Authors: Nunaphat S. Haruansan, M. Mosso, K. Johnson, and C. Foust

Applied Statistics for Environmental Studies for master's degree of Environmental Health

1. Introduction

• 1.1. Purpose of the Study

• 1.2. Importance of Data Analysis in Environmental Health

• 1.3. Overview of U.S. Census Bureau Data Utilization

2. Project Overview

• 2.1. Scope of the Project

• 2.2. Objectives

• 2.3. Methodology Summary

3. Group Assignment

• 3.1. Team Roles and Responsibilities

• 3.2. Data Collection and Distribution

• 3.3. Coordination and Collaboration

4. Hypothesis Formulation

• 4.1. Research Question

• 4.2. Hypothesis Statement

• 4.3. Rationale Behind the Hypothesis

5. Data Analysis

• 5.1. Descriptive Statistics

  • 5.1.1. Mean Calculation

  • 5.1.2. Median Calculation

  • 5.1.3. Range Calculation

  • 5.1.4. Standard Deviation Analysis

• 5.2. Demographic Analysis

  • 5.2.1. Analysis of Master's Degree Data for Females

• 5.3. Comparative Analysis

  • 5.3.1. Master's vs. Doctoral Degree Data

6. Hypothesis Testing

• 6.1. T-Test for Comparing Means

• 6.2. Interpretation of Results

7. Conclusion

• 7.1. Summary of Findings

• 7.2. Implications for Environmental Health

• 7.3. Recommendations for Further Research

8. Appendices

• 8.1. Appendix A: Supplementary Data

• 8.2. Appendix B: Calculation Details

9. Works Cited

• 9.1. References

• 9.2. Data Sources

Introduction:

Statistics! For many, just hearing the word conjures up feelings of dread, anxious groans, or even the urge to curl up in a fetal position. But when you break it down to its core, statistics is simply a set of tools and techniques used to describe, organize, and interpret data (Salkind, 2014). However, as soon as terms like mode, mean, confidence interval, null hypothesis, and nonparametric statistics enter the conversation, that familiar fear often resurfaces. Regardless of whether someone embraces or avoids statistics, the reality is that our modern world relies heavily on it. Nearly every aspect of our lives, from the food we eat to the smartphones we purchase, has been influenced by some form of statistical analysis.

Embracing this world of statistical exploration is the team of Michelle Mosso, Kristi Johnson, Nunaphat Smykla-Haruansan, and Chad Foust—also known as Team Three. As students in EHS 625: Applied Statistics for Environmental Studies, Team Three has been tasked with producing a research paper utilizing data from the 2012 Statistical Abstract of the U.S. Census Bureau. The group analyzed four data sets from the Census Bureau, applying confidence intervals to each. A confidence interval is a statistical tool that provides the best estimate of a population value based on a sample (Salkind, 2014). It's a widely used technique for analyzing data across various sources, and what better data to use than that from the U.S. Census Bureau?

PROJECT OVERVIEW

This research paper is the culmination of a group project conducted by Chad Foust, Nunaphat Smykla-Haruansan, Kristi Johnson and Michelle Mosso. For this project, the group statistically analyzed data from the 2012 Statistical Abstract of the U.S. Census Bureau. Specifically, the data that was analyzed pertained to 1) Degrees Earned by Level and Sex: 1960 to 2009; 2) Degrees Earned by Level and Race/Ethnicity: 1990 to 2009; 3) Bachelor’s Degrees Earned by Field: 1980 to 2009 and 4) Master’s and Doctoral Degrees Earned by Field: 1980 to 2009. The primary statistical focus of each of the four data sets concerned the 95% confidence interval. The paper is broken into four data set sections, each of which contains data values, calculations and conclusions drawn. 

Section 299 of Group Assignment: Nuna s.Haruansan 

3a. Using only data from 2005-2009 master's Degrees, what would you predict, using a 95% confidence interval, to be the number of males and the number of females for 2010? Show all of your work, including assumptions and justification for the predictions. 

