**5.3. Team to collect the information recorded in the videos**

Any measurement or data collection instrument must collect two essential requirements: validity and reliability. In general terms, validity refers to the degree to which an instrument measures the variable it intends to measure. Validity is a concept from which different types of evidence have related [28, 29]. This evidence is the content (the degree to which an instrument reflects a specific implicit domain that is measured), criterion (validity of an instrument of measurement compared with an external judgment), and construct (quality of measurement related consistently with other measurements according to hypotheses derived theoretically and that concern the measured concept).

The reliability of the instrument is the degree to which its repeated application to the same subject or object produces the same results. If the correlation between the results of the different appliances is highly positive, the instrument is considered reliable (in psychometrics, Cronbach's alpha [30] is a coefficient used to measure the reliability of a measurement scale).

Applying the Hypothesis Testing (or dokimasia) to the tables of measurements of each one of the variables under observation, we could know if the measurement instrument calibrates from the accuracy.

The procedure for extracting information from the videos of the sessions was divided into two parts: Theory and Praxis.

From the theoretical point of view, the observers trained in the graduation of behaviors for the fields defined in this research: Inquiry, Persuasion, Positivity, Negativity, Internal Information, and External Information. This graduation of the behaviors for Positivity and Inquiry is illustrated in **Scheme 1**. Is it possible to do a finer gradation? Obviously, it is. Similarly, it noted that a specific exploration of facial gestures was not performed (frowning, opening or closing the eyes too much, changing the line of the mouth, and so on and so forth) [31–33]. It is a subject that opens a future work.

From practice, each component of the team in charge of registration, consisting of four people, gives independently the same scene (image and sound) of some of the videos captured of the activity carried out by the students. This brief scene, of the order of 10 minutes, is numerically

**5.5. Reliability and validity of measuring instruments**

where:

two items from two different courses:

*r* = cos(*α*) =

Confidence interval

Cronbach's alpha coefficient [30]:

Illustration with the Dimension Y = POS/NEG in time using moving averages.

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Pearson's Sample Correlation Coefficient [34] for the fundamental dimension, Y, referring to

\_\_\_\_\_\_\_\_\_\_\_

(*y*2*<sup>i</sup>* − *y*¯2) 2

> \_\_ *α* 2 \_\_*S* √ \_\_

<sup>≈</sup> \_\_\_\_\_\_\_\_ 1.9305 √ \_\_\_\_ 1.07 √

\_\_\_\_\_

2.456 <sup>≈</sup> 0.75 <sup>≈</sup> *<sup>p</sup>* (1)

*<sup>n</sup>* (2)

(*y*1*<sup>i</sup>* − *y*¯1)(*y*2*<sup>i</sup>* − *y*¯2) \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

∑ *i*=1 *N*

∑ *i*=1 *N*

\_\_\_\_\_\_\_\_\_\_\_\_

(*y*1*<sup>i</sup>* − *y*¯1*<sup>i</sup>* ) 2 √

√

Y¯ ± tn‐1;1 ‐ ‐

∑ *i*=1 *N*

**Scheme 1.** It indicates the domain of double polarity and the coding scale, in its dual polarity, of Positivity and Inquiry, with its 13 associated behaviors.

coded according to the behaviors observed in the same field. In general, the coding tables have 1080 rows, separated by intervals of 5 seconds. Once this process is finished, the four tables generated are analyzed by the psychologist and a statistician who study the convergences and divergences between the measures: the guideline, in the form of feedback, given to the observers is to identify the actions that promote relationships within the team. Gradually, the times of study of scenes are extended, until covering the session of complete learning about 90 minutes. The comparative analysis of the measures is the one that indicates if the instruments (the observers) present similarity in their registers [27]. After a work period of about 1 month, it was possible to certify that the observers were calibrated and reliable "instruments" (results illustrated in Section 5.5 between the control and experimental team).

#### **5.4. Time series**

The proportions X = IND/PER, Y = POS/NEG, and Z = II/IE constructed constitute numerical series of 1080 data that are called time series. After applying the initial condition with emphasis on emotions at 30 minutes, some of the graphs of the moving averages in time are below (**Graph 1**):

**Graph 1.** Represents the variation over time of the Time Series of the Quantities Positivity/Negativity (= Y) and of the ratio Internal Information/External Information (= Z).

#### **5.5. Reliability and validity of measuring instruments**

Illustration with the Dimension Y = POS/NEG in time using moving averages.



where:

coded according to the behaviors observed in the same field. In general, the coding tables have 1080 rows, separated by intervals of 5 seconds. Once this process is finished, the four tables generated are analyzed by the psychologist and a statistician who study the convergences and divergences between the measures: the guideline, in the form of feedback, given to the observers is to identify the actions that promote relationships within the team. Gradually, the times of study of scenes are extended, until covering the session of complete learning about 90 minutes. The comparative analysis of the measures is the one that indicates if the instruments (the observers) present similarity in their registers [27]. After a work period of about 1 month, it was possible to certify that the observers were calibrated and reliable "instruments"

**Scheme 1.** It indicates the domain of double polarity and the coding scale, in its dual polarity, of Positivity and Inquiry,

The proportions X = IND/PER, Y = POS/NEG, and Z = II/IE constructed constitute numerical series of 1080 data that are called time series. After applying the initial condition with emphasis on emotions at 30 minutes, some of the graphs of the moving averages in time are below (**Graph 1**):

**Graph 1.** Represents the variation over time of the Time Series of the Quantities Positivity/Negativity (= Y) and of the

(results illustrated in Section 5.5 between the control and experimental team).

