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Attachment A
| Construct | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-Value | |
|---|---|---|---|---|---|---|
| LAP-D | Cognitive Total | 30.43 (4.16) | 30.86 (4.19) | 0.43 | 0.10 | 0.53 |
| Language Total | 28.84 (4.34) | 29.51 (4.26) | 0.80 | 0.16 | 0.30 | |
| Fine Motor Total | 38.88 (4.97) | 39.68 (4.60) | 0.68 | 0.16 | 0.34 | |
| OMLIT | Support for Oral Language | 53.26 (9.71) | 53.82 (9.87) | 0.57 | 0.06 | 0.72 |
| Support for Print Knowledge | 53.27 (2.89) | 53.38 (2.83) | 0.11 | 0.01 | 0.81 | |
| Literacy Resources | 50.14 (5.62) | 50.69 (4.64) | 0.55 | 0.05 | 0.50 | |
| Arnett | Positive Affect | 51.20 (8.81) | 48.76 (9.31) | -2.44 | -0.24 | 0.10 |
| Not Punitive | 47.83 (6.59) | 46.49 (7.26) | -1.34 | -0.13 | 0.25 | |
| Engaged | 49.78 (11.75) | 46.64 (13.8) | -3.14 | -0.31 | 0.15 | |
| Sample size (centers/classrooms) | 55 | 110 | ||||
| Measure | Control Mean (SD) | Treatment 1 RSL Mean (SD) | Treatment 2 BELL Mean (SD) | Treatment 3 (BTL) Mean (SD) |
|---|---|---|---|---|
| Support for Oral Language | 50.14 (5.62) | 50.70 (4.97) | 49.81 (4.62) | 51.54 (4.26) |
| Support for Print Knowledge | 53.27 (5.62) | 53.44 (4.97) | 52.89 (4.62) | 53.81 (4.26) |
| Support for Print Motivation | 54.41 (9.03) | 51.65 (7.24) | 53.67 (8.05) | 54.20 (6.48) |
| Literacy Resources | 50.14 (5.62) | 50.70 (4.97) | 49.81 (4.62) | 51.54 (4.26) |
| Sample Size (centers/classrooms) | n=54 | n=38 | n=36 | n=36 |
| Subtest | Control Mean (SD) | Treatment 1 RSL Mean (SD) | Treatment 2 BELL Mean (SD) | Treatment 3 (BTL) Mean (SD) |
|---|---|---|---|---|
| Cognitive | 30.43 (4.16) | 31.56 (4.52) | 31.33 (3.95) | 29.71 (3.91) |
| Fine Motor | 38.88 (4.97) | 39.98 (4.58) | 40.33 (4.10) | 38.76 (5.03) |
| Language | 28.84 (4.34) | 29.76 (4.38) | 30.43 (4.17) | 28.41 (4.09) |
| Sample Size (centers/classrooms) | n=53 | n=36 | n=33 | n=35 |
| Sample Size (children) | 580 | 350 | 319 | 350 |
| Measure | Control % | RSL % | BELL % | BTL % | |
|---|---|---|---|---|---|
| Spanish-language preference | 49.1 | 47.2 | 48.5 | 45.7 | |
| Sample Size (teachers) | n=53 | n=36 | n=33 | n=35 | |
| Chi-square test of independence, df = 3, p = 0.99 | |||||
| Education | High school only | 21.6 | 30.6 | 30.3 | 37.1 |
| Some college | 13.7 | 13.9 | 15.2 | 11.4 | |
| AA or BA | 64.7 | 55.6 | 54.6 | 51.4 | |
| Sample Size (teachers) | n=51 | n=36 | n=33 | n=35 | |
Chi-square test of independence, df = 6, p = 0.84 2 Teachers had missing data. |
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| Percent of classrooms with all English-speaking children | 36 | 32 | 33 | 44 | |
| Percent of classrooms with all Spanish-speaking children | 46 | 47 | 58 | 42 | |
| Percent of classrooms with mixture of language | 18 | 21 | 9 | 14 | |
| Sample Size (centers/classrooms) | n=53 | n=36 | n=33 | n=35 | |
Exhibit A5 summarizes results from models for Year 2004 OMLIT construct outcomes, where all three treatment-groups combined were contrasted to the control group. The data were analyzed in two-level hierarchical linear models where classrooms (level-1) were nested in randomization blocks (level-2). The models included a random intercept term for blocks. Treatment impacts (any of the three treatment groups contrasted to control) were estimated in models that controlled for year 2003 baseline OMLIT construct measures27, and year 2003 baseline value of the Arnett “positive, punitive, detached” construct. The models were specified as shown below.
