 0.6500 0.0 0.0
## Detection Rate 0.00 0.0500 0.2000 0.0 0.0
## Detection Prevalence 0.25 0.1000 0.2500 0.3 0.1
## Balanced Accuracy NA 0.5330 0.5824 NA NASince the attendance seems to be a reliable indicator, we assess it more in details and we substitute it with the weekly evaluations. The accuracy of the model is lower, but the model shows some interesting features:
- Exa01 is not needed anymore, which means that we can predict Exa02 fairly in advance, and act accordingly.
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 2 0 3 0 0
## 7 2 0 0 0 0
## 9 4 0 1 0 0
## 10 4 0 2 0 0
## 6 1 0 1 0 0
##
## Overall Statistics
##
## Accuracy : 0.15
## 95% CI : (0.0321, 0.3789)
## No Information Rate : 0.65
## P-Value [Acc > NIR] : 1
##
## Kappa : -0.1333
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.1538 NA 0.1429 NA NA
## Specificity 0.5714 0.9 0.6923 0.7 0.9
## Pos Pred Value 0.4000 NA 0.2000 NA NA
## Neg Pred Value 0.2667 NA 0.6000 NA NA
## Precision 0.4000 0.0 0.2000 0.0 0.0
## Recall 0.1538 NA 0.1429 NA NA
## F1 0.2222 NA 0.1667 NA NA
## Prevalence 0.6500 0.0 0.3500 0.0 0.0
## Detection Rate 0.1000 0.0 0.0500 0.0 0.0
## Detection Prevalence 0.2500 0.1 0.2500 0.3 0.1
## Balanced Accuracy 0.3626 NA 0.4176 NA NASince the overall score of each week seems promising, we assess it more in details, and we substitute it with detailed scores about (a) team and (b) invividual performance.
The accuracy of the model is as high as our benchmark, but the model shows some interesting features:
- Exa01 is not needed anymore, which means that we can predict Exa02 fairly in advance, and act accordingly.
- Midterm is not needed anymore, which means that we can simply assess the team every week, and act accordingly.
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 5 0 0 0 0
## 7 0 2 0 0 0
## 9 0 2 3 0 0
## 10 1 1 1 3 0
## 6 1 1 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.65
## 95% CI : (0.4078, 0.8461)
## No Information Rate : 0.35
## P-Value [Acc > NIR] : 0.006015
##
## Kappa : 0.5556
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.7143 0.3333 0.7500 1.0000 NA
## Specificity 1.0000 1.0000 0.8750 0.8235 0.9
## Pos Pred Value 1.0000 1.0000 0.6000 0.5000 NA
## Neg Pred Value 0.8667 0.7778 0.9333 1.0000 NA
## Precision 1.0000 1.0000 0.6000 0.5000 0.0
## Recall 0.7143 0.3333 0.7500 1.0000 NA
## F1 0.8333 0.5000 0.6667 0.6667 NA
## Prevalence 0.3500 0.3000 0.2000 0.1500 0.0
## Detection Rate 0.2500 0.1000 0.1500 0.1500 0.0
## Detection Prevalence 0.2500 0.1000 0.2500 0.3000 0.1
## Balanced Accuracy 0.8571 0.6667 0.8125 0.9118 NA
## Confusion Matrix and Statistics
##
##
## 8 7 9 10 6
## 8 5 0 0 0 0
## 7 0 2 0 0 0
## 9 0 2 3 0 0
## 10 1 1 1 3 0
## 6 1 1 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.65
## 95% CI : (0.4078, 0.8461)
## No Information Rate : 0.35
## P-Value [Acc > NIR] : 0.006015
##
## Kappa : 0.5556
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 8 Class: 7 Class: 9 Class: 10 Class: 6