3b. In examining all of the data in Section 299, provide a list of conclusions that can be drawn from this data. 

From the given information: Master’s degree in Male and Female from 2005-2009 

Hypothesis: 

In 2010, the numbers of Master’s degree are equal on both male and female at 5% significant level. 

The null hypothesis: there is no different between the number of Master’s degree in female and male

Research Hypothesis: the number of Master’s degree in female is greater than male 

We don’t know if in 2010 female will be greater than male, so we are going to compare in the t- tailed test because this is a small sample size. We can also compute with one tailed test and because this is a match paired sample when we use t-test, it is assumed the data is normally distributed (Statistics lectures, 2012). 

Step 1:  Compute Mean, Median, Range, and Standard deviation: 

Master’s degrees for Male from 2005-2009: 

Mean of master’s degree for Male from 2005-2009: 234+238+238+246+260/5 = 1216/5= 243.2 

Median of Master’s degrees for Male from 2005-2009 is 238  

Mode of Master’s degrees for Male from 2005-2009 is 238 

Range of these set scores is: 260-234= 26 

Standard deviation of Masters’ degrees for Male from 2005-2009: 

Step 2:  Master’s degree for Female: 

Mean of Master’s degrees for Female from 2005-2009: 

341+356+366+379+397/5 = 1839/5= 367.8 

Median of Master’s degrees for Female from 2005-2009 is 366 

Mode of Master’s degrees for Female from 2005-2009 is none 

Range of these set scores is: 397-356= 41 

Standard deviation of Masters’ degrees for Female from 2005-2009: 

= (233.327, 253.073)  

Therefore, at a 95% chance that the confidence interval contains the true population mean averaged in Master’s degree male from 2005-2009 is between (233.327, 253.073) (GraphPad, 1995-2015). 

Calculate 95% confidence interval for Master’s degree Female from 2005-2009: 

Questions: 

Do any of the results surprise you? If so, why do you think they turned out the way they did? 

If we constructed the 95% confidence interval for predicted value in the year 2010, results below are the prediction value. 

Summary Finding: 

Based on the 95% CI range, the overall number of male and female students’ year 2010 would be increasing to the higher value. The Master’s degree male is approximately greater than 400; while female is greater than 260. This result is not surprising if we are observing the entire data, we can say that the female graduates are increasing yearly.

Test Hypothesis: Using T-test to compare Means:  

Use T-value or a paired t-test calculation to compare the means of the two set scores that have relationship to each other.  T-test is used to analyzing a single sample of differences for small n (Salkind, 2014 P. 235). 

Following is the Formulas to find the t value and degree of freedom which we are testing an independent sample between two populations

T –test Formula (Salkind, 2014 P. 202).

df = 6 α = 0.05, two-tailed test in this Variables with critical values are ± 2.3060 

Hypothesis Conclusion: 

Male is significantly different from Female, t (8) = -11.7017, p < .05. We are 95% confident that the mean difference lies between 107.2375 and 141.9625. 

One tail test is used to test hypothesis at 0.05 critical t-value. The conclusion is that t-value corresponds to sample statistics is fall out the critical region, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the number of Master’s degree in Female different to male. The result is statistically significant at p < 0.05. For two tailed tests, the absolute value of the calculated t exceeds the critical value (±11.701723>2.3060), so the means are significantly different. We are going to accept research hypothesis that Master’s degree of female is greater than male.  

What do you surmise is causing the trend(s) you see? 

Finalized by the National Center for Education Statistics (NCES) data from government, private, surveys contains the field of education statistics, schools, colleges, enrollments, and graduates for evaluating education data additional information of the population trends derives from attitude of education, characteristic of education (labor force factor, government finances, and economic at present time) (NCES, 2013). 

The Enrollment trend appearing on Sex and Age: 

From 2000-2012, the enrollment from age 25-35 had grown in the numbers approximately 35 percent. Female enrollment age of 25 increased by 34 percent; 25 and greater were 40 percent. While male enrollment age of 25 grew nearly 36 percent; 25 and older increased approximately 28 percent (NCES, 2013). 

