Relationship between Maths Scores and Gender

The Research Method Cycle and its Major Components

Case 2

Among the many denunciations of quantitative research, the rejection of the null hypothesis, based on predictions, statistical analysis, regression analysis in particular, stemming from data collection, is viewed as problematic within the research continuum, due to the issues of significance (Berk,2004;Creswell, 2009; Myers, Gamst, & Guarino,2006). The research method cycle considers the null and alternative hypotheses for the research questions and allows for either statistical tests to accept or reject the null hypothesis the research method cycle also entertains a literature search. When it comes to substantiate a research method process, the use of literature review is of utmost importance, the writer/researcher contends. A literature review offers a theoretical lens for interpreting how some studies contribute to an intended or specific research inquiry.

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In this assignment, the learning outcomes set to review, distinguish the patterns of hypotheses, and research questions appear to be merged in a continuum of three articles that seems to create a framework for statistical analysis. The writer/researcher is privileged to be part of the learning process offered in this course. However, the briefly required discussions for the readings seem to constrain the analysis usually seen in statistical techniques. The writer/researcher claims it is due to the chosen research topics (education), methods that are limited in scope, and seems to crowd the framework for considering the research variables, and questions, not elucidated in all three articles. This quantitative experience needs further teaching materials beyond the veil of learning quantitative analysis from the veracity of hard and old articles, not related to health sciences, the writer/researcher further contends. It is hoped that the analysis is objectively captured and graded as such. It seems that more efforts are needed from this course. In any fashion, the framework for analysis is set, and the dilemma to apply, and elucidate the required answers must be minimized.

Seeing the research method cycle as a complete package is necessary to make inferences in a research study especially when general linear models are used to perform regression analysis, t-test, ANOVA, MANOVA, etc., from large data sets (Berk, 2004). In the three articles, one key factor was that the sample sizes were large, and the data came from existing populations. Consistent with the many variables seen in the articles, it is plausible to say that a multiple regression model could have been essential to generalize from predictive variations in the variable values.

Part I Aske and Corman (2001)

 This research article posited that to determine if a relationship exists between school characteristics and students, based on standardized tests performance in the metropolitan Denver area, one needs to substantiate the concept of accountability through statistical analyses that show correlations between 6 variables: 1) student attendance, 2) percent of students eligible for free lunch, 3) student enrollment stability, 4) student-teacher ratio, 5) average number of teachers’ absence, and 6) the percent of  tenured teachers (Aske & Corman, 2008, p.3). The most significant variables were: 1) student attendance, 2) percent of students eligible for free lunch, 3) student enrollment stability, and 6) the percent of tenured teachers.

For a population sample consisting of 6 regions in the greater metropolitan Denver, Colorado region, there was a positive correlation between the schools’ composite scores or student performance (the dependent variables), and the independent variables: 1) student attendance, 2) percent of students eligible for free lunch, 3) student enrollment stability. In terms of rationale for the chose variables, it appears that the research’s focus to assess relationship between the student’s performances and the schools’ charactersitics, was guided by the notion of accountability, which was based on school districts’ status of unsatisfactory to excellent (p.2). Beyond this rationale, the writer/researcher saw other elements of bias attached to the variable 2: student eligible for lunch. The literature presented offered a limited view that student’s performance was tied to free lunch. The regression analysis presented utilizing minority students (Black and Hispanics) excluding white students, linked to poverty seems to also suggest that there is a correlation between economic status, learning, and student’s performances. The multicollinearity claim presented was not sufficient due to the limited chosen independent variables, the writer/researcher claims. In this case, a multiple regression analysis could have been done to assert such claim. In fact, the research’s objective to assess students test performances with schools’charcteristics was well delineated. As stipulated by Myers, Gamst, & Guarino (2006), if the research problem expresses concerns that imply a prediction of one variable in relation to knowledge of others, one should have been able to see a model in which the criterion variable was well analyzed. In this research, also it was not evident how schools ‘characteristics contributing to student performances were only related to only 4 variables: attendance, free lunch, student enrollment stability, and percent of tenured teachers. There were some missing elements using the poverty variable to fostering a relationship between drops in testing performance grades. A t– Test could have been performed, in this instance to inform that only positive and negative effects are statistically significant forecasters in the model. (Myers, Gamst, & Guarino, 2006, p.172).