## Sensitivity 0.7143 0.3333 0.7500 1.0000 NA
## Specificity 1.0000 1.0000 0.8750 0.8235 0.9
## Pos Pred Value 1.0000 1.0000 0.6000 0.5000 NA
## Neg Pred Value 0.8667 0.7778 0.9333 1.0000 NA
## Precision 1.0000 1.0000 0.6000 0.5000 0.0
## Recall 0.7143 0.3333 0.7500 1.0000 NA
## F1 0.8333 0.5000 0.6667 0.6667 NA
## Prevalence 0.3500 0.3000 0.2000 0.1500 0.0
## Detection Rate 0.2500 0.1000 0.1500 0.1500 0.0
## Detection Prevalence 0.2500 0.1000 0.2500 0.3000 0.1
## Balanced Accuracy 0.8571 0.6667 0.8125 0.9118 NA| Prediction | Rounded.prediction | Actual.value | |
|---|---|---|---|
| 4 | 8.300 | 8 | 8 |
| 6 | 7.400 | 7 | 7 |
| 17 | 7.400 | 7 | 9 |
| 19 | 8.300 | 8 | 8 |
| 23 | 9.875 | 10 | 10 |
| 25 | 7.400 | 7 | 10 |
| 26 | 9.875 | 10 | 10 |
| 29 | 9.000 | 9 | 9 |
| 33 | 9.000 | 9 | 10 |
| 34 | 8.300 | 8 | 6 |
| 36 | 8.300 | 8 | 10 |
| 39 | 7.400 | 7 | 6 |
| 41 | 9.000 | 9 | 9 |
| 42 | 8.300 | 8 | 8 |
| 47 | 8.300 | 8 | 8 |
| 48 | 7.400 | 7 | 7 |
| 49 | 7.400 | 7 | 9 |
| 57 | 8.300 | 8 | 8 |
| 64 | 9.000 | 9 | 9 |
| 65 | 9.875 | 10 | 10 |
As a comparison between the two models:
- Increase of the accuracy: 0.55 VS 0.65
- Increase of the mean value of the F1 Score = (2 * Precision * Recall) / (Precision + Recall): 0.6224242 VS 0.6666667
- Increase of Kappa, which takes into account the accuracy that would have happened anyway through random predictions : 0.4078947 VS 0.5555556
- increase in Sensitivity (true positive): 0.2857143, -0.6666667, 0.35, 0.4, NA
- increase in Specificity (true negative): 0.1538462, 0, 0.075, 0.0235294, -0.0473684
| Seed | KPI | Exa02…f.Exa01. | Exa02…f.Exa01..Group | Exa02…f.Weekly.Evaluation…Decision.tree. | Check | |
|---|---|---|---|---|---|---|
| Accuracy | 1 | Accuracy | 0.3000000 | 0.5500000 | 0.6500000 | TRUE |
| 1 | F1 Score | 0.3260684 | 0.6224242 | 0.6666667 | TRUE | |
| Kappa | 1 | Kappa | 0.0604027 | 0.4078947 | 0.5555556 | TRUE |
| Accuracy1 | 2 | Accuracy | 0.4000000 | 0.6000000 | 0.6000000 | TRUE |
| 1 | 2 | F1 Score | 0.5357143 | 0.6697436 | 0.6111111 | FALSE |
| Kappa1 | 2 | Kappa | 0.1780822 | 0.4719472 | 0.4838710 | TRUE |
| Accuracy2 | 3 | Accuracy | 0.2500000 | 0.6000000 | 0.5000000 | FALSE |
