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Statistical Quantitative Data Analysis

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Question:

Discuss about the Statistical Quantitative Data Analysis.
 
 

Answer:

Introduction

Quantitative data analysis is the investigation of the different claims or hypotheses by using numerical data which is collected by researchers. It is important to arrange the research study in a particular manner and avoid different types of biases during the research study. If the research study consists of different types of biases, errors or mistakes, then we will not get the unbiased and reliable results for the research study and we do not use these estimates or models for further investigation. In the process of investigation, we need to develop the research hypotheses, collect the data, then analyze this data by using different tools and techniques of statistical analysis. After this statistical analysis we can conclude different results for the hypotheses established for the given research study. Quantitative analysis becomes a very important in the every field for making effective decisions. In this era of competition, every industry or organization use the statistical analysis during the process of policy making. The use of optimization techniques is found very useful for making more profit. The qualitative methods of data analysis will be great value for attempting to draw the useful results from a large qualitative data. It is found very beneficial to analyze the data for making effective decisions in the industry or organizations. The statistical data analysis helps us in recognizing the data structure and identifying the different sources of the variation. The quantitative analytical approach is useful for reporting the summary results in the numerical terms within specific degree of confidence. The quantitative research is very useful for uncover the trends in though and opinions.  The purpose of the quantitative data analysis is to discover the meanings, variations and patterns of the relationships between the different variables under study.

The statistical data analysis is very useful in the analysis of the quantitative and qualitative data. There are so many tools and techniques for the analysis of the statistical data. Here, we want to analyze the given quantitative data by using the different tools and techniques of the statistical analysis. The use of quantitative analysis is very helpful in the process of decision making and employing the new policies. In different companies or industries, the use of statistical analysis is becomes mandatory. Also, for production department, the advanced use of statistical quality control is essential in the competitive environment. Also, statistical analysis found very useful in the research of medical science, environment science, pharmaceutical sciences, social sciences, etc. For this analysis, we need to use the different tools and techniques such as descriptive statistics, inferential statistics, and graphical analysis for the given data. We have to check some claims regarding the variables in the given data by using testing of hypothesis. Let us see this statistical analysis in detail.

Description of Data set

The process of the data collection is very important for statistical analysis of the variables under study. For this research study, about 50 subjects are selected for this study. Well prepared questionnaires are used for the data collection from the 50 subjects or respondents for this study. Information regarding the different ten variables by using the questions is collected for each person or respondent. For this research study, the information or data is collected for the different variables such as the gender of the respondents, education level of the respondent, region of the respondents, marital status of the respondents, age of the respondent, monthly earning of the respondent and monthly expense of the respondents. For this research study, the nominal scale is used for the variables gender, region and marital status of the respondents. The ordinal scale is used for the variable education level of the person while the ratio scale of measurement is used for the variables earning, expense and age of the respondents. Data is given in the separate excel file.

 

Research Hypotheses

For this research study, the research hypotheses or claims are established as below:

There is a difference exists in the average monthly income for the persons based on education level.

There is a difference exists in the average monthly expense for the persons based on education.

Is there any statistically significant difference observed for the average income for the persons from the rural and urban area? Is there a difference in the income based on area of the person?

Is there any significant difference between the expenses of the persons based on the area of the persons?

Is the education of the person is independent from the area of the person?

We have to check these hypotheses by using different tests of hypotheses.

Descriptive Summary

For the given data set, there are 26 males and 24 females. The proportion of the male participants is given as 52% while the proportion of the female participants is given as 48%. From the frequency distribution of the variable education, it is observed that there are 27 persons having education less than graduation while there are 23 persons with education graduation or more. The proportion of the persons with education less than graduation is given as 54% while the proportion of the persons with education graduation or more is given as 46%. It is observed that 29 persons are originated from the rural area while 21 persons are originated from urban area. In the given sample, it is observed that 30 persons are unmarried while 20 persons are married.

