analysis of the reasons of students math achievement test

8/12/2019 Analysis of the Reasons of Students Math Achievement Test

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Quantitative Techniques Prof. Sofia Waleed

Superior University2

Definition of Variables:

Dependent Variable:

1. Math Achievement Test : Math achievement test is a dependent variable

which depends on five other Independent variables.

Independent Variable:

1. Gender : Gender is the first independent variable which is ask to the

student while collecting there personal information.

2. Father's Education : Another independent variable is the education

of the father of the student.

3. Mother's Education : Mothers education is the third independent

variable which is asked to the student while collecting the data.

4. Scholastic Aptitude Test - Math : Marks of scholastic aptitude test - math

is an other independent variable which is used in this analysis.5. Geometry: An other independent variable is Geometry which


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is ask to the student whether they study it or not.

6. Grades in High School : Last independent variable is grades in high

school of the student.

Relationship among Variables (Logical Basis):

1-The relationship among the different variables is on the basis of the logic that

all those students whether male or female get good marks in there math

achievement test, who have good grades in high school, then good marks in

there scholastic aptitude test - math, then we have two other major factor and

they are fathers education & there mothers education. Because both the father

& the mother play very important role in the education of there child. There is a

positive relation in the dependent & independent variable, each independent

variable is effecting the dependent variable because in any case where the

mothers or fathers education is low the student is not a top level student

because the student cant get good grades in the math achievement test , which

is try to be proved by the help of a diagram.

2- George Arthur Morgan & Nancy L. Leech explain the reasons about good

grades in math achievement test of a high school student in there book. SPSS for

0

5

10

15

20

25

30

Male Female Male Female Male Female

Grades in Geometry

Scholastic AptitudeTest - MathMother's Education

Father's Education


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Introductory Statistics. Gender & other courses related to math taken by a student

in the school are the major reasons but with these reasons we have two more

reasons and that are fathers & mothers education.

Scope of the study:

With the help of this study we can prove that all these became the

factors for a student to get good grades in math achievement test, which also can

help to all the new coming students how wants study math.

Importance of the study:

The importance of the study is we can examine all those students

hows father & mother became the reason of there good marks with other some

other factures, because all these things helps a student to get better grades in there

math achievement test.

Objectives of the study:

The main objective of this study is to know all those major actors

which helps a student to improve there math achievement marks.


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Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

gender * geometry in h.s. 75 100.0% 0 .0% 75 100.0%

The table of cross tabs is providing the information about the relation between

gender & geometry in h.s, the table shows that we have 75 valid numbers of

students was in this analysis & there is no one is missing in this test.

gender * geometry in h.s. Crosstabulation

geometry in h.s.

Totalnot taken taken

gender male Count 10 24 34

Expected Count 17.7 16.3 34.0

% within geometry in h.s. 25.6% 66.7% 45.3%

female Count 29 12 41



Total Count 39 36 75



There are total 34 males students from which 24 have taken the geometry as a

subject & 10do not take it as a subject, the percentage of student who take

geometry are 66.7% where students who dont take is as a subject are 25.6%. Then


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we have female students there are 41 female students from which 12 do not study

geometry & 29 have studied geometry. 33.3% of females did not take geometry as a

subject & 74.4% have studied it. From the total of students 45.3% are males &

54.7% are females.This cross tab table fulfills all three assumptions:

1. Both variables are normal.

2. The expected Count is more then one.

3. 80% of the percentages are more then 5%.

There is a relationship in the variables because there is a difference in there

percentages.

Chi-Square Tests

Value dfAsymp. Sig. (2-sided)

Exact Sig. (2-sided)

Exact Sig. (1-sided)

PointProbability

Pearson Chi-Square 12.714 a 1 .000 .000 .000

Continuity Correction b 11.112 1 .001

Likelihood Ratio 13.086 1 .000 .000 .000

Fisher's Exact Test .000 .000

Linear-by-Linear Association 12.544 c 1 .000 .000 .000 .000

N of Valid Cases 75

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 16.32.

b. Computed only for a 2x2 table

c. The standardized statistic is -3.542.

To verify the relationship we use chi-square test. In this table we use Pearson Chi-

Square because the boxes are less then 9. Against Pearson Chi-Square & under

Asymp. Sig. value we have .000. This is less than the level of significance (0.05). So

we can say that there is relationship between the variables.


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Symmetric Measures

Value Approx. Sig. Exact Sig.