| 2 | 3 | F1 Score | 0.3413462 | 0.6356643 | 0.6511785 | TRUE |
| Kappa2 | 3 | Kappa | 0.0131579 | 0.4736842 | 0.3750000 | FALSE |
| Accuracy3 | 4 | Accuracy | 0.3000000 | 0.5500000 | 0.6500000 | TRUE |
| 3 | 4 | F1 Score | 0.3260684 | 0.6224242 | 0.6666667 | TRUE |
| Kappa3 | 4 | Kappa | 0.0604027 | 0.4078947 | 0.5555556 | TRUE |
| Accuracy4 | 5 | Accuracy | 0.3000000 | 0.3500000 | 0.4000000 | TRUE |
| 4 | 5 | F1 Score | 0.3750000 | 0.3694444 | 0.5481481 | TRUE |
| Kappa4 | 5 | Kappa | -0.0447761 | 0.0441176 | 0.1666667 | TRUE |
| Accuracy5 | 6 | Accuracy | 0.3000000 | 0.5500000 | 0.4000000 | FALSE |
| 5 | 6 | F1 Score | 0.3751804 | 0.5976190 | 0.5767196 | FALSE |
| Kappa5 | 6 | Kappa | 0.1222571 | 0.4461538 | 0.2476489 | FALSE |
| Accuracy6 | 7 | Accuracy | 0.3000000 | 0.5000000 | 0.4500000 | FALSE |
| 6 | 7 | F1 Score | 0.3500000 | 0.5941520 | 0.4503968 | FALSE |
| Kappa6 | 7 | Kappa | -0.0218978 | 0.2957746 | 0.2926045 | FALSE |
| Accuracy7 | 8 | Accuracy | 0.4500000 | 0.5500000 | 0.4500000 | FALSE |
| 7 | 8 | F1 Score | 0.4888889 | 0.5748834 | 0.4641414 | FALSE |
| Kappa7 | 8 | Kappa | 0.2253521 | 0.3877551 | 0.3230769 | FALSE |
| Accuracy8 | 9 | Accuracy | 0.4000000 | 0.6000000 | 0.4000000 | FALSE |
| 8 | 9 | F1 Score | 0.4013072 | 0.6345238 | 0.4989899 | FALSE |
| Kappa8 | 9 | Kappa | 0.1143911 | 0.4444444 | 0.2282958 | FALSE |
| Accuracy9 | 10 | Accuracy | 0.3500000 | 0.7000000 | 0.5500000 | FALSE |
| 9 | 10 | F1 Score | 0.3762626 | 0.7119048 | 0.5250000 | FALSE |
| Kappa9 | 10 | Kappa | 0.0714286 | 0.5729537 | 0.4078947 | FALSE |
| Seed | KPI | Exa02…f.Exa01. | Exa02…f.Exa01..Group | Exa02…f.Weekly.Evaluation…Decision.tree. | Check |
|---|---|---|---|---|---|
| 1 | Accuracy | 0.30 | 0.55 | 0.65 | TRUE |
| 2 | Accuracy | 0.40 | 0.60 | 0.60 | TRUE |
| 3 | Accuracy | 0.25 | 0.60 | 0.50 | FALSE |
| 4 | Accuracy | 0.30 | 0.55 | 0.65 | TRUE |
| 5 | Accuracy | 0.30 | 0.35 | 0.40 | TRUE |
| 6 | Accuracy | 0.30 | 0.55 | 0.40 | FALSE |
| 7 | Accuracy | 0.30 | 0.50 | 0.45 | FALSE |
| 8 | Accuracy | 0.45 | 0.55 | 0.45 | FALSE |
| 9 | Accuracy | 0.40 | 0.60 | 0.40 | FALSE |
| 10 | Accuracy | 0.35 | 0.70 | 0.55 | FALSE |
Appendix
The complete dataset, before normalization and removal of row 18
