Predicting Student Proficiency Test Scores
Transcript of Predicting Student Proficiency Test Scores
Outline of the project
Abstract
Introduction
Literal review
Methodology
Analysis of results
Conclusion
Abstract
This paper attempts to examine the relationship between the family income and the
test score. The poverty and others factors affects on the school district's performance.
The Cincinnati Enquirer gathered data from Ohio Department of Taxation (The
Cincinnati Enquirer, November 30, 1997). The methodology used in this study is
multiple regressions to indicate the relation between the factors which are existing in
the report such as (family income, ADC (Aid for Dependent Children), the percentage
of students who pass exams and the percentage of students who qualify for free or
reduced price lunches. A portion of the data collected for the 608 school district.
Introduction
Many people have commented on the relationship between income levels and test
scores in public schools. Test scores from schools in more affluent neighborhoods
tend to be better than test scores from schools in poorer neighborhoods
In the United States, public schools are run by school districts, which are independent
special-purpose governments, or dependent school systems, which are under the
control of state and local government.
Proficiency scores measure a student's mastery of skills and understanding in a topic
area. The evaluation for the school district is very difficult to determine exactly what
factor which affect on test score. In our case family income played a critical role more
than teacher pay, Class size and number of instructor assistant is the strongest
predictor of how students will perform. The analysis indicate that each public school
district's fourth, sixth, ninth and twelfth grade proficiency exam scores along with
Median family income and the degree of welfare and the free or reduced priced lunch
which children have it. Although the family income gives many of facilities but
sometimes' 'Poor kids can achieve at the same levels as affluent kids. Poverty just
makes it harder. We used multiple regression to calculate Correlation analysis so,
dependent variable which the variable that is being predicted (the family income) and
independent variables which the variables that provides the basis for estimation
(percentage of students passing the tests.
ADC is the percentage of each school district's student on ADC; Aid to Families with
Dependent Children (AFDC) was a federal assistance program in effect from 1935 to
1996, which was administered by the United States Department of Health and Human
Services. This program provides financial assistance to children whose families had
low or no income.
It was criticized for offering incentives for women to have children, and for providing
disincentives for women to join the workforce
the percentage of Free lunch or reduced-price are the percentage of students who
quality for free or reduce lunch.
It means a lunch served by a school district participating in the national school lunch
program to a student qualifying for national school lunch program benefits based on
family size-income criteria.
Literal review
Donald Haurin co-author of the study and professor of economics at Ohio State
Student scores do not affect on the education issues only but sometimes it convert the
district's house prices high to low Or vice versa. Homebuyers pay attention to schools
when considering which house to buy.
Among blacks without a high school education, almost half (47.1%) of those age 25-
34 had incomes below the federal poverty.
Among black women age 25-34 without a high school education, nearly two out of
three (61.5%) lived in poverty.
Notice that the family income reflects strong effect on student proficiency test scores,
because when all members family live in the atmosphere of the poverty, they don't
care. They will look for how can cover their needs not how can improve their children
proficiency score. They will exploit their children to improve family positron better
than going to high school education or to deduct part of family income to pay high
expenditure in professional school.
Differences in family incomes, education levels reflected in student test scores. So
educators say children who grow up in poverty are not doomed to fail in school.
The result is that overall funding for districts with high poverty rates is often higher
than the funding for more affluent districts.
Test score or the student?
A disadvantaged student in a different school district could end up improving his test
scores more than the privileged student, all because he went to a high-quality school.
But in the end, if his test scores are not as high as that of the privileged student, the
school will not get as much credit.
Teachers see the problems brought by poverty first hand: First-graders who come to
school without knowing their numbers, alphabet or full name. Parents' moves around
the city force their children to change schools annually.
"The money is not always spent wisely," said Ohio Senate President Richard
Finan. R-Evendale. "Sometimes it's difficult to know what it's spent on."
"If you pay people more money and they do the same old things, it doesn't improve achievement," we have to exploit the money to create new approach in running the system of education. No kid ever learned chemistry because you put a $20 bill on his table. He learns because you bought him a book or a chemistry teacher,"
Donald Haurin
Parents who own their own home may be helping to boost their children’s educational achievements and even reduce behavioral problems, according to a new nationwide study.
The research showed that for children living in owned homes rather than rental units, math achievement scores are up to 9 percent higher, reading achievement is up to 7 percent higher and behavioral problems are 1 to 3 percent lower.