The writer/researcher adheres to the notion that student enrollment stability (SES) correlates with performance, and teacher’s tenure, although the data did not show how teachers’ tenure contributed to higher tests performances. Using a 6 academic years framework for the study, added some benchmarks for policy makers. The writer/researcher could not ascertain why the researchers used the 2001-2002 time period to tie increase in students’ attendance rates with students’ proficiency across the 6 years period. The result can be a type 1 error, in which, a researcher claims that there is a statistical significance where none exists, by rejecting the null hypothesis. Another consideration is that the authors could have performed some regression analysis with numerous times series data within a linear regression parameter. In this case, year 2003 to 2007 showing various test performance scores across counties and schools would have been captured and analyzed. In addition, the writer/researcher did not see any hypothesis formulation.

Part II Greenblatt et al. (2004)

The striking contrasts and difficulties presented by Greenblatt et al.’s (2004) article on implementing the research question dealt with a series of long articles that the authors canvassed to tackle the research questions issues from a qualitative and quantitative standpoint. The writer/researcher considered the articles written by Wolf (2003), Gordon (2000), and Sturm (2003). The writer/researcher could not download the remaining articles.

In all the articles, one salient concern was how to construct research qualitative and quantitative research dealing with student learning, instructional methods, and children exploration. Wolf’s (2003) article sought to establish a balance between students experience and information literacy skills relating to curriculum design, and information problem solving. The salient research question was qualitative in nature: How does Big 6 support metacognition strategies and knowledge in students? It was a qualitative research question in which students’ subjective experiences were elucidated to determine factors affecting learning in relation to knowledge acquisition, responsibilities and strategies. The sample size consisted of 23 students: 17 Caucasians and 6 East Indian Indus. Contrarily with Aske and Corman’s(2008) research whose an emphasis was placed on percent of students eligible for free lunch and testing performances, the students in this research were not eligible for free or reduce lunch , due to their upper middle-class status. No correlation existed between the knowledge acquisition strategies, and tasks variables.

Gordon (2000) asked the pertinent question: Is there an instructional method more effective than another is/? The goal was to address the behavior of 10^th grade students involved in research projects, based on classroom instruction, and genetics. It was a mixed-methods research. The purpose of mixed-methods research allows for an associative qualitative and quantitative framework to better understand the meaning, perceptions, or views of a sampled population, quantifying the research questions, thus generating statistical analyses (Creswell, 2009). Sturm (2003) posited that North Carolina Children from ages ranging from 2 to 18 have a variety of learning interests before entering school or a library. Using a 2000 survey fostered by the State Library of North Carolina, the research asked the following questions: What do children find interesting? What topics do children prefer exploring? (p.1).

Part III Fisher and Frey (2008)

At the heart of Fisher and Frey’s (2008) article, the writer/ researcher found at the onset, several problems. The statistical analyses were absent. The first problem addresses the issue of sample size and population. Out of 88 teacher surveys, and 500 student surveys, one would be inclined to accept a sample from a population of 588 participants, but this set of participants in which 13 teacher interviews, 12 student interviews, and 30 classroom observations were conducted, seems to suggest that the sample size was not representative to generalize about the unknown teachers and high school populations.

The second issue refers to the qualitative nature of this research, in which a huge sample size was considered. It is argued that for qualitative strategy of inquiry, small sample sizes are important (Creswell, 2009). Albeit such reality, this research could have been better steered as a mixed-methods design. Wooley (2009, p.17) sees integration of data in adopting a mixed- methods approach, and a narrow view of the world is not needed.

The third issue deals with the ambiguity of the purpose of the study which was “to explore the similarities and differences between high schools students and their teachers’ perceptive on the usefulness of content literacy strategies” (p.1). In expressing this purpose, the researchers seemed to indicate that some correlations were essential to determine, or a relationship pattern was to establish. In this case correlation covariance’s would need to be determined to predict how well an interrelationship between high school students and teachers’ perceptive could exist , based on specific variables (Myers, Gamst, & Guarino, 2006). The research was qualitative, but sent mixed signals about an N sample size. Furthermore, the “content literacy strategies for learning” parameter greatly differed from the students, and teachers’ perspectives. Additionally, the research on teachers’ use of strategies was strictly pedagogical, and offered no basis for the students’ content approach to literacy.

Part IV

To complete table 3, the writer/researcher opted to use the data set with the English scores to generate the statistical analyses such as t-test, one way ANOVA, two way ANOVA, and Chi-Square test of independence. The wrier/researcher substituted the variable English score to Mathscore because he could not find the data set from Table 3 with such data view in SPSS. The sample size utilized consists of N= 1410.