## UID Class Group A1a A1b A1 A2a A2b A2 A3a A3b A3 A4a A4b A4 A5a
## 1 23 2 8 71 20.00 5.5 80 18.68 5.9 8 20.00 6.0 4 19.34 4.7 6
## 2 37 2 16 70 17.01 5.2 73 17.35 5.4 6 19.42 5.7 7 20.00 5.4 11
## 3 25 1 14 80 17.50 5.9 70 20.00 5.4 4 17.69 5.3 5 18.14 4.8 5
## 4 8 2 8 80 18.55 5.9 60 17.77 4.7 2 19.00 4.4 4 19.15 4.7 6
## 5 44 2 8 70 19.78 5.4 60 20.00 4.8 8 18.50 5.9 4 20.00 4.7 6
## 6 10 3 1 80 17.78 5.9 80 20.00 6.0 8 18.38 5.9 13 19.34 6.0 2
## 7 53 2 4 71 0.00 4.3 60 17.23 4.6 6 17.22 5.5 1 17.02 5.1 9
## 8 34 1 14 0 16.47 1.0 70 20.00 5.4 3 20.00 4.8 5 20.00 4.9 5
## 9 5 2 16 77 17.97 5.7 80 20.00 6.0 8 20.00 6.0 7 20.00 5.4 11
## 10 59 1 6 72 18.26 5.4 60 20.00 4.8 3 17.41 4.6 12 20.00 5.9 7
## 11 77 2 12 70 17.97 5.3 60 20.00 4.8 6 20.00 5.7 10 20.00 5.7 2
## 12 76 1 2 80 15.68 5.7 61 19.01 4.8 5 19.00 5.5 2 18.68 3.8 3
## 13 17 1 14 80 18.26 5.9 65 20.00 5.1 4 20.00 5.4 5 20.00 4.9 5
## 14 22 1 2 0 17.69 1.1 70 19.15 5.3 3 19.00 4.7 2 18.84 3.8 1
## 15 43 1 14 80 19.07 5.9 70 17.23 5.2 3 20.00 4.8 5 20.00 4.9 5
## 16 41 3 11 70 18.84 5.3 80 17.67 5.9 8 17.80 5.9 13 20.00 6.0 11
## 17 20 2 12 77 16.48 5.6 60 16.69 4.6 4 18.64 5.3 10 19.34 5.7 2
## 18 1 1 2 0 20.00 1.2 60 18.02 4.7 5 20.00 5.6 2 20.00 3.9 1
## 19 62 3 13 80 20.00 6.0 80 19.72 6.0 8 20.00 6.0 10 0.00 4.5 6
## 20 9 2 16 77 18.13 5.7 60 16.65 4.6 2 18.52 4.4 10 19.75 5.7 2
## 21 72 3 15 80 20.00 6.0 80 18.24 5.9 7 20.00 5.8 12 18.68 5.8 8
## 22 57 3 1 65 20.00 5.1 80 17.57 5.9 8 17.97 5.9 13 16.76 5.8 2
## 23 67 1 6 72 17.71 5.4 61 16.19 4.6 3 19.32 4.8 12 20.00 5.9 8
## 24 63 3 10 80 20.00 6.0 80 18.31 5.9 8 19.42 6.0 7 20.00 5.4 10
## 25 16 2 7 77 18.59 5.7 80 18.81 5.9 6 19.38 5.7 3 19.34 4.5 2
## 26 36 3 15 80 18.03 5.9 80 18.52 5.9 4 19.65 5.4 12 17.37 5.7 8
## 27 27 2 7 80 18.28 5.9 73 17.69 5.4 6 20.00 5.7 3 17.11 4.4 2
## 28 48 1 9 80 16.29 5.8 70 16.41 5.2 3 20.00 4.8 9 20.00 5.6 4
## 29 73 3 11 80 15.95 5.8 80 18.92 5.9 8 20.00 6.0 13 20.00 6.0 11
## 30 15 1 9 80 14.94 5.7 70 20.00 5.4 3 18.57 4.7 9 19.34 5.6 4
## 31 79 3 11 80 15.59 5.7 80 17.62 5.9 6 16.82 5.5 13 19.34 6.0 11
## 32 56 3 15 80 20.00 6.0 80 17.35 5.8 6 20.00 5.7 12 20.00 5.9 8
## 33 40 3 3 80 20.00 6.0 80 20.00 6.0 8 20.00 6.0 6 20.00 5.3 11
## 34 50 3 13 80 20.00 6.0 80 18.31 5.9 6 16.64 5.5 10 20.00 5.7 6
## 35 2 1 6 72 20.00 5.5 61 18.66 4.8 3 18.30 4.7 12 19.34 5.8 8
## 36 32 3 5 70 17.21 5.2 80 17.78 5.9 7 20.00 5.8 8 17.86 5.4 11
## 37 28 2 7 70 19.17 5.4 60 16.30 4.6 8 17.41 5.8 3 20.00 4.6 2
## 38 3 1 9 80 17.33 5.8 65 20.00 5.1 3 19.43 4.8 9 20.00 5.6 4
## 39 47 1 9 0 16.19 1.0 70 19.75 5.4 5 19.42 5.5 9 16.76 5.4 4
## 40 64 3 3 80 20.00 6.0 80 20.00 6.0 4 18.52 5.3 6 20.00 5.3 11
## 41 18 3 11 80 20.00 6.0 80 20.00 6.0 8 18.57 5.9 13 16.69 5.8 11
## 42 26 3 5 65 17.34 4.9 80 15.09 5.7 8 17.94 5.9 8 18.68 5.4 11
## 43 29 2 7 77 15.21 5.5 80 19.14 5.9 8 20.00 6.0 3 19.34 4.5 2
## 44 33 3 11 80 20.00 6.0 80 20.00 6.0 7 20.00 5.8 13 20.00 6.0 