# A Quantitative Analysis Gender And Mathematical Achievement Education Essay

In quantitative research, the survey begins with the preparation of the hypothesis. This hypothesis is tested based on a model utilizing collected informations. Quantitative research provides counsel through these Numberss or informations. From these informations, decision can so be drawn through deductive logical thinking.

The quantitative method ‘s strength depends upon its dependability or repeatability. Furthermore, the consequences of quantitative research are based on mathematical theoretical accounts, recognized theories and regulations. The strong statistical foundation of quantitative research systematizes and formalizes the proceedings of a survey. The regulations that are applied to analyze and prove the informations are widely accepted, therefore, differences in readings are minimum compared to that of qualitative research.

There are two ways to near quantitative research utilizing the research design. The experimental design and non experimental design are both really wide classs. Basically, the difference between the two is how the independent variable is treated. In the experimental design, the independent variable is manipulated. A set-up is created where in there are controlled and experimental variables.

In a non-experimental design, the relationship or association between variables are explored based on given parametric quantities and informations. The independent variables are non manipulated and are hence, non randomized. Here, the research is much easier to carry on compared to an experimental 1. However, it should be clear that the relationship being tested here do non connote causality. Another term to depict this sort of design is correlativity design since, fundamentally, the ground for the relationship is left ill-defined.

The groundss from a non-experimental design are non every bit powerful as that of experimental designs. If an experiment is designed and executed decently, non merely can it find relationships, it can besides find causality. However, a cleanly executed experimentation is really hard to accomplish. It requires a batch of inventiveness, resources, experiences and clip.

As mentioned earlier, quantitative research design is a really wide class. The non-experimental design is subdivided into study surveies and relationship/difference surveies. The study designs are farther classified as description, exploratory and comparative. Difference or relationship surveies are categorised as correlational and developmental. Developmental designs have subgroups of cross-sectional, longitudinal and prospective, and retrospective / ex station facto ( Davies 2007 ; LoBiondo-Wood 2006 ; Brown 1998 ) .

In the involvement of this assignment, concentration will be based on statistical methods – descriptive and illative statistics. The former allows the research worker to depict and sum up informations whilst the latter allows a research worker to do anticipations and generalise findings based on the information.

## Purpose

The chief purpose of this survey is to research whether gender makes a difference to mathematics accomplishment in primary school. The survey has the intent of make fulling the spreads and to lend to the bing argument on gender and mathematics attainment.

## Background of the survey

This assignment informations draw from a longitudinal study of students in eight English primary schools to research the effects of gender on mathematics attainment. To guarantee proper representative sample and equal opportunity of choice, students were selected by simple random trying in rural countries, urban countries and different socioeconomic background. The research workers chose these students from enrolment registry to analyze the mathematics trial tonss in October and June

## Aims

To whether mathematics attainment is higher in males than females at twelvemonth 4 October trials.

To research if mathematics attainment is higher in males than females across old ages.

To make full spreads in this country and add to the argument on the relationship between gender and maths accomplishment at primary school.

## Hypothesis

Since this survey involves gender difference and mathematical attainment, nominal measuring will be used to clear up variables into classs which will do them reciprocally sole. This sort of measuring will let the least sum of mathematical use where the frequence of each event can be counted and the sum of each class is represented in per centum. In this instance the nominal variable is considered to be dichotomous – gender ( male / female ) . A research hypothesis is used to steer this survey. The independent variable ( forecaster ) is gender ( male and female ) and dependent variable ( standard ) is maths attainment as entire mean mark.

Null hypothesis ( H0 ) : Gender has no consequence on mathematics attainment.

Research hypothesis ( H1 ) : Gender has consequence on mathematics attainment.

## Legal-ethical issues

It is expected that the rights of the students ( topics ) have been good protected. It is besides assumed that the research workers explained the intent of the survey to parents and instructors and informed consent was obtained from the parents / instructors before the students undertook these trials. Besides to guarantee confidentiality of the consequences, research workers might hold given the participants with anonym and their names were non made populace ( Davies 2007 ; Sarantakos 2005 ) .

## Sample / Measures / process

This survey is based on the national trial in mathematics for students twelvemonth 2 ( about 7 old ages ) with different degrees though non all students achieve or take the trial as required. A graded random sample of 389 participants was obtained from the eight participating schools where there were 206 males and 183 females. A 95 % assurance interval was accepted throughout calculation.

## Outline of the research inquiry / country

This survey aims to find whether there is a relationship between sex and consequences in mathematics scrutinies. It will seek to reply the inquiry “ Is sex related to attainment? ” In order to turn to the research inquiry, statistical analysis utilizing descriptive and illative statistics shall be performed.

The descriptive statistics will cut down the majority of the informations by sum uping the characteristics as a whole. Measures of cardinal inclination such as mean, average and manner, and steps of variableness such as scope and standard divergence are normally used to depict datasets. Charts ( pie chart ) and graphs ( histogram ) will besides be produced to visually stand for the distribution of the information. A histogram in statistic is a graphical show of tabulated frequences which are shown as bars. It is a signifier of informations binning and shows what proportion of instances fall into each of several classs. However, these chart and graph simply describe or demo us the informations. They do non prove any hypothesis though they are really utile when it comes to exploratory informations analysis.

