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 ? = .05, the Sig (2-tailed) is equal to 0.003 that indicates there is correlation exists between gender and CTBS Language NCE score.

;