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Module 03 Long Project Session

PART ONE

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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
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
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
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.

; 