The following research questions with the corresponding hypotheses are proposed with their corresponding statistical tests.:

RQ1: Can math scores lead to student improvement across gender lines?

H1_null: math scores lead to students’ improvements across gender lines

H1_alt: there is a statistical difference math scores are more likely to be associated with increased performance among female students.

RQ2: Can math scores negatively have an impact across gender lines?

H2_null: low math scores are more likely to negatively reflect among male students

H2_alt: there is a statistical difference that math scores likely affect male students’ performance

RQ3:what is the significance of math scores outcomes among gender lines?

H3_null: math scores are expected to increase across gender lines

H3_alt: there is statistically significant difference of math scores across gender lines

RQ4: what is the relationship between math scores and gender lines?

H4_null: math scores inversely increases across gender lines

H4_alt: there isno statistically significance difference between math scores across gender lines

RQ5: What is the significance of math scores across gender lines?

H5_null: Attitudes towards math scores performance are directly related to students’ performances across gender lines.

H5_alt: There is no statistical significance that math scores affect student’s attitudes across gender lines.

Table 4 T-test shows the one-sample statistics performed. The one- sample t-Test in table 5, a predictor of weight suggests a 2-tailed statistical significance between math scores and gender with a 95% CI with lower value of 80.46 and upper value for math test scores, and gender lower value of 1.36, and upper value of 1.46.

A one-way ANOVA was conducted relating the type of math test scores students received as satisfactory. The observed F values in table 6a, F (3, 3) =3.814 and 1.941 were not significant, p>.001. The ANOVA in table 6, and table 8  Levene’s test of equality of error of variances to test the null hypothesis that the error variance of the equality across groups (gender), shows the Levene’s tests for math test scores were not significant across the variables, and gender, indicating homogeneous variances. It satisfied research question 4 with the associated alternative hypothesis 4:

RQ4: what is the relationship between math scores and gender lines?

H4_alt: there isno statistically significance difference between math scores across gender lines. In table 9, the test between subjects, the F for the corrected model for StudentGen also shows no significant with a partial eta squared .002, which is p >.001.

 In performing a two way ANOVA, the mean differences observed in tables 10, 11, and 12 show for male and female were not significant at the .05 level. The writer/researcher used the previous education data set to perform the statistical analysis. Using paired sample statistics, as shown in table 13 and table 14, the same observations shows across math test scores and student gender lines, the standard deviation was normally distributed, and a weak correlation exits between the variables. This finding seems to satisfy research question 2 and its hypotheses:

RQ2: Can math scores negatively have an impact across gender lines?

H2_null: low math scores are more likely to negatively reflect among male students.

Nonetheless, in table 15, the paired sample test showed that math test scores are significant across student gender lines. The corresponding research question is RQ3, and the corresponding hypotheses:

RQ3:what is the significance of math scores outcomes among gender lines?

H3_null: math scores are expected to increase across gender lines.

H3_alt: there is statistically significant difference of math scores across gender lines.

A Chi-Square performed shows in table 16 and 17 that equal probabilities occur within the StudentGen variable, and distribution of math test scores was normal with mean =81, and standard deviation (SD) of 15.524. Thus the null hypothesis is rejected.

                        Table 3: Variables and Statistical Analyses

Table 6 Univariate Analysis of Variance                                  

Table 11 Univariate Analysis of Variance Two way ANOVA

References

• Aske, D., & Corman, R. (2008). The relationship between school chracteristics and student performance on standardized tests in the Denver metro region. Arden, 13(2), 2-7.
• Berk, R.A. (2004). Regression analysis. A constructive critique. Thousand Oaks, CA: Sage.
• Creswell, J.W. (2009). Research design. Qualitative, quantitative, and mixed methods approaches. (3^rd ed.). Thousand Oaks, CA: Sage.
• Fisher, D., & Frey, N. (2008). Student and teacher perspectives on the usefulness of content literacy strategies. Literacy Research and Instruction, 47(4), 1-14.
• Greenblatt, M., & Dickinson, G., & Simpson, C. (2004). Implementing the research question. Knowledge Quest, 33(2), 1-5.
• Myers, L. S., Gamst, G., & Guarino, A.J. (2006). Applied multivariate research. Design and interpretation. Thousand Oaks, CA: Sage.
• Wooley, C.M. (2009). Meeting the mixed methods challenge of integration in a sociological study of structure and agency. Journal of Mixed Methods Research, 3(1), 7-25.