Results

Factorial Structure of the Teacher-Version. The CFA on the six-dimensions model for the Classroom practices section brought to a few thoughtful adjustments. Modification indexes suggested correlating a few residual errors. Some authors (Beckstead, 2002; Gerbing & Anderson, 1984) advanced that when correlations between error terms are theoretically plausible they can be included in CFAs without undermining the factorial validity of the model. In my case, items with correlated residuals tended to have similar formulations and meanings, which makes correlations plausible (e.g., “Most teachers appear to draw pleasure from teaching” and “Most teachers appear to love their job”). One dimension (Class Management) and one item from the student-version (SS1, see Table 4.7) showed unacceptable psychometric properties and largely worsened the model fit, thus they were removed from the model. This five-dimensions model reported acceptable fit

indexes: MLR c² (190) = 279.38, p = .000; RMSEA = .07; CFI = .91; SRMR = .08. Factor loadings were all significant and are reported in Table 4.7.

l Classroom Practices

Rules (R)

R1. Students know the consequences for breaking the rules .59

R2. Most people know the school rules .53

R3. At school, some time is spent to explain the rules clearly to students .76

R4. It is easy to obtain information about the school rules .64

R5. The rules are clear and easy to understand .75

R6. Teachers enforce the rules .68

R7. Teachers intervene when a student doesn’t keep to the rules .70

Student Support (SS)

SS1. There are professionals meant to help students with academic or personal problems - SS2. When they have problems, students seek the help of adults in the school .55 SS3. If students have personal problems, they can easily get help from adults in the school .65 SS4. If students have academic problems, they can easily get help from teachers .87 Student Involvement (SI)

SI1. Students are asked their opinion on the school functioning .69

SI2. When it is important, teachers ask students’ opinions before making decisions for them .72 SI3. There are moments or situations when students can express their opinion on the school .79

SI4. Students participate to define rules .54

Positive Teaching (PT)

PT1. Most teachers appear to draw pleasure from teaching .65

PT2. Most teachers appear to love their job .61

PT3. Teachers explain what we are about to learn .58

PT4. Teachers explain why what we study is important .58

PT5. Teachers use methods that make their subject interesting .66

Encouragement (E)

E1. Teachers tell us that we can do it .60

E2. Teachers encourage students to do their best .70

E3. Teachers compliment us when we work hard to learn .78

Table 4.7. Items and factor loadings of the Classroom Practices scale of the teacher-version.

Note. R = Rules; SS = Student Support; SI = Student Involvement; PT = Positive Teaching; E=

Encouragement; as detailed in the text item SS1 was removed from the final model.

Also for the School atmosphere section, after consulting the modification indexes and theoretical reflection, I correlated a few error terms (e.g., “In general, students get along with one another” and “In general, relations among students are friendly”). The expected five-dimensions model obtained good fit indexes: MLR c² (193) = 264.88, p = .001; RMSEA = .06; CFI = .93;

SRMR = .07. Factor loadings were all significant and are reported in Table 4.8.

School Atmosphere l Student Relations (SR)

SR1. Students help each other .70

SR2. In general, students get along with one another .61

SR3. Students treat one another respectfully .69

SR4. Students can count on each other .65

SR5. In general, relations among students are friendly .63

Student-Teacher Relations (STR)

STR1. Students and teachers feel good together .84

STR2. In general, students and teachers get along with each other .53 STR3. Students feel close to most of their teachers and they trust them .74 STR4. In general, relations between students and teachers are friendly .83 Educational Climate (EC)

EC1. At my school, you can really learn and get a good education .51

EC2. At my school, you can feel that students’ success is the priority for teachers .57

EC3. At my school, you can feel that studying is important .66

EC4. At my school, we are expected to do our best .63

EC5. In general, what we learn is interesting .51

Sense of Belonging (SB)

SB1. I would rather be in a different school .76

SB2. At my school, I feel at ease .85

SB3. I am proud to be a teacher of this school .88

SB4. This school is important for me .66

SB5. I love my school .90

Interpersonal Justice (IJ)

IJ1. Punishments are fair .63

IJ2. Students are treated with justice .45

IJ3. Rules are fair .90

Table 4.8. Items and factor loadings of the School Atmosphere scale of the teacher-version

Note. SR = Student Relations; STR = Student-Teacher Relations; EC = Educational Climate; SB = Sense of Belonging; IJ = Interpersonal Justice.

Cronbach’s alphas (Table 4.9) were all above .70, indicating good internal consistency.

Pearson’s bivariate correlations (Table 4.9) showed that all dimensions were positively correlated.

Classroom Practices 1 2 3 4 5 6 7 8 9 10 11 M (SD) a

1 Rules - 5.12 (.67) .87

2 Student Support .46** - 5.11 (.63) .72

3 Student Involvement .41** .53** - 4.56 (.86) .78

4 Positive Teaching .54** .68** .45** - 5.01 (.58) .77

5 Encouragement .35** .63** .56** .65** - 5.28 (.63) .71

School Atmosphere

7 Student Relations .35** .36** .43** .36** .34** .29** - 4.58 (.58) .81

8 Student-Teacher Rel. .57** .39** .47** .46** .43** .35** .63** - 4.88 (.59) .82

9 Educational Climate .64** .49** .45** .61** .48** .36** .51** .72** - 5.15 (.54) .71

10 Sense of Belonging .50** .23* .25* .40** .30** .41** .40** .58** .64** - 5.11 (.90) .90

11 Interpersonal Justice .60** .28** .38** .49** .42** .29** .29** .50** .63** .51** - 5.09 (.69) .67 Table 4.9. Descriptive statistics, intercorrelations and Cronbach’s alphas for the MSCQ teacher-version

Factorial Structure of the Parent-Version. I conducted a CFA on the expected five-factor model, allowing all factors to covary, consistently with the theoretical model. The model reported good fit indices: MLR c²(179) = 269.83, p = .000; RMSEA = .04; CFI = .97; SRMR =.04. Factor loadings, reported in Table 4.10, were all significant and ranged from l = .43 to l= .89.