Nominal by Nominal Phi -.412 .000 .000

Cramer's V .412 .000 .000

N of Valid Cases 75

The table of Symmetric Measures is use to check that which type of relationship is

there in the variables. We are using phi so that against phi & under Approx. sig. value

we have .000, which there is a relation ship but weak.


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This graph is a result of Simple Scatter Plot. In this graph we are trying to know that

is there any correlation-ship between the two variables (math achievement &

scholastic aptitude test). In the graph we have the value of Quadratic = 0.621 &

Linear = 0.62, the difference is 0.001. This is less then the value of significance (0.05)so we can say that there is a correlation-ship between the both variables.

Correlations

math achievement

test

scholastic aptitude

test - math

math achievement test Pearson Correlation 1 .788 **

Sig. (2-tailed) .000

N 75 75

scholastic aptitude test - math Pearson Correlation .788 ** 1


N 75 75

**. Correlation is significant at the 0.01 level (2-tailed).

Now we have table of correlation to know that which type of relation we have

Among the variables, against the Person Correlation & under Scholastic aptitude test

we have the value of (.788), which means that there is 79% relationship, which

shows strong relationship.


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In this Scatter Plot graph we are trying to know that is there any correlation-ship

between the two variables (math achievement & Father Education). In the graph we

have the value of Quadratic = 0.18 & Linear = 0.145, the difference is 0.035. This is

less then the value of significance (0.05) so we can say that there is a correlation-ship

between the both variables.


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Correlations

math achievement

test father's education



N 75 73

father's education Pearson Correlation .381 ** 1


N 73 73


In this table of correlation to are trying to know that which type of relation we have

Among the variables, against the Person Correlation & under Fathers Education we

have the value of (.381), which means that there is 38% relationship, which shows

moderate relationship.


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This Scatter Plot graph we have to know that is there any correlation-ship between

the two variables (math achievement & Mothers Education). In the graph we have

the value of Quadratic = 0.126 & Linear = 0.114, the difference is 0.012. This is less

then the value of significance (0.05) so we can say that there is a correlation-ship

between the both variables.


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Correlations

math achievement

test

mother's

education



N 75 75

mother's education Pearson Correlation .338 ** 1


N 75 75


In this table of correlation to are trying to know that which type of relation we have

Among the variables, against the Person Correlation & under Mothers Education we

have the value of (.338), which means that there is 34% relationship, which shows

moderate relationship.

Variables Entered/Removed b

Model Variables Entered

Variables

Removed Method

1 scholastic aptitude

test - matha

. Enter

a. All requested variables entered.

b. Dependent Variable: math achievement test

The information we get from this table is, there is the dependent variable & that is

math achievement test & we have to examine that is the independent variable

scholastic aptitude test have any effect on the dependent variable.


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Coefficients a

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta

1 (Constant) -14.687 2.541 -5.779 .000

scholastic aptitude test -

math.056 .005 .788 10.918 .000

a. Dependent Variable: math achievement test

The table of coefficients shows against the scholastic aptitude test & under sig. the

value is (.000). This means that there is an effect of the independent variable ondependent variable.

Now we use the formula for the prediction of values.y = a + bxWhere:a = constantb = slop of independent variablex = independent variabley = dependent variable

y = -14.687 + 0.056 (500)y = -14.678 + 28y = 13.32

Model Summary

Model R R Square Adjusted R Square

Std. Error of the

Estimate

1 .788 a .620 .615 4.13897

a. Predictors: (Constant), scholastic aptitude test - math

In the model summary under adjusted R square we have the value of (.615). This

means 62%. So the model summary shows that the dependent variable (math

achievement) is affected by the independent variable (scholastic aptitude test) by

62%.


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Variables

Removed Method

1 father's

education a . Enter




math achievement test & we have to examine that is the independent variable &

that is fathers education is any effect on the dependent variable.

Coefficients a

Model


Standardized

Coefficients


1 (Constant) 8.526 1.385 6.156 .000

father's education .875 .252 .381 3.475 .001


The table of coefficients shows against the fathers education & under sig. the value

is (.001). This means that there is an effect of the independent variable on

dependent variable.

Now we use the formula for the prediction of values.y = a + bxWhere:

a = constantb = slop of independent variablex = independent variabley = dependent variable

y = 8.526 + 0.875 (10)y = 8.526 + 8.75y = 17.276


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Model Summary


Std. Error of the

Estimate

1 .381 a .145 .133 6.04815

a. Predictors: (Constant), father's education



achievement) is affected by the independent variable (fathers education) by 13%.



