RESULTS AND DISCUSSION

RESULTS AND DISCUSSION

Data Analysis

Data analysis is the most essential chapter of the study. The chapter justifies the literature through the generation of the results using the right data analysis technique (Onwuegbuzie & Frels, 2016). The study adopted various data analysis techniques to answer the research question. Both descriptive and inferential data analysis techniques were adopted. Descriptive statistics involved visual displays such as histograms, bar graphs, and box plots. The visual provides the general distribution of the data set. Inferential statistics involved the use of t-test and regression analysis. The t-test analysis is key in examining the difference in scores across different groups. Regression analysis establishes the relationship between dependent and independent variables. The generation of results was through the use of R-studio software.

Research Question

Is there a relationship between attitude in math and overall GPA score?

Hypothesis

H0: There is no relationship between attitude in math and overall GPA score

H1: There is a relationship between attitude in math and overall GPA score.

Histogram

The Histogram below provides the distribution of GPA scores among the students. The score is positively skewed as illustrated in the histogram.

Figure 1: Distribution of GPA scores

Bar Graph

The graph below provides an overview of how gender is distributed. Most of the scores captured were from the female candidates.

Figure 2: Distribution of respondents by Gender

Box Plot

The box plot below provides the distribution of GPA scores across gender. The graph shows that females have a high GPO compared to males.

Figure 2: Distribution of GPA Score by Gender

Scatter Plot

The plot below shows the relationship between GPA score and level of efficiency in Math.

Figure 2: Comparing GPA score with how good a student is in Math

Two Sample-test

Two Sample t-test is an inferential statistical technique that compares means for two groups (LEE, 2019). The dependent variable is the overall GPA score while the independent variable is gender. The results from the t-test show that there is a significant difference between females and males in terms of the overall score.

Bartlett test of homogeneity of variances

data:  OVERALLGPA by gender

Bartlett’s K-squared = 14.533, df = 1, p-value = 0.0001377

Regression Analysis

Regression analysis is a statistical technique that is used to establish whether a relationship exists between dependent and independent variables (Sen & Srivastava, 2013). The report generates values of the coefficient of determination from which an explanation regarding the variation of dependent variable done. The coefficient of determination in regression analysis explains the proportion of change in the dependent variable that is caused by the independent variable (Liu, 2017). The technique further produces a model in which the coefficients are provided to explain the relationship.

The study adopted the use of multiple regression analysis. The purpose of using regression analysis is to establish the impact of the independent variable on the dependent variable. The dependent variable in the study was the overall GPA score while the independent variables entailed the following attitude components:

1. Affective
2. Cognitive Capability
3. Value
4. Difficulty
5. Interest
6. Effort

The results of the analysis are as from the tables below.

Table 1: Table for the measures of central tendency and variation

Table 2: Table for the coefficients of the regression model

Table 3: table for the coefficient of determination

Discussion

The model summary table provides the values of coefficient of determination (R squared) and adjusted R. The model has one predictor variable hence coefficient of determination shall apply. The coefficient of determination is 0.4053 (R²=0.4053). The value signifies that the model accounts for or explains 41% of the variability in the overall GPA. The remaining 59% of the variability in overall GPA is unexplained and other factors not in the model might be explaining such variability. The p-value shows that the model is a significant predictor of over performance with ;( F (5,168) =0.111, P=0.02354). The p-value is less than 0.05 hence we reject the null hypothesis that states that there is no relationship. Therefore, Affective, cognitive ability, value, difficulty, interest, and effort have a significant impact on the overall GPA score. The coefficient table provides the coefficient of each predictor variable. Given the coefficient, the model is as follows.

Overall GPA Score = 1.29064 + 0.03817(Affective) + 0.08503(Cognitive Capability) + 0.02787(Value) 0.04527 (Difficulty) + 0.16800 (Effort)

The findings providing essential insight for students wishing to pursue a statistically related course. The determinants in the model provide the bases for improvement in the overall GPA. Improving effective aspect by a unit improves the performance by 0. 03817. This implies an effective attitude such as feeling intimated solving a statistical problem, feeling stressed taking statistical classes to harm the performance (Ashaari et al., 2011). Therefore, working toward improving such aspects will see a significant improvement in the overall GPA. Improving the cognitive ability by a unit as shown in the findings would lead to an increase in performance by 0. 085. Components under the cognitive ability such as thinking style, error minimization while doing calculations and understanding statistical equation would greatly improve the performance.

Additionally, improving the value mean by a unit increases the chances of scoring good graded by 0. 028. The components of value mean such prioritizing statistics studies, viewing statistics as useful in the studies and application of statistics in day to day activities would significantly improve the overall performance (Ashaari et al., 2011). Finally, factors such as difficulty attitude and effort form key predictors of overall performance.