One problem for school districts is that the value-added approach is difficult for researchers to measure, and difficult for the public to understand. Proficiency test scores, however, are readily available and easy to understand, which makes them more influential with the public, Haurin said.
Results for: Data
Regression Analysis: Median Income versus Rank; % Passed; ...
The regression equation is
Median Income = 9384 + 1.94 Rank + 256 % Passed + 130 % on ADC
- 210 % Free Lunch
First: There are relations between Median income and (Rank, % passed, on ADC and
free lunch);
For each the rank School or country will achieve, the median income will increase
by1.94$, ceteris paribus.
Each the percentage of passed student increase the median income will goes up by
256$, ceteris paribus.
Each the percentage of ADC increase, the median income will increase by 130$,
ceteris paribus.
Each the percentage of free lunch increase, the median income will decrease by 210$.
R-Sq = 56.0% fifty six percent of the variation in the median income is accounted for by
these four variables.
Correlations: Rank; % Passed; % on ADC; % Free Lunch; Median Income
Rank % Passed % on ADC % Free Lunch
% Passed -0.973
% on ADC 0.698 -0.755
% Free Lunch 0.746 -0.790 0.889
Median Income -0.667 0.694 -0.593 -0.704
% passed and % free lunches have strong Correlation with median income and % on ADC has
the weakest correlation with median income.
The correlation between the percent on ADC and percent of free lunch is 0.889 which is
above the 0. 7 rule of thumb level, indicating multi collinearly. One of those two variables
should be dropped.
Analysis
The Cincinnati Enquirer, November 30, 1997, Collected data on the math, reading,
Science, writing and citizenship proficiency exams given to fourth-, sixth-, ninth-, and
twelfth grades in early 1996. When we use the statistic is the sciences of collecting,
analyzing and interpreting data to assist in making more effective decisions.
The data collected for the 608 School district. The variables classified into dependent
and independent (x,x,x) variables. Therefore, the multiple regression and Correlation
analysis, is the better way to help us better explain or predict the dependent variable
Y=a + b1X1 + b2X2 + b3X3+b4X4
Median Income = 9384 + 1.94 Rank + 256 % Passed + 130 %
on ADC- 210 % Free Lunch
Y (median income) is the value of the Dependent variable what is being predicted or
explained
a (Alpha) 9384 is the Constant or intercept, indicates that the regression equation
intersects the Y axis at 6.3 when both (Rank, %passed ,%ADC, free lunch ).
The b2 of 1.9 indicates that for each increase of one in the Rank, the median will
increase 1.9 dollar in the median income, ceteris paribus. The b2 of256% indicates
that for each increase of one student passing the exam, the median income will
increase by 256 dollars, ceteris paribus. The b3 of130% indicates that for each
increase one percent in the Aid for dependent Children, the median income will
increase by 130 dollars, ceteris paribus. The b3 of 210 indicates that for each increase
one percent-of free lunch, the median income will decrease by 210 dollars.
Coefficient of multiple Determinations: the percent of variation dependent variable Y,
explained by the Set of independent variables x1,x2,x,3,x4, so R-Sq = 56.0%,
indicates that the percent of variation in the median income, explained by the set of
(percentage of students passing the test, percent on school district's on ADC, percent
on free lunch.
The characteristics of coefficient of multiple indicates that, If can range from 0
indicates little association between the set of independent variables and dependent
variable, So R = 0.56 is near to1 means that, the relation between the median income
(dependent variable) and the independent variables for instance Rank of Schools,
percent of passing student pass, percent of school district's students on ADC and the
percent of free lunch, are the percentage of students who Quality for free or reduced
price lunch ) is the strong association.
Coefficient of Multiple Determination= ssR/ss total
7603435585 /13580287552=0.56
By Minitab output, use the regression Sum of square, SSR then divided by the total
sum of squares, SS total.
The ANOVA Table uses to calculate the residual or error variation, this is random
error. Df (Degree of freedom) in the" repression "row is the number of independent
variables, so K = 4. The degrees of freedom in the "Error "is n-(k+1) = 608-(4+1)
=603.
Total variation = SS total =13580287552 and Residual error or error variance = SSE
=5976851967
Therefore, The regression variation = ss total - SSE
13580287552 -5976851967 =7603435585
Correlations: Rank; % Passed; % on ADC; % Free Lunch; Median Income
Using correlation Matrix indicates that, % passed and % free lunches have strong
Correlation with median income and % on ADC has the weakest correlation with
median income indicates that, the correlation between the percent on ADC and
percent of free lunch is 0.889 which is above the 0. 7 rule of thumb level, indicating
multicollinearity. One of those two variables should be dropped.