Level-1 Model:
Y(2004)jk = β0k + β1k(Trtjk) + β2k(Y(2003)jk) + β3k(Arnett(2003)jk) + rjk
Level-2 Model:
β0k = γ00 + uk
β1k = γ10
β2k = γ20
β3k = γ30
rjk ˜ N(0, σ2)
uk ˜ N(0, ζ00)
where
| Y(2004)jk | = | OMLIT construct from year 2004 observation of classroom j nested in block k. |
| Y(2003)jk | = | OMLIT construct from year 2003 observation of classroom j nested in block k. |
| (This term was omitted from models for phonological awareness and literacy activities because those measures were not available from the 2003 classroom observational data.) | ||
| Trtjk | = | 1 if classroom j nested in block k was in Treatment Groups 1, 2, or 3; |
| = | 0 if control group. | |
| Arnett(2003)jk | = | Arnett “positive, punitive, detached” construct from year 2003 observation of classroom j nested in block k |
The parameter estimate y10 from the model above is the estimated treatment effect. The value of y10 is entered Exhibit A5 in the column labeled "Mean Difference T-C". In Exhibit A5, the values shown in the column labeled "Control Mean (SD)" were calculated as the simple mean and standard deviation of the OMLIT construct values of the n=54 classes in the control group. The value of the mean shown in the column labeled "Treatment Mean (SD)" was calculated as the sum of the treatment effect, y10, and the control group mean. The standard deviation shown in the column was calculated as the standard deviation of OMLIT construct values of the n=107 classes in the combined group of the three treatment groups. The effect size was calculated by dividing the treatment effect, y10, by the Year 2004 control group standard deviation. The p-value corresponds to a two-sided test of the null hypothesis that the treatment effect is equal to zero.
| Construct | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-value |
|---|---|---|---|---|---|
| Support for Oral Language | 50 (10) | 55.86 (8.60) | 5.86 | .59 | .000 |
| Support for Phonological Awareness | 50 (10) | 52.12 (9.11) | 2.12 | .21 | .181 |
| Support for Print Knowledge | 50 (10) | 55.30 (10.40) | 5.30 | .53 | .002 |
| Support for Print Motivation | 50 (10) | 55.84 (9.10) | 5.84 | .58 | .000 |
| Literacy Resources | 50 (10) | 50.85 (9.54) | .85 | .08 | .586 |
| Literacy Activities | 50 (10) | 53.90 (9.76) | 3.90 | .39 | .018 |
| Sample Size (centers/classrooms) | n=54 | n=106 |
| The effect sizes are standardized measures of the magnitude (size) of treatment effects. The standardization makes possible the comparison of the sizes of treatment effects, between different outcome measures. For example, if the effect sizes of a treatment on outcome measures A and B are 0.50, and 0.25, respectively, then the size of the treatment impact on A is twice the size of the impact on B. For each outcome measure, the effect size is equal to the estimated treatment impact, divided by the control group standard deviation. |
Exhibit A6 summarizes results from models for Year 2004 OMLIT construct outcomes, where each of the treatment groups was contrasted to the control group. The data were analyzed in analyzed in two-level hierarchical linear models where classrooms (level-1) were nested in randomization blocks (level-2). The models included a random intercept term for blocks. Impacts of each of three treatments contrasted to control were estimated in models that controlled for year 2003 baseline OMLIT construct measures28, and year 2003 baseline value of the Arnett “positive, punitive, detached” construct. The models were specified as shown below.