11
## 45 71 3 5 80 17.34 5.8 80 18.02 5.9 8 20.00 6.0 11 19.15 5.8 11
## 46 70 2 12 71 20.00 5.5 73 17.60 5.4 4 20.00 5.4 10 18.02 5.6 2
## 47 31 3 10 80 20.00 6.0 80 20.00 6.0 6 20.00 5.7 7 20.00 5.4 10
## 48 46 3 1 65 17.40 4.9 80 20.00 6.0 7 18.52 5.7 13 19.34 6.0 2
## 49 60 1 2 80 17.69 5.9 61 18.81 4.8 4 18.67 5.3 2 19.01 3.8 1
## 50 30 3 1 80 18.26 5.9 80 19.06 5.9 8 17.97 5.9 13 20.00 6.0 2
## 51 38 3 15 70 17.48 5.2 80 19.14 5.9 6 20.00 5.7 12 17.14 5.7 8
## 52 69 3 10 80 18.02 5.9 80 16.83 5.8 6 18.26 5.6 7 18.52 5.3 10
## 53 39 3 13 70 20.00 5.4 80 20.00 6.0 4 20.00 5.4 10 18.43 5.6 6
## 54 58 2 4 70 20.00 5.4 60 18.52 4.7 2 20.00 4.5 1 20.00 6.0 9
## 55 42 1 14 80 17.15 5.8 65 17.88 5.0 5 17.97 5.5 5 18.68 4.8 5
## 56 49 3 13 80 20.00 6.0 80 20.00 6.0 8 19.00 5.9 10 0.00 4.5 6
## 57 75 2 8 80 18.73 5.9 60 20.00 4.8 1 18.13 5.4 4 18.02 4.6 6
## 58 21 2 8 71 20.00 5.5 60 20.00 4.8 6 20.00 5.7 4 18.52 4.7 6
## 59 6 3 10 80 17.11 5.8 80 19.34 6.0 6 17.69 5.6 7 20.00 5.4 10
## 60 68 3 3 70 18.70 5.3 80 17.44 5.8 4 17.92 5.3 6 18.68 5.2 11
## 61 45 3 15 80 18.00 5.9 80 17.62 5.9 8 18.70 5.9 12 20.00 5.9 8
## 62 35 2 7 70 20.00 5.4 60 16.71 4.6 2 19.42 4.5 3 18.43 4.5 2
## 63 14 1 14 80 20.00 6.0 70 20.00 5.4 3 18.57 4.7 5 16.76 4.7 5
## 64 12 2 4 70 17.32 5.2 80 17.60 5.9 4 17.51 5.3 1 20.00 6.0 9
## 65 52 2 16 80 0.00 4.8 73 19.09 5.5 6 19.42 5.7 7 20.00 5.4 11
## 66 13 3 5 65 17.10 4.9 80 18.35 5.9 7 17.00 5.6 8 20.00 5.5 11
## A5b A5 A6a A6b A6 A7a A7b A7 A8a A8b A8 A9a A9b A9
## 1 20.00 5.4 80 20.00 6.0 0 15.59 15.59 10 0.00 76.00 64 24 83.61
## 2 17.19 5.8 75 20.00 5.7 72 18.09 90.09 3 18.46 82.46 70 25 90.00
## 3 20.00 5.0 70 19.30 5.4 78 0.00 78.00 4 18.04 83.04 73 25 93.00
## 4 20.00 5.4 80 0.00 4.8 0 0.00 0.00 10 18.22 94.22 64 25 84.00
## 5 20.00 5.4 80 18.06 5.9 0 13.58 13.58 10 20.00 96.00 64 1 80.00
## 6 18.33 1.1 77 18.11 5.7 78 20.00 98.00 13 18.06 98.06 60 25 80.00
## 7 20.00 5.6 80 20.00 6.0 80 18.40 98.40 9 17.33 92.33 73 3 83.84
## 8 17.22 4.8 70 18.40 5.3 78 17.72 95.72 4 17.51 82.51 73 1 91.25
## 9 17.50 5.9 75 19.00 5.6 72 18.76 90.76 3 20.00 84.00 70 21 86.92
## 10 0.00 4.3 72 20.00 5.5 0 20.00 20.00 8 18.46 91.46 80 25 100.00
## 11 20.00 1.2 80 16.79 5.8 75 16.65 91.65 6 18.85 85.85 70 7 82.57
## 12 19.32 4.5 73 19.45 5.5 61 17.83 78.83 5 20.00 86.00 80 2 90.00
## 13 18.84 4.9 70 0.00 4.2 78 17.72 95.72 4 20.00 85.00 73 5 85.21
## 14 17.96 5.4 73 20.00 5.6 61 18.04 79.04 5 19.23 85.23 80 25 100.00
## 15 18.64 4.9 70 20.00 5.4 78 18.73 96.73 4 0.00 65.00 73 23 92.00
## 16 20.00 6.0 70 18.85 5.3 78 0.00 78.00 