We noticed that the Rank it is not significant has effects on correlations.
Correlations: % Passed, % on ADC, % Free Lunch, Median Income
% Passed % on ADC % Free Lunch
% on ADC -0.755
% Free Lunch -0.790 0.889
Median Income 0.694 -0.593 -0.704
The result indicates that, the same result 0.889 is the correlation between the percent
of ADC and percent of free lunch, then drop free lunch because of it lower significant
than ADC.
Inferences in Multiple linear Regressions
Multiple regression analysis has been viewed only as a way to describe the
relationship between a dependent variable (the family income) and several
independent variables (Rank, % passed, % free lunch, % ADC).
Global test: testing the Multiple Regression model
The null hypothesis is H0:B1=B2=B3=B4
The alternate hypothesis H1: Not all the BI 'S are 0
The degree of freedom is n- (k+1) 608-(4+1) =603.
K is the value corresponds to the number of independent variables.
The critical value of F is found in appendix B.4. Using the table for the.05
significance level, move horizontally to 4 degree of freedom in the numerator, then
down to 603, because the maximum value 120 and then infinity. Therefore we choose
120 to give the critical value- 2.45.
Now If F value is less than or equal 2.45, we Do not reject the null hypothesis. From
Mini tab data F equal 191.78 so we reject H0 (null hypothesis) and accept the
alternate hypothesis, H1.
Evaluating individual Regression coefficient
The critical value for t is in Appendix B-2 For a two tailed test.
For Rank for % passed for% ADC for free lunch
H0:B1=0 H0:B2=0 H0: B3=0 H0: B4=0
H0:B2=0 H0:B2=0 H0: B3=0 H0: B4=0
THE DECISION
The test statistic is the t distribution with n -( k+1)= 608 -( 4+1)= 603 degree of
freedom, Using the .05 significance level and Appendix B-2. The decision rule is to
reject Ho if the computed value of t is less than- 1.972 or Greater than 1.972.
The T value of rank equal 0.60, so the decision will do not reject Ho, the null
hypothesis.
The T value of passing student Exam equal 3.59, so the decision will reject Ho and accept H1.
The T value of percent of ADC equal 4.32, so the decision will reject Ho and accept H1,
The (T- value) of percent of free lunch equal -9.60, so the decision will reject H0 and accept H1.
CONCLUSION
The poverty has a strong effect on the students and the school district's performance.
There is strong correlation between the family income and student score. Therefore
the government should increase the fund to support the school district. When parent
have high income level and they own private houses will affects on their children
performance. Homeownership seems to benefit children because the environments in
homes – including such things as safety, maintenance and the availability of
educational materials – are on average better than those in rental units, the study
suggests. In addition, the greater stability of homeowners is good for children’s
development.
Teacher salary, having a master’s degree or higher, years of teaching experience, and
extra academic opportunities stand out as variables contributing in some degree to
actual district performance.
We have reached an extremely important fact. It is clear that home environment is the
chief factor influencing success of children in school. Statistically, socio-economic
status of the family is the major factor. It is clear that we must focus on the home
environment to improve public education in the U.S. There are two approaches. The
first is to augment the home environment by external changes and improvements.
The second is to change the home environment itself. The latter is actually simple,
but not easy, mainly because it requires a transformation in the way we consider the
family.
Reference
Use Methodology and analysis from (statistical techniques in business and economic) lind/Marchal/Wathen
. By Julie Mack | Kalamazoo Gazette (Differences in family incomes, education levels reflected in student test scores
By Jon Hurdle new state test scores show less than expected drop in student proficiency
STUDENT PROFICIENCY TEST SCORES IMPACT HOME VALUES, STUDY FINDS Written by Jeff Grabmeier
Improving SES Quality State Approval, Monitoring, and Evaluation of SES Providers Steven Ross, Jennifer Harmon, and Kenneth Wong
With assistance from Janis Langdon, Lynn Harrison, James Ford, and Laura Neergaard
Performance-Based Rewards for Teachers: A Literature Review
Owen Harvey-Beavis*For distribution at the 3rd Workshop of Participating Countries on OECD’s Activity Attracting,Developing and Retaining Effective Teachers4-5 June 2003, Athens, Greece