Level-1 Model:
Y(2004)jk = β0k + β1k(Trtjk) + β2k(Trt2jk) + β3k(Trt3jk) + β4k(Y(2003)jk) + β5k(Arnett(2003)jk) + rjk
Level-2 Model:
β0k = γ00 + uk
β1k = γ10
β2k = γ20
β3k = γ30
β4k = γ40
β5k = γ50
rjk ˜ N(0, σ2)
uk ˜ N(0, ζ00)
where
| Y(2004)jk | = | OMLIT construct from year 2004 observation of classroom j nested in block k. |
| Y(2003)jk | = | OMLIT construct from year 2003 observation of classroom j nested in block k. |
| (This term was omitted from models for phonological awareness and literacy activities because those measures were not available from the 2003 classroom observational data.) | ||
| Trt1jk | = | 1 if classroom j nested in block k was in Treatment Groups 1; = 0 else. |
| Trt2jk | = | 1 if classroom j nested in block k was in Treatment Groups 2; = 0 else. |
| Trt3jk | = | 1 if classroom j nested in block k was in Treatment Groups 3; = 0 else. |
| Arnett(2003)jk | = | Arnett “positive, punitive, detached” construct from year 2003 observation of classroom j nested in block k |
The parameter estimates y10, y20, y30 from the model above are the estimated impacts of Treatments 1, 2, and 3, as contrasted to control, respectively. The values y10, y20, y30 are entered Exhibit A6 in the column labeled "Mean Difference T-C". In Exhibit A6, the values shown in the column labeled "Control Mean (SD)" were calculated as the simple mean and standard deviation of the OMLIT construct values of the n=54 classes in the control group. The values of the mean shown in the columns labeled "Treatment Mean (SD)" were calculated as the sum of each of the three treatment effects, y10, y20, y30, and the control group mean. The standard deviation shown in those columns were calculated as the standard deviation of OMLIT construct values of each of the three treatment groups. The effect sizes were calculated by dividing the treatment effects, y10, y20, y30, by the Year 2004 control group standard deviation. The p-values correspond to two-sided tests of the null hypothesis that the treatment effects are equal to zero.
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The results corresponding to classes with Spanish-dominant teachers, shown in the top panel of Exhibit A7 were obtained by fitting the model described for Exhibit A5, to the subset of data consisting of classes with Spanish-dominant teachers. Similarly, the results for English-dominant teachers were obtained by fitting the model described in Exhibit A5 to the subset of classes with English-dominant teachers. Effect sizes were calculated by dividing the estimated treatment effect by the full sample Year 2004 control group standard deviation.
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Exhibit A8 summarizes results from models for Year 2005 OMLIT construct outcomes, where all three treatment groups combined were contrasted to the control group. The analytic model corresponding to Exhibit A8 is the same model as previously described from Exhibit A5. The only difference is that Exhibit A8 results are from models that were fit to the data from 2005. Therefore, the outcome variable is
Y(2005)jk = OMLIT construct from year 2005 observation of classroom j nested in block k.
and all other model terms are as specified previously. The effect size is calculated as the impact divided by the Year 2004 control group standard deviation.
| Construct | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-value |
|---|---|---|---|---|---|
| Support for Oral Language | 49.81 (10.38) | 55.92 (9.36) | 6.11 | .61 | .000 |
| Support for Phonological Awareness | 48.16 (7.73) | 53.05 (9.90) | 4.89 | .49 | .001 |
| Support for Print Knowledge | 48.41 (11.18) | 55.83 (9.99) | 7.42 | .74 | .000 |
| Support for Print Motivation | 50.90 (10.85) | 55.19 (9.48) | 4.29 | .43 | .012 |
| Literary Resources | 48.91 (9.04) | 51.69 (8.40) | 2.77 | .28 | .045 |
| Literary Activities | 47.38 (11.37) | 55.38 (8.50) | 8.00 | .80 | .000 |
| Sample Size (centers/classrooms) | n=53 | n=104 |
Exhibit A9 summarizes results from models for Year 2005 OMLIT construct outcomes, where each of the treatment groups was contrasted to the control group. The analytic model corresponding to Exhibit A9 is the same model as previously described from Exhibit A6. The only difference is that Exhibit A9 results are from models that were fit to the data from 2005. Therefore, the outcome variable is
Y(2005)jk = OMLIT construct from year 2005 observation of classroom j nested in block k.
and all other model terms are as specified previously. The effect size is calculated as the impact divided by the Year 2004 control group standard deviation.
