CHAPTER 3: METHODOLOGY
3.7 Data Analysis
3.7.3. Inferential Analysis
The purpose of inferential analysis is not focus only on describing data but generalize a wide inference on the sample data (Ho, 2006). Inferential analysis can provide more answers to the researchers compared with descriptive analysis.
3.7.3.1. Pearson Correlation Matrix
During the analysis, strength, importance and direction of the variables are measured with Pearson Correlation Matrix (Sekaran & Bougie, 2013). Positive correlation coefficient, r represents a perfect positive linear relationship with dependent variable while negative correlation coefficient, r represents a perfect negative linear relationship with dependent variable (Hair, Bush & Ortinau, 2006). Meanwhile, it indicated as no relation when zero is obtained from r. The correlation coefficient, r is ranging from -1 to +1 in which the strength and direction between independent variables and dependent variable are measured.
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In other words, it helps to find out whether the two variables are associated with each other.
On the other hand, P-value is used to determine statistical significance in a hypothesis testing. A small P-value that is less than 0.05 indicates a strong evidence in rejecting null hypothesis (H0) and accepting alternative hypothesis (H1) while a large P-value that is more than 0.05 indicates a strong evidence in accepting null hypothesis (H0) and rejecting alternative hypothesis (H1). “+” or
“-” symbols refer to the direction of the correlation. “+” correlation indicates positive correlation between two variables, for instance when one variable increases, the other variable increase. Whereas, “-” correlation indicates negative correlation between two variables, for instance when one variable increases, the other variable decrease. Rules of thumb for different types of relationships are shown in the table as below:
Table 3.3. Pearson Correlation Study Size of Correlation Interpretation
0.90 - 1.00 (-0.90 - -1.00) Very High Positive (Negative) Correlation
0.70 - 0.90 (-0.70 - -0.90) High Positive (Negative) Correlation 0.50 - 0.70 (-0.50 - -0.70) Moderate Positive (Negative)
Correlation
0.30 - 0.50 (-0.30 - -0.50) Low Positive (Negative) Correlation 0.00 - 0.30 (0.00 - -0.30) Little if any Correlation
Source: Hinkle, D. E., Wiersma, W., & Jurs, S. G. (1994). Applied statistics for the behavioural sciences. Houghton Mifflin Company. Boston, USA.
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3.7.3.2. Multiple Regression Analysis
Multiple regression analysis is a common and adaptable data analytic system.
According to Cohen, Cohen, West and Aiken (2013), it is a system used to study the relationship and factors of interest between the dependent variable and independent variables. The relationship between the variables can be simple and complex depends on the situation. It can be straight line, curvilinear, general, conditional, and combination of all these possible patterns. Multiple regression analysis is widely applicable to the hypotheses developed in the research study that related to social science, health science, education and business.
Researchers would want to figure out the extent of variation produced by independents variables on the dependent variable. R is used to measure relationship between dependent variable and one independent variable while 𝑅2
is used to measure the relationship between dependent variable and multiple independent variables. The multiple regression framework is computed as followed:
Y = a + b1X1 + b2X2 + b3X3 + … Where Y = dependent variable X = independent variable a = constant value
b = coefficient
Under this model, r is used to measure the relationship between dependent variable and one independent variable while R is used to measure the relationship between dependent variable and multiple independent variables.
The value of R is between 0 and 1 with 0 represents no relationships while 1 equals a positive relationship between dependent variable and independent variables. By using multiple independent variables, researchers can further understand the research topic and make accurate predictions.
On the other hand, 𝑅2 is used to measure the variation of the dependent variable that is caused by the independent variables. However, 𝑅2 is derived from the
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Pearson Correlation Coefficient by squaring the r value (Zou, Tuncali, &
Silverman, 2003). 𝑅2 has a range from 0 to 1 which indicates that a value approximately to 1has a greater variance to accounted by the model. For instance, 𝑅2 with a value of 0.73 means that 73% of the data variation can be explained by the model.
3.7.3.3. Simple Regression Analysis
Simple regression analysis is used to measure the linear relationship between the dependent variable and one independent variable. The dependent variable is also refers as response variable while independent variable is called as predictor or explanatory variable. Based on Seber and Lee (2012) book of Introduction to Linear Regression Analysis, the simple linear regression model is as followed:
Y = 𝛽0 + 𝛽1 x+ 𝜀
Where Y = Dependent variable 𝛽0 = Y-interception
𝛽1 = Gradient of regression line x = Independent variable 𝜀 = Random error component
The parameter 𝛽0 and 𝛽1 are refer as regression coefficient. The 𝜀, random error component is always assume with a mean of zero and constant variance in the simple linear regression. It can be measure through least square estimation, maximum likelihood estimation, and confidence interval analysis. According to Altman et al (1983), confidence interval is a helpful tool to interpret the significant of the differences. Confidence interval analysis method is used under this research study to determine the quality of prediction of value of Y at the chosen value of independent variable.
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3.8 Conclusion
The methods to carry out the research were specified in this chapter. Quantitative research, descriptive study and exploratory study are described in the research design.
The methods in collecting data and the process in designing the sample as well as the tools in conducting the research and processing the data have further specified. The analysis methods that have been applied are Pearson Correlation, Multiple Regression and Simple Linear Regression. The statistical analysis outcomes are generated in the next chapter.
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