In nominal informations, manner is the descriptive statistic that is most normally used despite the fact that it is non stable and can change extensively from sample to try. However, descriptive statistics can merely depict the information. It does non give any illative penetration sing the relationships of the variables.

The void hypothesis is gender has no consequence on mathematics attainments. In order to prove this hypothesis, illative trials can be performed. The Pearson ‘s Chi Square trial for independency is really popular and widely used. However, that is applicable merely if the two variables being tested are both dichotomous and categorical. In the instance of this survey, merely the variable sex is categorical. The trial scores for the mathematics scrutiny is uninterrupted. In order to find if there is any relationship between the math tonss and sex, the Pearson ‘s Correlation coefficient is computed. In this trial of association, the void hypothesis being tested is the independency of the variables ( sex versus mathematics mark ) .

The t-test is besides a utile trial if there is any important difference between the average tonss of two groups. In order to use this trial, some premises about the discrepancy should be made foremost.

The Levene ‘s trial is a statistical tool that tests the equality of discrepancies. Therefore, if the discrepancies turn out to be equal or unequal, so the proper premise can be made for the t-tests ( Brown 1998 ; Diamond 2001 ; LoBiondo-Wood 2006 ) ..

## Methodological attack / Data of the analysis

Since this survey involves gender difference and mathematical attainment, nominal measuring will be used to clear up variables into classs which will do them reciprocally sole. This sort of measuring will let the least sum of mathematical use where the frequence of each event can be counted and the sum of each class is represented in per centum. In this instance the nominal variable is considered to be dichotomous – gender ( male / female ) . Statistical package SPSS for Windows, version 17.0 was used to analyze the informations. By utilizing descriptive statistics such as per centums and frequences, all the research variables were computed.

## Consequences

Chart 1. A pie chart that shows the demographics of the respondents.

Table 1. Basic Frequencies

Minimum

Maximum

Mean

Std. Deviation

Y4_O_M_age

5.35

11.93

8.7945

1.3

Y4_J_M_age

5.778

12.138

9.50704

1.3

Y5_O_M_age

6.49

13.06

9.4287

1.3

Y5_J_M_age

6.76

13.51

10.2508

1.5

Y6_O_M_age

7.532

14.392

1.09232E1

1.6

Y6_J_M_age

7.630

14.294

1.17147E1

1.5

## Table 2. Distribution of tonss by sex

Sexual activity

Nitrogen

Mean

Std. Deviation

Std. Error Mean

Y4_O_M_age

Male

193

8.9

1.3

0.1

Female

174

8.7

1.

0.1

Y4_J_M_age

Male

196

9.7

3

0.1

Female

177

9.3

1.4

0.1

Y5_O_M_age

Male

190

9.6

1.3

0.1

Female

167

9.2

1.2

0.1

Y5_J_M_age

Male

185

10.4

1.5

0.1

Female

166

10.1

1.4

0.1

Y6_O_M_age

Male

170

1.1

1.5

0.1

Female

158

1.1

1.6

0.1

Y6_J_M_age

Male

169

1.9

1.5

0.1

Female

153

1.2

1.4

0.1

Histogram

## Distribution of trial tonss of Y4 October mathematics age

Figure 1. Shows the distribution of trial tonss of Y4 October mathematics age

## The distribution of trial tonss of Y4 June mathematics age

Figure 2. Presents the distribution of trial tonss of Y4 June mathematics age

## The Distribution of trial tonss of Y5 October mathematics age

Figure 3. Shows the distribution of trial tonss of Y5 October mathematics age

## The Distribution of trial tonss of Y5 June mathematics age

Figure 4. Shows the distribution of trial tonss of Y5 June mathematics age

## The distribution of trial tonss of Y6 October mathematics age

Figure 5. Shows the distribution of trial tonss of Y6 October mathematics age

## The distribution of trial tonss of Y6 June mathematics age

Figure 6. Shows the distribution of trial tonss of Y6 June mathematics age

## Correlations

Table 3. Pearson ‘s Correlation

Sexual activity

Y4_O_M_age

Pearson Correlation

-.088

Sig. ( 2-tailed )

.094

Nitrogen

367

Y4_J_M_age

Pearson Correlation

-.119*

Sig. ( 2-tailed )

.021

Nitrogen

373

Y5_O_M_age

Pearson Correlation

-.139**

Sig. ( 2-tailed )

.009

Nitrogen

357

Y5_J_M_age

Pearson Correlation

-.106*

Sig. ( 2-tailed )

.046

Nitrogen

351

Y6_O_M_age

Pearson Correlation

-.104

Sig. ( 2-tailed )

.059

Nitrogen

328

Y6_J_M_age

Pearson Correlation

-.065

Sig. ( 2-tailed )

.247

Nitrogen

322

Table 4

## Independent Samples Test

Levene ‘s Test for Equality of Discrepancies

t-test for Equality of Means

F

Sig.