From the analysis of the given data for the expenditure and earning, it is found that the mean income per month for the persons involved in this research study is given as $7763 approximately with the sample standard deviation of $1566 approximately. From the given data, it is observed that mean monthly expense for the persons in the sample is $4581 approximately with sample standard deviation of $862 approximately.

From the given histogram and box plot for the variable monthly income, it is observed that the data for the variable monthly income do not follow normal or approximate normal distribution. The data for the variable monthly income is negatively skewed. Also, it is observed that the histogram for the variable monthly expense do not indicate the normal or approximate normal distribution. Also data for the monthly income is negative skewed. The histograms and box plots are given in the appendix section.

Testing of Hypothesis

By using testing of hypothesis we have to check different claims. We have to use different tests for checking these hypotheses. We will use two sample t test for checking the significant differences in the averages of the monthly income and expense. The significance level for this test is considered as 5%. Let us see the results for these tests as below:

First Hypothesis:

There is a difference exists in the average monthly income for the persons based on education level.

For checking the statistically significant difference in the average monthly income for the persons based on education level, null hypothesis is not rejected (t = -1.4872, p = 0.1435) at the 5% level of significance. There is insufficient evidence to conclude that there is a significant difference exists in the average monthly income for the persons with education less than graduate and education with graduate or more.

Second Hypothesis:

There is a difference exists in the average monthly expense for the persons based on education.

The null hypothesis is not rejected (t = -1.8399, p = 0.0720) at the 5% level of significance. There is insufficient evidence to conclude that there is a significant difference exists in the average monthly expense for the persons with education less than graduate and education with graduate or more.

Third Hypothesis:

There is a difference in mean monthly income for rural and urban persons.

For checking the significant difference between the average income for the rural and urban area by using two sample t test, it is observed that there is no any significant difference (t = -0.5292, p = 0.5991) is found for the average monthly income for the persons in rural and urban area.

Fourth Hypothesis:

There is a difference in mean monthly expense for rural and urban persons.

Using the same test, it is found that there is no any significant difference (t = 1.1226, p = 0.2672) in the average monthly expense for the persons in the rural and urban area.

Fifth Hypothesis:

H0: Education of person is independent from area of person.

Ha: Education of person is not independent from area of person.

There is sufficient evidence (Chi-square = 0.1440, p = 0.7044) to conclude that two variables are independent from each other.

Confidence Intervals

After using the analysis for confidence intervals for mean monthly income, we are about 95% sure that the mean monthly income of the person will be between $7318 and $8208 approximately. Also, we are about 95% confident that the mean monthly expense for the persons will lies between $4336 and $4826 approximately. The details calculations and results for these confidence intervals are given in the appendix section.

Conclusions

  1. From the analysis of the given data for the expenditure and earning, it is revealed that the mean age of the persons involved in this research study is given as 24.62 years with sample standard deviation of 2.26 years.
  2. From the analysis of the given data for the expenditure and earning, it is found that the mean income per month for the persons involved in this research study is given as $7763 approximately with the sample standard deviation of $1566 approximately.
  3. From the given data, it is observed that mean monthly expense for the persons in the sample is $4581 approximately with sample standard deviation of $862 approximately.
  4. No sufficient evidence found for statistically significant difference between average incomes per month as per education levels of the persons in the sample data.
  5. Also, there is no any sufficient evidence for difference between mean expenses per month for the persons with different education levels.
  6. It is found that there is no any significant difference (t = 1.1226, p = 0.2672) in the average monthly expense for the persons in the rural and urban area.
  7. From the results of Chi square test for independence of two categorical variables, it is found that education and area of the person is independent from each other.
 

References

Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd.

Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.

Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer - Verlag Inc.

Hogg, R., Craig, A., and McKean, J. (2004).  An Introduction to Mathematical Statistics. Prentice Hall.

Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.

Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.

Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.

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