# Module 03 Long Project Session Essays

Module 03 Long Project Session

PART ONE

1. T-Test

Group Statistics GROUP N Mean Std. Deviation Std. Error Mean PTEST 1 8 75.25 26.768 9.464 2 8 65.88 28.847 10.199

Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper PTEST Equal variances assumed .132 .722 .674 14 .511 9.375 13.913 -20.466 39.216 Equal variances not assumed .674 13.922 .511 9.375 13.913 -20.482 39.232

Equal variances not assumed line will be used for ‘Independent Samples Test’ as Assuming equal variances (Levene's Test for Equality of Variances) the Sig value is greater than 0.05. The t-test for Equality of Means is not significant as the Sig. (2-tailed) = 0.511 is greater than 0.05.

2. Regression

Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 GROUPa . Enter a. All requested variables entered. b. Dependent Variable: PTEST

Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .177a .031 -.038 27.826 a. Predictors: (Constant), GROUP

ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 351.562 1 351.562 .454 .511a Residual 10840.375 14 774.312 Total 11191.937 15 a. Predictors: (Constant), GROUP b. Dependent Variable: PTEST

Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 84.625 21.999 3.847 .002 GROUP -9.375 13.913 -.177 -.674 .511 a. Dependent Variable: PTEST

The value of r is equal to 0.177 and the value of r-squared is 0.031. Therefore, 3.1 percentage of variance in the PTEST (dependent variable) accounted for by the GROUP (independent variable).

Lower t statistics (-0.674) for GROUP variable indicate that the regression test is not significant (or higher Sig = 0.511, which is greater than 0.05).

The t-statistic for the predictor (GROUP) is equal to the square root of the F-statistic.

3. Oneway ANOVA

Descriptives PTEST N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound 1 8 75.25 26.768 9.464 52.87 97.63 18 99 2 8 65.88 28.847 10.199 41.76 89.99 14 99 Total 16 70.56 27.315 6.829 56.01 85.12 14 99

Test of Homogeneity of Variances PTEST Levene Statistic df1 df2 Sig. .132 1 14 .722

ANOVA PTEST Sum of Squares df Mean Square F Sig. Between Groups 351.562 1 351.562 .454 .511 Within Groups 10840.375 14 774.312 Total 11191.938 15

ONEWAY ANOVA shows that the test is not significant as the value of Sig = 0.511 is greater than 0.05. Smaller F-statistic indicates that variance between groups is smaller than the variance within them.

The descriptive statistics (Mean, Std. Deviation and Std. Error of Mean) are identical for the t-test and for the One-way ANOVA test.

4. Univariate Analysis of Variance

Between-Subjects Factors N GROUP 1 8 2 8 SEX 1 8 2 8

Descriptive Statistics Dependent Variable:PTEST GROUP SEX Mean Std. Deviation N 1 1 74.50 38.371 4 2 76.00 14.071 4 Total 75.25 26.768 8 2 1 58.50 12.819 4 2 73.25 40.401 4 Total 65.88 28.847 8 Total 1 66.50 27.831 8 2 74.62 28.046 8 Total 70.56 27.315 16

Tests of Between-Subjects Effects Dependent Variable:PTEST Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 791.188a 3 263.729 .304 .822 Intercept 79665.062 1 79665.062 91.915 .000 GROUP 351.562 1 351.562 .406 .536 SEX 264.062 1 264.062 .305 .591 GROUP * SEX 175.562 1 175.562 .203 .661 Error 10400.750 12 866.729 Total 90857.000 16 Corrected Total 11191.938 15 a. R Squared = .071 (Adjusted R Squared = -.162)

Estimated Marginal Means

GROUP Dependent Variable: PTEST GROUP Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound 1 75.250 10.409 52.571 97.929 2 65.875 10.409 43.196 88.554

The Univariate Analysis of Variance shows that test is not significant. The smaller F-statistics values of GROUP, SEX indicates that SEX and GROUP do not significantly affect PTEST.

PART TWO

First, use CTBS Language NCE Score (interval) as DV, and gender (categorical; coded 0=female, 1=male) as IV; Try some predictive models:

1. ANALYZE: COMPARE MEANS: INDEPENDENT SAMPLES TTEST (remember to specify the two categories of gender)

T-Test

Group Statistics gender N Mean Std. Deviation Std. Error Mean CTBS Language NCE score female 162 52.9940 17.25516 1.35569 male 154 46.9814 18.18235 1.46518

Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper CTBS Language NCE score Equal variances assumed .597 .440 3.016 314 .003 6.01259 1.99351 2.09027 9.93492 Equal variances not assumed 3.012 310.703 .003 6.01259 1.99616 2.08490 9.94029

Equal variances not assumed line will be used for ‘Independent Samples Test’ as Assuming equal variances (Levene's Test for Equality of Variances) the Sig value is greater than 0.05. The t-test for Equality of Means is significant as the Sig. (2-tailed) = 0.003 is less than 0.05.

2. ANALYZE: COMPARE MEANS: ONEWAY ANOVA

Oneway ANOVA

Descriptives CTBS Language NCE score N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound female 162 52.9940 17.25516 1.35569 50.3167 55.6712 1.01 98.99 male 154 46.9814 18.18235 1.46518 44.0868 49.8760 1.01 98.99 Total 316 50.0638 17.93921 1.00916 48.0782 52.0493 1.01 98.99

Test of Homogeneity of Variances CTBS Language NCE score Levene Statistic df1 df2 Sig. .597 1 314 .440

ANOVA CTBS Language NCE score Sum of Squares df Mean Square F Sig. Between Groups 2854.121 1 2854.121 9.097 .003 Within Groups 98517.691 314 313.751 Total 101371.812 315

ONEWAY ANOVA shows that the test is significant as the value of Sig = 0.003 is less than 0.05. Larger F-statistic indicates that variance between groups is larger than the variance within them.