T

df

Sig. ( 2-tailed )

Average Difference

Std. Error Difference

95 % Confidence Interval of the Difference

Lower

Upper

Y4_O_M_age

Equal discrepancies assumed

1.6

.21

1.68

365

.09

.23

.13

-.04

.50

Equal discrepancies non assumed

1.69

364.54

.09

.23

.13

-.04

.49

Y4_J_M_age

Equal discrepancies assumed

.71

.40

2.31

371

.02

.31

.14

.05

.58

Equal discrepancies non assumed

2.30

359.29

.02

.31

.13

.05

.59

Y5_O_M_age

Equal discrepancies assumed

2.75

.09

2.6

355

.01

.35

.13

.09

.62

Equal discrepancies non assumed

2.66

354.83

.01

.35

.13

.09

.62

Y5_J_M_age

Equal discrepancies assumed

.56

.46

2.0

349

.05

.31

.16

.01

.62

Equal discrepancies non assumed

2.0

347.12

.05

.31

.16

.01

.63

Y6_O_M_age

Equal discrepancies assumed

.04

.85

1.89

326

.06

.32

.17

-.01

.67

Equal discrepancies non assumed

1.89

323.36

.06

.33

.17

-.01

.67

Y6_J_M_age

Equal discrepancies assumed

.41

.52

1.16

320

.25

.19

.16

-.13

.51

Equal discrepancies non assumed

1.16

319.29

.25

.19

.16

-.13

.51

## Discussion

There are entire of 389 respondents in this survey. Based on Chart 1, 47.04 % of the respondents are females and 52.96 % are males.

Six mathematics scrutiny tonss were investigated in this survey, twelvemonth 4 October and June math age, twelvemonth 5 October and June math age, twelvemonth 6 October and June math age.

Based on Table 1, the average mark of pupils for the twelvemonth 4 October math age is 8.79, and with a minimal mark of 5.35 and a upper limit of 11.93. The average mark of pupils for the twelvemonth 4 June math age is 9.51, and with a minimal mark of 5.78 and a upper limit of 12.14. The average mark of pupils for the twelvemonth 5 October math age is 9.43, and with a minimal mark of 6.49 and a upper limit of 13.06. The average mark of pupils for the twelvemonth 5 June math age is 10.25, and with a minimal mark of 6.76 and a upper limit of 13.51. The average mark of pupils for the twelvemonth 6 October math age is 1.1, and with a minimal mark of 7.53 and a upper limit of 14.39. The average mark of pupils for the twelvemonth 6 June math age is 1.2, and with a minimal mark of 7.63 and a upper limit of 14.29.

The average tonss for the twelvemonth 6 October and June math age are really little. This figure seems incorrect at first. But the ground why the agencies are really little is due to the fact that a batch of respondents do non hold available tonss for these scrutinies. SPSS uses the entire figure of respondents as the factor for the calculation of the agencies. However, if you look at the lower limit and maximal tonss, the computed agencies would non fall between the two values. But, if the mean scores per test were computed without taking into consideration the losing values, it would be valid. The steps for fluctuation nevertheless, are all valid since losing values do non impact the calculation for the scope. The scope is merely the difference between the maximal mark and the minimal mark.

So, in order to obtain the average tonss without taking into consideration the losing values utilizing SPSS, the histograms for each of the 6 math scrutiny were obtained. The drumhead statistics that are used in the calculation of the histograms are valid. Since the values of the average tonss and standard divergences are used in bring forthing the histograms, the losing values are non taken into consideration for the calculations.

In order to find the presence of any relationship or association between sex and the math tonss, the Pearson ‘s correlativity coefficient is computed. Based on Table 3, tonss for Y4_J_M_age, Y5_O_M_age and Y5_J_M_age are correlated with sex at a 0.05 degree of significance.

The Levene ‘s trials show that for each of the math tonss, the discrepancy of the males is equal to the discrepancy of the females. Therefore, for the t-tests, equality of discrepancies shall be assumed.

Based on table 4, for Y4_J_M_age, there is a important difference between the average tonss of the males and females at the 0.05 degree of significance. The same consequences hold for Y5_O_M_age and Y5_J_M_age.

The consequences of the Pearson ‘s trial for correlativity and the t-tests are consistent.

## Conclusion / recommendation

A generalisation about the overall association of sex with mathematics attainment can non be evidently generalized. From the six sets of math tonss that were tested in this survey, merely three of those sets of tonss appear to hold an association with sex. The three sets of tonss that were found to be associated with sex are the tonss from twelvemonth 4 June math age, twelvemonth 5 October math age and twelvemonth 5 June math age.

Undeniably, this survey has suggested that farther in-depth, longitudinal surveies that gender makes a difference to mathematical attainment will be a manner frontward. It can besides be recommended that attention should be taken before one can utilize the result of the survey as statistically the void hypothesis is accepted but in world that may non be instance. This decision has merely been based on the statistical consequences computed and analysed. Furthermore, it should be remembered that the strength and quality of any survey / research grounds are enhanced by repeated tests which have consistent findings. This will thereby increase the credibleness of the findings and pertinence to any pattern. But this can non be said to be the instance, for case, some rows were deleted due to the fact that some pupils had non sat any trial the month and in making so might hold affected the full consequences.