**5.4. Time series**

with its 13 associated behaviors.

50 Behavior Analysis

ratio Internal Information/External Information (= Z).


Pearson's Sample Correlation Coefficient [34] for the fundamental dimension, Y, referring to two items from two different courses:

t two items from two different course:

$$r = \cos(\alpha) = \frac{\sum\_{i=1}^{\mathbb{N}} (y\_{ii} - \overline{y}\_{..})(y\_{ii} - \overline{y}\_{..})}{\sqrt{\sum\_{i=1}^{\mathbb{N}} (y\_{ii} - \overline{y}\_{..})^2 \sqrt{\sum\_{i=1}^{\mathbb{N}} (y\_{ii} - \overline{y}\_{..})^2}} \approx \frac{1.9305}{\sqrt{1.07} \sqrt{2.456}} \approx 0.75 \approx p \tag{1}$$

Cronbach's alpha coefficient [30]:

Confidence interval

$$
\overline{Y} \pm \mathbf{t}\_{n\text{-}1\text{-}1\text{ }\dots\text{ }}{}^{a}\_{\frac{a}{2}\sqrt{\mu}}\tag{2}
$$

with <sup>Y</sup>¯ <sup>=</sup> 0.63, *<sup>S</sup>* <sup>=</sup> 0.322, *<sup>α</sup>* at level 0.05, *<sup>r</sup>* <sup>=</sup> *<sup>n</sup>* <sup>−</sup> <sup>1</sup> <sup>=</sup> <sup>11</sup> <sup>−</sup> <sup>1</sup> <sup>=</sup> <sup>10</sup> <sup>=</sup> degrees of freedom where <sup>n</sup> is the number of measurements.

$$\begin{array}{l} \text{In number of measurements.}\\ \\ t\_{n-1;1-\frac{0}{2}} = t\_{10-1;1-\frac{0.05}{2}} = t\_{90.975} = 2.228 \text{ (for } Distribution \text{ t-Student)}. \\ \\ \text{conifoldence interval = } 0.63 \pm 2.228 \cdot \frac{0.322}{\sqrt{11}} = \begin{cases} 0.41 & \text{(minimum)} \\ 0.85 & \text{(maximum)} \end{cases} \end{array}$$

$$\text{confidence interval} = 0.63 \pm 2.228^\* \frac{0.322}{\sqrt{11}} = \begin{cases} 0.41 & \text{(minimum)}\\ 0.85 & \text{(maximum)} \end{cases} \tag{3}$$

Finally, we want to know if the measuring instrument calibrated for accuracy.

**Hypothesis test**: defined H<sup>0</sup> = Null Hypothesis and H<sup>1</sup> = Alternative hypothesis [35].

Process:

H0: μ = 0.56, the instrument is calibrated for accuracy.

H1: μ ≠ 0.56, the instrument is not calibrated. There is a systematic error.

$$t = \frac{\bar{Y} - \mu}{\frac{\bar{S}}{\sqrt{\mu}}} = \frac{0.63 - 0.56}{\frac{0.322}{\sqrt{11}}} \approx 0.72\tag{4}$$

**6. Dynamics**

series in the phased space acquire such forms:

From the time series of X (t), Y (t), and Z (t), the discretized column vectors are constructed (observed that although vectors with a minimum of 1000 elements allow making good estimations, the ideal is that contain over 5000 components for the stability of the Lyapunov coefficients). According to the significant learning of the team of students, the graphs of the time

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The time series and the graph obtained are those that allow incorporating elements of chaos theory in their study. They satisfy two fundamental conditions of this theory: sensitivity to initial conditions and the existence of Lyapunov exponents greater than zero. Applying to the experimental data, the Lorenz equations [36, 37] modified according to the fourth order Runge Kutta numerical method, the dynamics classified from the control parameter

where *Y*¯ = 0.63, μ = 0.56 is a control team (calibrated with valid procedures).

Different observational monitoring teams were employed to perform the measurements and obtain μ

r = n − 1 = 11–1 = 10

$$t\_{\imath -1; 1 \stackrel{a}{\!\!\!\!-1}} = \left\{ \begin{array}{c} t\_{10; 99} = 1.812; \end{array} \right. \\ t\_{10; 99} = 2.764; \quad t\_{10; 99} = 3.169$$

The numerical values of t extracted from [34].

**Graph 2** represents the Normal Distribution of the indicators t.

The accuracy calibrated instrument hypothesis is accepted.

**Graph 2.** Normal distribution of the indicators t.