Variables

Removed Method

1 mother's

education a . Enter





that is mothers education is any effect on the dependent variable.

Coefficients a

Model


Standardized

Coefficients


1 (Constant) 8.436 1.533 5.504 .000

mother's education 1.005 .328 .338 3.064 .003



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dependent variable.

Now we use the formula for the prediction of values.y = a + bxWhere:a = constantb = slop of independent variablex = independent variabley = dependent variable

y = 8.436 + 1.005 (10)y = 8.436 + 10.05

y = 18.486

Model Summary


Std. Error of the

Estimate

1 .338 a .114 .102 6.32165

a. Predictors: (Constant), mother's education



achievement) is affected by the independent variable (mothers education) by 10%.

Variables Entered/Removedb


Variables

Removed Method

1 grades in h.s. a . Enter




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that is grades in h.s is any effect on the dependent variable.

Coefficients a

Model


Standardized

Coefficients


1 (Constant) .397 2.530 .157 .876

grades in h.s. 2.142 .430 .504 4.987 .000




dependent variable.

Now we use the formula for the prediction of values.

y = a + bxWhere:

a = constant

b = slop of independent variable

x = independent variable

y = dependent variable

y = 0.397 + 2.142 (4)y = 0.397 + 8.568y = 8.965

Model Summary


Std. Error of the

Estimate

1 .504 a .254 .244 5.80018

a. Predictors: (Constant), grades in h.s.


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achievement) is affected by the independent variable (grades in h.s) by 24%.



Variables

Removed Method

1 grades in h.s.,

mother's

education,

scholastic aptitude

test - math,

father's

education a

. Enter



The information we get from this table is, there is the dependent variable & that ismath achievement test & we have to examine that is the independent variables &

that are (grades in h.s, mothers education, fathers education, aptitude test) are

effecting the dependent variable.

Coefficients a

Model


Standardized

Coefficients


1 (Constant) -17.100 2.329 -7.342 .000

scholastic aptitude test

- math.049 .005 .711 10.105 .000

father's education .568 .205 .247 2.770 .007

mother's education -.108 .256 -.038 -.423 .674

grades in h.s. .655 .295 .157 2.220 .030



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The table of coefficients shows against the (scholastic aptitude test, fathers

education, mothers education, grades in h.s) & under sig. the value is (.000, .000,

.007, .674, .030 respectively). This entire means that there is an effect of theindependen t variable on dependent variable except mothers eduction.

Now we use the formula for the prediction of values.

y = a + bx 1 + cx2 + dx 3 + ex 4 Where:a = constantb = slop of independent variable (scholastic aptitude test)c = slop of independent variable (fathers education) d = slop of independent variable (mothers education) e = slop of independent variable (grades in h.s)x1 = independent variable (scholastic aptitude test)x2 = independent variable (fathers education) x3 = independent variable (mothers education) x4 = independent variable (grades in h.s)y = dependent variable

y = -17.100 + 0.049 (500) + 0.568 (10) + (-0.108) 10 + 0.655 (4)y = -17.100 + 24.5 + 5.68 1.08 + 2.62y = 14.62

Model Summary


Std. Error of the

Estimate

1 .850a

.722 .706 3.52213

a. Predictors: (Constant), grades in h.s., mother's education, scholastic

aptitude test - math, father's education



achievement) is affected by all the independent variable including (scholastic

aptitude test, fathers education, mothers education, grades in h.s) by 71%.


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ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 2195.239 4 548.810 44.240 .000 a

Residual 843.566 68 12.405

Total 3038.804 72

a. Predictors: (Constant), grades in h.s., mother's education, scholastic aptitude test - math, father's

education


The table of ANOVA b is use only in multi regression to show the joint effects of

variables. To verify this we have to see against regression & under sig. the value is

(.000) this means that all the independent variables have jointly effect the

dependent variable.

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

scholastic aptitude test - math 75 490.53 94.553 10.918

The table shows one sample statistics of the t-test, in this table it is shown that the

mean of scholastic aptitude test-math is 490.53.