1 18.46 92.31 79 22 96.59
## 17 18.47 1.1 80 18.29 5.9 75 0.00 75.00 6 20.00 87.00 70 20 86.48
## 18 20.00 6.0 73 0.00 4.4 61 17.64 78.64 5 20.00 86.00 80 8 92.81
## 19 18.75 5.3 71 16.06 5.2 78 15.99 93.99 13 20.00 100.00 0 25 20.00
## 20 0.00 0.0 80 17.36 5.8 75 0.00 75.00 6 0.00 67.00 70 25 90.00
## 21 20.00 5.5 0 15.76 0.9 74 20.00 94.00 7 0.00 68.00 70 1 87.50
## 22 0.00 0.0 77 19.30 5.8 78 0.00 78.00 13 0.00 80.00 60 1 75.00
## 23 0.00 4.3 72 19.25 5.5 0 20.00 20.00 8 20.00 93.00 80 25 100.00
## 24 20.00 5.8 74 20.00 5.6 74 20.00 94.00 2 20.00 83.00 68 25 88.00
## 25 18.52 1.1 78 16.23 5.7 80 17.63 97.63 12 18.93 97.93 61 9 74.04
## 26 18.64 5.4 0 0.00 0.0 74 0.00 74.00 7 0.00 68.00 70 1 87.50
## 27 18.27 1.1 78 16.81 5.7 80 17.62 97.62 12 20.00 99.00 61 25 81.00
## 28 16.48 4.5 70 20.00 5.4 55 20.00 75.00 5 18.06 84.06 70 24 89.61
## 29 19.17 6.0 70 18.08 5.3 78 0.00 78.00 1 0.00 0.00 79 14 94.11
## 30 18.75 4.6 70 20.00 5.4 55 18.17 73.17 5 20.00 86.00 70 6 82.46
## 31 18.47 5.9 70 19.04 5.3 78 17.76 95.76 1 17.95 89.74 79 1 98.75
## 32 20.00 5.5 0 17.15 1.0 74 0.00 74.00 7 20.00 88.00 70 1 87.50
## 33 18.26 5.9 79 20.00 5.9 79 19.75 98.75 13 20.00 100.00 76 25 96.00
## 34 19.58 5.4 71 17.31 5.3 78 0.00 78.00 13 17.30 97.30 0 1 0.00
## 35 20.00 5.5 72 20.00 5.5 0 17.64 17.64 8 19.62 92.62 80 12 94.55
## 36 20.00 6.0 80 17.85 5.9 0 20.00 20.00 11 20.00 97.00 0 25 20.00
## 37 20.00 1.2 78 20.00 5.9 80 20.00 100.00 12 20.00 99.00 61 16 76.47
## 38 17.73 4.5 70 18.16 5.3 55 0.00 55.00 5 0.00 66.00 70 25 90.00
## 39 20.00 4.7 70 18.35 5.3 55 20.00 75.00 5 18.46 84.46 70 21 86.92
## 40 18.75 5.9 79 18.44 5.8 79 0.00 79.00 13 20.00 100.00 76 15 91.23
## 41 19.44 6.0 70 17.65 5.3 78 0.00 78.00 1 18.58 92.88 79 1 98.75
## 42 18.84 5.9 80 18.47 5.9 0 18.97 18.97 11 19.62 96.62 0 18 15.90
## 43 20.00 1.2 78 0.00 4.7 80 20.00 100.00 12 0.00 79.00 61 9 74.04
## 44 18.11 5.9 70 18.88 5.3 78 18.27 96.27 1 18.40 92.02 79 1 98.75
## 45 18.75 5.9 80 0.00 4.8 0 19.75 19.75 11 0.00 77.00 0 10 13.28
## 46 20.00 1.2 80 17.20 5.8 75 20.00 95.00 6 20.00 87.00 70 25 90.00
## 47 20.00 5.8 74 17.31 5.5 74 20.00 94.00 2 16.56 79.56 68 25 88.00
## 48 18.75 1.1 77 17.56 5.7 78 0.00 78.00 13 0.00 80.00 60 13 74.57
## 49 20.00 6.0 73 17.25 5.4 61 19.51 80.51 5 0.00 66.00 80 23 99.00
## 50 20.00 1.2 77 19.69 5.8 78 0.00 78.00 13 20.00 100.00 60 25 80.00
## 51 20.00 5.5 0 20.00 1.2 74 20.00 94.00 7 20.00 88.00 70 1 87.50
## 52 20.00 5.8 74 20.00 5.6 74 20.00 94.00 2 17.31 80.31 68 11 81.30
## 53 20.00 5.4 71 16.22 5.2 78 18.16 96.16 13 0.00 80.00 0 1 0.00
## 54 