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The results corresponding to classes with Spanish-dominant teachers, shown in the top panel of Exhibit A10 were obtained by fitting the model described for Exhibit A8, to the subset of data consisting of classes with Spanish-dominant teachers. Similarly, the results for English-dominant teachers were obtained by fitting the model described in Exhibit A8 to the subset of classes with English-dominant teachers. Effect sizes were calculated by dividing the estimated treatment effect by the full sample Year 2004 control group standard deviation.
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Exhibit A11 summarizes results from models for Year 2005 child-level outcomes (TOPEL scores), where all three treatment-groups combined were contrasted to the control group. The data were analyzed in three-level hierarchical linear models where students (level-1) were nested in classrooms (level-2), and classes were nested in randomization blocks (level-3). The models included a random intercept terms for classes and blocks. Treatment impacts (any of the three treatment groups contrasted to control) were estimated in models that controlled for child’s age, sex, and language spoken at home, and for classroom-level mean LapD Cognitive Total scores obtained from measurements taken in the fall of 2003 or the fall of 2004. The models were specified as shown below.
Level-1 Model:
Y(2005)ijk = π0jk + π1jk(Ageijk) + π2jk(SexMaleijk) + π3jk(HomeLang1ijk) + π4jk(HomeLang2ijk) + eijk
Level-2 Model:
π0jk = β00k + β01k(Trtjk) + β02k(MeanLapD_CTjk) + rjk
π1jk = β10k
π2jk = β20k
π3jk = β30k
π4jk = β40k
Level-2 Model:
β00k = γ000 + uk
β01k = γ010
β02k = γ020
β10k = γ100
β20k = γ200
β30k = γ300
β40k = γ400
eijk ˜ N(0,ø2)
rjk ˜ N(0,σ2)
uk ˜ N(0,ζ00)
where
| Y(2005)ijk | = | TOPEL outcome measure from spring 2005 for student i, nested in classroom j nested in block k. |
| Ageijk | = | Age at time of testing of student i, nested in classroom j nested in block k. |
| SexMaleijk | = | 1 if student i, nested in classroom j nested in block k is male; 0 if female |
| HomeLang1ijk | = | 1 if home language of student i, nested in classroom j nested in block k is English only; 0 if HomeLang2=1 or if home language is a mix of English and Spanish, a mix of English and some other language, or if some other language is the primary language in the home |
| HomeLang2ijk | = | 1 if home language of student i, nested in classroom j nested in block k is Spanish only or a mix of English and Spanish; 0 if HomeLang1=1 or if home language is a mix of English and Spanish, a mix of English and some other language, or if some other language is the primary language in the home |
| Trtjk | = | 1 if classroom j nested in block k was in Treatment Groups 1, 2, or 3; |
| = | 0 if control group. | |
| MeanLapD_CTjk | = | Class-level mean LapD Cognitive Total Score of class j nested in block k, calculated from tests administered in the fall of 2003 and fall of 2004. |
The parameter estimate y010 from the model above is the estimated treatment effect. The value of y010 is entered Exhibit A11 in the column labeled "Mean Difference T-C". In Exhibit A11, the values shown in the column labeled "Control Mean (SD)" were calculated as the simple mean and standard deviation of the TOPEL outcome measure values of the children in the control group. The value of the mean shown in the column labeled "Treatment Mean (SD)" was calculated as the sum of the treatment effect, y010, and the control group mean. The standard deviation shown in the column was calculated as the standard deviation of TOPEL outcome measure values of the children in the combined group of the three treatment groups. The effect size was calculated by dividing the treatment effect, y010, by the Year 2005 control group standard deviation. The p-value corresponds to a two-sided test of the null hypothesis that the treatment effect is equal to zero.