In my child’s school… CFA (l)

SS1. There are professionals meant to help students with academic or personal problems .43 SS2. When they have problems, students seek the help of adults in the school .66 SS3. If students have personal problems, they can easily get help from adults in the school .84 SS4. If students have academic problems, they can easily get help from teachers .76

SR1. Students help each other .88

SR2. In general, students get along with one another .87

SR3. Students treat one another with respect .86

SR4. Students can count on each other .88

SR5. In general, relations among students are friendly .89

STR1. Students and teachers feel good together .89

STR2. In general, students and teachers get along with each other .80 STR3. Students feel close to most of their teachers and they trust them .82 STR4. In general, relations between students and teachers are friendly .83

EC1. You can really learn and get a good education .74

EC2. You can feel that students’ success is the priority for teachers .86

EC3. You can feel that studying is important .60

EC4. Students are expected to do their best .54

EC5. In general, what students learn is interesting .70

IJ1. Punishment is fair .70

IJ2. Students are treated with justice .85

IJ3. The rules are fair .74

Table 4.10 Items and factor loadings of the parent-version

Note. SS = Student Support; SR = Student Relations; STR = Student-Teacher Relations; EC = Educational Climate; IJ = Interpersonal Justice; l = factor loading.

Cronbach’s alphas were good, supporting the internal consistency of the factors. Bivariate two-tailed Pearson’s correlations indicated that all factors were positively correlated. These values and descriptive statistics for each factor were reported in Table 4.11.

1 2 3 4 5 6 M (SD) a

1 Student Support - 4.64 (.88) .76

2 Student Relations .48** .47** - 4.48 (1.05) .94

3 Student-Teacher Rel. .67** .66** .68** - 4.71 (.90) .90

4 Educational Climate .69** .73** .58** .78** - 5.10 (.72) .82 5 Interpersonal Justice .58** .54** .51** .71** .68** - 4.87 (1.05) .80 Table 4.11 Descriptive statistics, correlations and Cronbach’s alpha for the MSCQ parent-version

Measurement Invariance Across Students, Teachers and Parents. Each step in the analysis of measurement invariance is reported in Table 4.12. The teacher-version questionnaire achieved full configural and metric invariance with both student and parent-versions. Full scalar invariance was also obtained between teachers and parents. With students, however, some items appeared to have non-invariant thresholds. After consulting the modification indexes and a theoretical evaluation, they were freed from constraints, obtaining a partial scalar invariance.

When testing for measurement invariance between students and parents, configural and metric invariance were achieved for all items. Full scalar invariance could not be reached due to an excessive worsening of the fit indices. After the examination of the modification indices and theoretical reflection, one item was freed (EC5) and partial scalar invariance was reached. Overall, the findings support the conclusion of measurement invariance among the different informants.

Model tested (model

compared with) χ² df p CFI RMSE

A SRMR Δχ² Δdf p ΔCFI ΔRMS

EA Invariance between teachers and students

Section 1. Classroom Practices

Configural 460.211 380 .000 .953 .037 .060 - - - - -

Metric (vs configural) 487.292 397 .001 .947 .038 .069 26.226 17 .070 -.006 .001 Scalar (vs metric) 550.838 414 .000 .920 .046 .073 62.249 17 .000 -.027 .008 - Less I4 537.912 413 .000 .927 .044 .072 55,326 16 .000 -.020 .006 - Less PT3 528.697 412 .000 .931 .043 .072 44.113 15 .000 -.016 .005 - Less R7 522.132 411 .000 .935 .042 .072 36.918 14 .001 -.012 .004 - Less R6 505.528 410 .001 .944 .039 .070 18.512 13 .139 -.003 .001

Section 2. School Atmosphere

Configural 527.254 387 .000 .944 .049 .057 - - - - -

Metric (vs configural) 562.882 403 .000 .936 .051 .072 32.225 16 .009 -.008 .002 Scalar (vs metric) 637.202 420 .000 .913 .058 .074 87.970 17 .000 -.023 .007 - Less EC5 620.670 419 .000 .919 .056 .073 68.640 16 .000 -.017 .005 - Less SR3 608.838 418 .000 .924 .055 .073 54.192 15 .000 -.012 .004 - Less SB5 598.936 417 .000 .927 .053 .072 42.245 14 .000 -.009 .002

Invariance between teachers and parents

Configural 537.841 320 .000 .945 .057 .052 - - - - -

Metric (vs configural) 571.746 335 .000 .940 .058 .066 31.631 15 .007 -.005 .001 Scalar (vs metric) 612.858 350 .000 .933 .059 .066 47.462 15 .000 -.007 .001 Invariance between students and parents

Configural 528.971 358 .000 .964 .038 .043 - - - - -

Metric (vs configural) 558.692 374 .000 .961 .039 .050 29.008 16 .024 -.003 .001 Scalar (vs metric) 644.638 390 .000 .946 .045 .053 105.887 16 .000 -.015 .006 - Less EC5 592.959 389 .000 .957 .040 .051 38.227 15 .001 -.004 .001 Table 4.12. Model comparison indices for measurement invariance across students, teachers and parents.