20.00 5.6 80 17.02 5.8 80 0.00 80.00 9 0.00 75.00 73 25 93.00
## 55 0.00 3.8 70 17.11 5.2 78 19.03 97.03 4 17.18 82.18 73 25 93.00
## 56 19.31 5.4 71 19.23 5.4 78 20.00 98.00 13 18.52 98.52 0 1 0.00
## 57 20.00 5.4 80 17.49 5.8 0 0.00 0.00 10 0.00 76.00 64 1 80.00
## 58 20.00 5.4 80 17.38 5.8 0 20.00 20.00 10 20.00 96.00 64 25 84.00
## 59 20.00 5.8 74 14.48 5.3 74 18.38 92.38 2 16.92 79.92 68 19 84.17
## 60 20.00 6.0 79 0.00 4.7 79 0.00 79.00 13 17.69 97.69 76 4 87.99
## 61 18.26 5.4 0 20.00 1.2 74 19.05 93.05 7 0.00 68.00 70 1 87.50
## 62 17.11 1.0 78 0.00 4.7 80 20.00 100.00 12 18.93 97.93 61 25 81.00
## 63 18.26 4.9 70 20.00 5.4 78 18.41 96.41 4 20.00 85.00 73 23 92.00
## 64 19.17 5.6 80 17.44 5.8 80 0.00 80.00 9 0.00 75.00 73 17 88.65
## 65 0.00 4.8 75 19.06 5.6 72 0.00 72.00 3 0.00 64.00 70 1 87.50
## 66 16.77 5.8 80 20.00 6.0 0 0.00 0.00 11 20.00 97.00 0 25 20.00
## Attendance MidTerm Exa01 Exa02 Total.du.cours..Brut.
## 1 5.5 5.68 10.00 8.33 5.6
## 2 5.5 4.45 8.79 10.00 5.3
## 3 5.4 5.88 10.00 9.79 5.8
## 4 5.2 5.68 6.40 7.98 5.0
## 5 5.4 5.06 9.05 8.98 5.3
## 6 5.9 5.27 8.69 6.54 5.2
## 7 5.5 4.04 4.94 8.64 4.5
## 8 5.3 6.00 5.29 8.47 5.1
## 9 5.7 5.27 6.34 9.64 5.2
## 10 5.4 5.68 7.39 8.57 5.3
## 11 5.4 4.45 7.95 10.00 5.2
## 12 5.2 3.55 5.65 7.25 4.2
## 13 5.3 5.68 6.92 9.47 5.3
## 14 5.3 4.04 5.25 8.25 4.5
## 15 5.4 5.68 4.50 8.47 4.9
## 16 5.8 4.04 6.99 8.69 4.8
## 17 5.3 4.05 10.00 9.34 5.2
## 18 5.2 4.04 5.65 8.25 4.5
## 19 5.7 5.77 7.92 8.42 5.4
## 20 5.1 4.24 8.09 9.09 4.9
## 21 5.7 4.95 6.89 10.00 5.2
## 22 5.3 5.68 6.59 6.54 4.9
## 23 5.5 5.47 9.99 9.52 5.7
## 24 5.8 5.68 6.55 7.10 5.1
## 25 5.6 5.27 7.57 9.94 5.4
## 26 5.3 4.04 6.55 10.00 4.8
## 27 5.6 5.27 7.82 8.19 5.2
## 28 5.3 4.65 6.64 6.19 4.6
## 29 5.8 4.86 6.60 9.14 5.1
## 30 5.2 5.27 5.90 6.39 4.7
## 31 5.8 4.65 7.88 8.69 5.1
## 32 5.6 5.27 8.18 10.00 5.5
## 33 6.0 5.06 7.77 9.52 5.4
## 34 5.7 4.86 7.69 5.62 4.7
## 35 5.5 6.00 7.52 9.82 5.6
## 36 5.7 4.95 5.18 9.59 5.0
## 37 5.5 4.86 8.12 8.84 5.2
## 38 5.2 5.27 6.00 5.79 4.6
## 39 5.2 5.36 6.14 6.19 4.7
## 40 5.8 5.77 5.97 9.02 5.2
## 41 5.9 5.36 7.74 9.14 5.4
## 42 5.7 5.47 8.54 8.39 5.4
## 43 5.3 5.36 4.00 4.00 4.2
## 44 5.9 4.86 8.09 8.99 5.3
## 45 5.5 4.86 7.97 8.99 5.2
## 46 5.5 4.45 7.44 8.09 4.9
## 47 5.7 6.00 6.54 8.44 5.3
## 48 5.3 4.95 7.45 6.54 4.8
## 49 5.4 4.24 5.30 8.55 4.6
## 50 5.7 5.68 7.64 7.39 5.2
## 51 5.5 5.27 10.00 10.00 5.7
## 52 5.7 5.68 9.58 8.34 5.6
## 53 5.6 5.68 6.89 7.47 5.1
## 54 5.4 4.45 8.44 7.54 4.9
## 55 5.4 5.68 7.34 9.57 5.4
## 56 5.8 5.27 7.44 8.52 5.2
## 57 5.2 5.68 5.50 