| Subtest | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-Value |
|---|---|---|---|---|---|
| Definitional Vocabulary | 78.79 (16.43) | 82.43 (17.77) | 3.64 | 0.22 | 0.017 |
| Phonological Awareness | 88.74 (16.19) | 93.28 (15.95) | 4.54 | 0.28 | 0.003 |
| Print Knowledge | 95.89 (15.31) | 102.82 (14.66) | 6.93 | 0.45 | 0.000 |
| Early Literacy Index | 84.93 (16.32) | 91.12 (16.70) | 6.19 | 0.38 | 0.000 |
| Sample Size (children) | n=509 | n=1014 |
Exhibit A12 summarizes results from models for Year 2005 child-level outcomes (TOPEL scores), where each of the treatment groups were contrasted to the control group. The data were analyzed in same model as specified for Exhibit A11, except that three dummy variables representing the contrasts of each of the three treatment groups to the control group were entered in the level-2 model instead of the single treatment dummy (representing the contrast of all three treatments combined to control) that was utilized for the Exhibit A11 models.
Other than the differences shown below, all other model terms were identical to those used in the model for Exhibit A11:
Level-2 Model:
π0jk = β00k + β01k(Trt1jk) + β01k(Trt2jk) + β01k(Trt3jk) + β02k(MeanLapD_CTjk) + rjk
where
Trt1jk = 1 if classroom j nested in block k was in Treatment Group 1; = 0 else.
Trt2jk = 1 if classroom j nested in block k was in Treatment Group 2; = 0 else.
Trt3jk = 1 if classroom j nested in block k was in Treatment Group 3; = 0 else.
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Exhibit A13 summarizes results from models for Year 2005 child-level outcomes (TOPEL scores), where treatment-groups 1 and 3 combined were contrasted to the control group. The results shown in Exhibit A13 are from the same model as specified for Exhibit A11, except that Treatment Group 2 data are omitted from the analysis. Thus, the treatment dummy becomes a contrast of the combined effect of Treatments 1 and 3, contrasted to control.
Other than the differences shown below, all other model terms were identical to those used in the model for Exhibit A11:
Level-2 Model:
π0jk = β00k + β01k(Trtjk) + β01k(Trt2jk) + β02k(MeanLapD_CTjk) + rjk
where,
| Trtjk | = | 1 if classroom j nested in block k was in Treatment Groups 1 or 3; |
| = | 0 if control group. |
| Subtest | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-Value |
|---|---|---|---|---|---|
| Definitional Vocabulary | 78.79 (16.43) | 83.72 (17.49) | 4.93 | 0.30 | 0.001 |
| Phonological Awareness | 88.74 (16.19) | 95.09 (15.86) | 6.35 | 0.39 | 0.000 |
| Print Knowledge | 95.89 (15.31) | 105.51 (13.38) | 9.62 | 0.63 | 0.000 |
| Early Literacy Index | 84.93 (16.32) | 93.59 (15.94) | 8.66 | 0.53 | 0.000 |
| Sample Size (children) | n=509 | n=674 |
The results shown in the top panel of Exhibit A14 are from the same model as specified for Exhibit A13, except that only data from classes with Spanish-dominant teachers were included (data from classes with English-dominant teachers were omitted). Similarly, the results in the bottom panel of Exhibit A14 are from the same model as specified for Exhibit A13, except that only data from classes with English-dominant teachers were included (data from classes with Spanish-dominant teachers were omitted). Effect sizes were calculated by dividing the estimated treatment effect by the full sample Year 2005 control group standard deviation.
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The results shown in Exhibit A15 are from the same model as specified for Exhibit A13, except that data from children from homes where English is the only language spoken are excluded. Effect sizes were calculated by dividing the estimated treatment effect by the full sample Year 2005 control group standard deviation.
| Subtest | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-Value |
|---|---|---|---|---|---|
| Definitional Vocabulary | 76.37 (16.69) | 81.49 (17.90) | 5.12 | 0.31 | 0.004 |
| Phonological Awareness | 87.94 (16.62) | 94.56 (16.20) | 6.62 | 0.41 | 0.000 |
| Print Knowledge | 95.09 (15.43) | 105.57 (13.32) | 10.48 | 0.68 | 0.000 |
| Early Literacy Index | 83.33 (16.82) | 92.62 (16.26) | 9.29 | 0.57 | 0.000 |
| Sample Size (children) | n=404 | n=525 |
The results shown in Exhibit A16 are also from the same model as specified for Exhibit A13, except that only data from children from homes where English is the only language spoken are included.