The descriptive statistics (Mean, Std. Deviation and Std. Error of Mean) are identical for the t-test and for the One-way ANOVA test.

3. REGRESSION : LINEAR

Regression

Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 gendera . Enter a. All requested variables entered. b. Dependent Variable: CTBS Language NCE score

Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .168a .028 .025 17.71301 a. Predictors: (Constant), gender

ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 2854.121 1 2854.121 9.097 .003a Residual 98517.691 314 313.751 Total 101371.812 315 a. Predictors: (Constant), gender b. Dependent Variable: CTBS Language NCE score

Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 52.994 1.392 38.080 .000 gender -6.013 1.994 -.168 -3.016 .003 a. Dependent Variable: CTBS Language NCE score

The value of r is equal to 0.168 and the value of r-squared is 0.028. Therefore, 2.8 percentage of variance in the CTBS Language NCE score (dependent variable) accounted for by the Gender (independent variable).

Higher t statistics (-3.016) for gender variable indicate that the regression test is significant (or lower Sig = 0.003, which is less than 0.05). The t-statistic for the predictor (gender) is equal to the square root of the F-statistic.

Second, use CTBS Language NCE Score (interval) as DV, and gender (categorical; coded 0=female, 1=male) and engprof2 (categorical, recoded from engprof as 0=no nonEnglish

proficiency [engprof=0 or 4], 1=some non-English proficiency [engprof=1, 2, 3], as IV; try as predictive models:

4. GENERAL LINEAR MODEL : UNIVARIATE [gender and engprof2 are both fixed factors]

Univariate Analysis of Variance

Between-Subjects Factors Value Label N gender 0 female 162 1 male 154 any non-english proficiency 0 no 192 1 yes 124

Descriptive Statistics Dependent Variable:CTBS Language NCE score gender any non-english proficiency Mean Std. Deviation N female no 56.3753 18.17537 102 yes 47.2457 13.91422 60 Total 52.9940 17.25516 162 male no 50.1500 17.72213 90 yes 42.5255 18.01875 64 Total 46.9814 18.18235 154 Total no 53.4572 18.18610 192 yes 44.8095 16.27189 124 Total 50.0638 17.93921 316

Levene's Test of Equality of Error Variancesa Dependent Variable: CTBS Language NCE score F df1 df2 Sig. 1.729 3 312 .161 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + gender + engprof2 + gender * engprof2

Tests of Between-Subjects Effects Dependent Variable:CTBS Language NCE score Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 8177.200a 3 2725.733 9.125 .000 Intercept 724200.886 1 724200.886 2424.504 .000 gender 2251.680 1 2251.680 7.538 .006 engprof2 5275.644 1 5275.644 17.662 .000 gender * engprof2 42.572 1 42.572 .143 .706 Error 93194.612 312 298.701 Total 893388.982 316 Corrected Total 101371.812 315 a. R Squared = .081 (Adjusted R Squared = .072)

Estimated Marginal Means

Grand Mean Dependent Variable:CTBS Language NCE score Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound 49.074 .997 47.113 51.035

The Univariate Analysis of Variance shows that test is significant. The higher F-statistics values of gender and engprof2 indicates that CTBS Language NCE score is significantly affected by gender and any non-English proficiency.

5. [Multiple] REGRESSION : LINEAR [include interac [interaction (product) of gender and engprof2] along with gender and engprof2 as IVs]

Regression

Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 any non-english proficiency, gender, interaca . Enter a. All requested variables entered. b. Dependent Variable: CTBS Language NCE score

Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .284a .081 .072 17.28296 a. Predictors: (Constant), any non-english proficiency, gender, interac

ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 8177.200 3 2725.733 9.125 .000a Residual 93194.612 312 298.701 Total 101371.812 315 a. Predictors: (Constant), any non-english proficiency, gender, interac b. Dependent Variable: CTBS Language NCE score

Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 56.375 1.711 32.944 .000 interac 1.505 3.987 .034 .378 .706 gender -6.225 2.499 -.174 -2.491 .013 any non-english proficiency -9.130 2.812 -.249 -3.247 .001 a. Dependent Variable: CTBS Language NCE score

The value of r is equal to 0.284 and the value of r-squared is 0.081. Therefore, 8.1 percentage of variance in the CTBS Language NCE score (dependent variable) accounted for by the Gender, any non-English proficiency, and interac (independent variables).

The higher F-statistics values of gender and engprof2 indicates that CTBS Language NCE score is significantly affected by gender and any non-English proficiency.

ONE MORE ANALYSIS

We will check whether, there is a correlation exists between gender and CTBS Language NCE score.

Correlations

Descriptive Statistics Mean Std. Deviation N gender .49 .501 316 CTBS Language NCE score 50.0638 17.93921 316

Correlations gender CTBS Language NCE score gender Pearson Correlation 1.000 -.168** Sig. (2-tailed) .003 N 316.000 316 CTBS Language NCE score Pearson Correlation -.168** 1.000 Sig. (2-tailed) .003 N 316 316.000 **. Correlation is significant at the 0.01 level (2-tailed).

For a two-tailed test for significance at α = .05, the Sig (2-tailed) is equal to 0.003 that indicates there is correlation exists between gender and CTBS Language NCE score.