8.48 5.0
## 58 5.4 5.27 6.08 9.48 5.1
## 59 5.6 5.68 6.95 8.29 5.2
## 60 5.5 4.45 10.00 9.37 5.3
## 61 5.6 5.06 6.00 10.00 5.1
## 62 5.2 5.88 6.74 8.34 5.2
## 63 5.4 5.68 7.72 9.97 5.5
## 64 5.6 4.45 8.43 9.04 5.2
## 65 5.3 5.27 7.39 10.00 5.3
## 66 5.7 4.86 4.50 9.24 4.8Diagnostic for the model with Exa 02 as a function of Exa 02
##
## Call:
## lm(formula = scale(Exa02) ~ scale(Exa01), data = new_scores)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6086 -0.4270 0.2016 0.7886 1.4031
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.148e-16 1.220e-01 0.000 1.0000
## scale(Exa01) 2.175e-01 1.230e-01 1.769 0.0818 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9838 on 63 degrees of freedom
## Multiple R-squared: 0.04731, Adjusted R-squared: 0.03219
## F-statistic: 3.128 on 1 and 63 DF, p-value: 0.08178
## Test stat Pr(>|Test stat|)
## scale(Exa01)
## Tukey test 1.0194 0.308
## named integer(0)## named integer(0)Diagnostic for the model with Exa 02 as a function of Group and Exa 02
##
## Call:
## lm(formula = scale(Exa02) ~ scale(Exa01) + as.factor(Group),
## data = new_scores)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.62610 -0.22442 0.04366 0.23241 0.95268
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.58923 0.27060 -5.873 3.92e-07 ***
## scale(Exa01) 0.06346 0.07771 0.817 0.41814
## as.factor(Group)2 1.22839 0.39940 3.076 0.00346 **
## as.factor(Group)3 2.17077 0.41288 5.258 3.34e-06 ***
## as.factor(Group)4 1.43149 0.41289 3.467 0.00112 **
## as.factor(Group)5 2.01712 0.38619 5.223 3.76e-06 ***
## as.factor(Group)6 2.15344 0.41433 5.197 4.10e-06 ***
## as.factor(Group)7 1.77888 0.38191 4.658 2.56e-05 ***
## as.factor(Group)8 1.63384 0.36245 4.508 4.21e-05 ***
## as.factor(Group)9 -0.46093 0.38981 -1.182 0.24285
## as.factor(Group)10 1.11347 0.38205 2.914 0.00540 **
## as.factor(Group)11 1.87128 0.36238 5.164 4.60e-06 ***
## as.factor(Group)12 2.00906 0.41527 4.838 1.40e-05 ***
## as.factor(Group)13 0.65158 0.38195 1.706 0.09449 .
## as.factor(Group)14 2.20201 0.35035 6.285 9.18e-08 ***
## as.factor(Group)15 2.78502 0.36233 7.686 6.58e-10 ***
## as.factor(Group)16 2.50728 0.38192 6.565 3.42e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5401 on 48 degrees of freedom
## Multiple R-squared: 0.7812, Adjusted R-squared: 0.7083
## F-statistic: 10.71 on 16 and 48 DF, p-value: 7.319e-11
## Test stat Pr(>|Test stat|)
## scale(Exa01)
## as.factor(Group)
## Tukey test 0.4141 0.6788
## GVIF Df GVIF^(1/(2*Df))
## scale(Exa01) 1.324842 1 1.151018
## as.factor(Group) 1.324842 15 1.009421
## 34
## 34## 34
## 34