| Subtest | Control Mean (SD) | Treatment Mean (SD) | Mean Difference T-C | Effect Size | P-Value |
|---|---|---|---|---|---|
| Definitional Vocabulary | 86.97 (12.45) | 91.52 (12.86) | 4.55 | 0.28 | 0.034 |
| Phonological Awareness | 91.69 (14.20) | 96.78 (14.47) | 5.08 | 0.31 | 0.023 |
| Print Knowledge | 98.97 (14.47) | 104.11 (13.66) | 5.14 | 0.34 | 0.023 |
| Early Literacy Index | 90.37 (13.17) | 96.20 (14.17) | 5.83 | 0.36 | 0.015 |
| Sample Size (children) | n=105 | n=149 |
The results summarized in Exhibit A17 were obtained from the following two-level HLM model. The results in all three panels of the exhibit utilized the same model specification, but the results in the middle panel were obtained when the model was fit to data only from classes with Spanish-dominant teachers, and the results in the bottom panel correspond to the subset of data from classes with English-dominant teachers.
The two-level random intercept HLM models were of the form:
Level 1
Yij = β0j + β1 (TeacherBA) + rij
Level 2
β0j = γ00 + u0j
where Yij is a 2003 OMLIT measures on the ith class nested in the jth block, the β0j are random intercept terms for the j blocks, and TeacherBA is coded as 1 if the teacher has a bachelor degree or higher and zero otherwise.
In the Exhibit, the column labeled "Estimate of Effect" shows the parameter estimate β1, the column labeled "standard error of effect" gives the standard error of β1. The column labeled "effect size" shows the estimate, β1, divided the Year 2004 control group standard deviation of the measure, i.e., 10. The p-value is a two-sided test of the null hypothesis that β1 = 0.
| Construct | Estimate of Effect | Standard Error of Effect | Effect Size | P-value | |
|---|---|---|---|---|---|
| Full Sample | Support for Oral Language | 0.01 | 1.67 | .00 | .997 |
| Support for Print Knowledge | 1.05 | 0.48 | .10 | .031 | |
| Support for Print Motivation | -1.25 | 1.32 | .12 | .345 | |
| Literacy Resources | 1.04 | 0.83 | .10 | .213 | |
| Arnett: Positive Affect | 2.99 | 1.51 | .30 | .049 | |
| Arnett: Not Punitive | -0.03 | 1.18 | -.00 | .981 | |
| Arnett: Engaged | 3.44 | 2.20 | .30 | .121 | |
| English-Dominant Teachers | Support for Oral Language | 0.23 | 2.72 | .02 | .932 |
| Support for Print Knowledge | 1.02 | 0.77 | .01 | .193 | |
| Support for Print Motivation | -2.17 | 2.26 | .02 | .342 | |
| Literacy Resources | -0.19 | 1.40 | .02 | .893 | |
| Arnett: Positive Affect | 4.27 | 2.32 | .04 | .070 | |
| Arnett: Not Punitive | -1.38 | 1.77 | .01 | .438 | |
| Arnett: Engaged | 2.01 | 3.43 | .02 | .560 | |
| Spanish-Dominant Teachers | Support for Oral Language | 0.46 | 2.32 | .00 | .841 |
| Support for Print Knowledge | 1.61 | 0.64 | .02 | .015 | |
| Support for Print Motivation | 0.15 | 1.74 | .02 | .937 | |
| Literacy Resources | 2.68 | 1.07 | .03 | .015 | |
| Arnett: Positive Affect | 1.45 | 2.22 | .01 | .515 | |
| Arnett: Not Punitive | 1.78 | 1.82 | .02 | .331 | |
| Arnett: Engaged | 4.34 | 3.36 | .04 | .202 | |
| Note: Overall sample of 157 includes 82 English-dominant teachers and 75 Spanish-dominant teachers. |