One-Sample Test

Test Value = 500

t df Sig. (2-tailed)

Mean

Difference

95% Confidence Interval of

the Difference


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Lower Upper

scholastic aptitude test

- math-.867 74 .389 -9.467 -31.22 12.29

The table of one sample test have the value of test variable which is 500 & it have to

be compared with the value of t-test which is 490.53. The significance value of

scholastic aptitude test math is not significant because the value of sig. against

scholastic aptitude test-math is (0.389) which is greater then the significance value

(0.05).



father's education 73 4.73 2.830 .331


mean of Fathers education is 4.73.

One-Sample Test

Test Value = 500

t df Sig. (2-tailed) Mean Difference

95% Confidence Interval of the

Difference

Lower Upper

father's education -1.495E3 72 .000 -495.274 -495.93 -494.61


be compared with the value of t-test which is 4.73. The significance value of Fathers

education significant because the value of sig. against Mothers education is (0.000)

which is less then the significance value (0.05).



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mother's education 75 4.11 2.240 .259

The table shows one sample statistics of the t-test, in this table it is shown that themean of Mothers education is 4.11.

One-Sample Test

Test Value = 500

t df Sig. (2-tailed)

Mean

Difference


Difference

Lower Upper

mother's education -1.918E3 74 .000 -495.893 -496.41 -495.38


be compared with the value of t-test which is 4.11. The significance value of

Mothers education significant because the value of sig. against Mothers education

is (0.000) which is less then the significance value (0.05).



grades in h.s. 75 5.68 1.570 .181


mean of grades in h.s test-math is 5.68.

One-Sample Test

Test Value = 500

t df Sig. (2-tailed) Mean Difference


Difference


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Lower Upper

grades in h.s. -2.727E3 74 .000 -494.320 -494.68 -493.96

The table of one sample test have the value of test variable which is 500 & it have tobe compared with the value of t-test which is 5.68. The significance value of grades

in h.s is significant because the value of sig. against scholastic aptitude test-math is

(0.000) which is less then the significance value (0.05).

Group Statistics

gender N Mean Std. Deviation Std. Error Mean

scholastic aptitude test - math male 34 516.18 99.423 17.051

female 41 469.27 85.802 13.400

math achievement test male 34 14.7550 6.03154 1.03440

female 41 10.7479 6.69612 1.04576

father's education male 33 5.55 2.818 .491

female 40 4.05 2.689 .425

mother's education male 34 4.59 2.324 .399

female 41 3.71 2.112 .330

grades in h.s. male 34 5.50 1.638 .281

female 41 5.83 1.515 .237

The table shows Group Statistics of the t-test of all the variables, in the table mean of

all the groups (males & females) are given separately, it is shown that the mean of

every group is compared individually.

Independent Samples Test

Levene's Test for

Equality of

Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed)

MeanDifference

Std. ErrorDifference

95% Confidence

Interval of the

Difference

Lower Upper


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scholastic

aptitude test

- math

Equal

variances

assumed

.860 .357 2.193 73 .031 46.908 21.388 4.28289.53

5

Equal

variances

not

assumed

2.163 65.681 .034 46.908 21.686 3.60690.21

0

math

achievement

test

Equal

variances

assumed

.537 .466 2.697 73 .009 4.00704 1.48548 1.046486.967

60

Equal

variances

not

assumed

2.724 72.472 .008 4.00704 1.47092 1.075156.938

94

father's

education

Equal

variances

assumed

1.269 .264 2.314 71 .024 1.495 .646 .207 2.784

Equal

variances

not

assumed

2.304 67.068 .024 1.495 .649 .200 2.791

mother's

education

Equal

variances

assumed

1.258 .266 1.718 73 .090 .881 .513 -.141 1.903

Equal

variances

not

assumed

1.703 67.549 .093 .881 .517 -.152 1.913

grades in h.s. Equal

variances

assumed

.574 .451 -.903 73 .369 -.329 .365 -1.056 .397

Equal

variances

not

assumed

-.897 68.145 .373 -.329 .367 -1.062 .403

In the table of Independent Sample Test we will see under Levene's Test for Equality

of Variances & then sig. value of every independent value. There is no value which is

less then the significance value (0.05) so we will consider only Equality Variances


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Assumptions. Under Sig. (2-tailed) against scholastic aptitude test math is (0.031)

which is less then (0.05) then we have math achievement test, father's education,

mother's education, grades in h.s. respectively with there significance value (0.009,

0.024, 0.090, 0.369 respectively).

analysis of the reasons of students math achievement test

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