1) Degree-Granting Institutions: Granting by institution had contributed to the growing number in Master’s degree level. As reported in fall 2011, there were nearly 3.8 million graduated were hired in colleges and universities professional and nonprofessional staff. The majority of staffs were in the faculty or graduate assistants; the rest were in managerial and nonprofessional (NCES, 2013). In additional, almost 84 percent of full-time graduates students received supportive financial aids. Respectively, the higher cost such as private institutions received more percentage than lower cost (public institutions). Therefore, the full-time students can channeled to obtain financial to a variety of programs such as federal aid, state, institutional aid, and other sources (Private nonprofit institutions throughout grants, loans, work-study, tuition waivers or reimbursement from employers (as cited in Digest of Education Statistics, 2013, table 331.50 & 332.30). For 2011–12 year alone each student approximately received financial aids for totaled of $15,510 (NCES, 2013). 

2) Finances—Projections: Based on the trend on Table 291-294, for school years ending in years 1990-2010 demonstrated $9,800,000,000 of voluntary support for higher education in form of gift, funding, trust, award, agencies, and contract research. Because of the economic downturns, the master’s is now the fastest-growing degree. According to the New York Time, approximately people who have a master’s are the same proportion that had a bachelor’s or higher compared in 1960. There is a study trend toward professionalizing degrees. Dr. Stewart quotes “master’s education was moving very rapidly to become the entry degree in many professions.” As stated by Professor Richard K. Vedder, the market is overflown from college’s graduates. Thus, it has become essential for the job seekers to obtain higher degrees to stand out from Ivy League undergraduate’s colleges (Pappano, Laura, 2011). 

(For statistical programing results, please see Appendix A)

Section 300 of Group Assignment. M. Mosso

5a. Using the data from all five years of data collected, what would you predict, using a 95% confidence interval, for each category of ethnicity for Master’s Degrees or 2010? 

White (1990)                                                               MEAN 

254,299-357,526.8=-103,227.8                                1,787,684/5=357.526.8 

(103,227.8)²=10,655,978,692.84 

White (2000) 

320,485-357,526.8=--37,041.8 

(-37,041.8)²=1,372,094,947.24 

White (2005) 

379,350-357,526.8=21,828.2 

(21,828.2)²=476,252,058.24 

White (2008) 

409,312-357,526.8=51785.2 

(51785.2)²=2,681,706,939.04 

White (2009) 

424,188-357,526.8=66,659.2 

(66,659.2)²=4,443,448,944.6399 

TOTAL=19,629,481,581.99  

Black (1990)                                                  MEAN 

15,336-48152.8 =-32,816.8                       240,764/5=48152.8 

(32.816.8)²=1,076,942,362.24     

Black (2000) 

35,874-48,152.8=-12,278.8 

(12,278.8) ²=150,768,929.44

Black 2005 

54,482-48152.8=6,329.2 

(6329.2) ²=40,058,792.64 

Black 2008 

65,062-48152.8=16,909.2 

(16.909.2) ²=285,921,044.64 

Black 2009 

70,010-48152.8=21,857.2 

(21,857.2) ²=477,737,191.84 

TOTAL=2,031,428,300.8 

2,031,428,300.8/4=507,857,075.2 

√507,857,075.2=22,535.6845 

95% Confidence interval for the data  

70,010+/-1.96x22,535.68=44,169.9328 

70,010-44,169.9328=25,840.0672 

70,010+44,169.9328=114,179.9328 

HISPANIC 1990                                         

 7,892-26,974=-19082 

(-19082) ²=364,122,724 

HISPANIC 2000 

19,253-26,974=-7,721 

(7,721) ²=56,613,841 

HISPANIC 2005 

31,485-26,974=4,511 

(4511) ²=20,349,121 

HISPANIC 2008 

36,801-26,974=9827 

(9827) ²=96,569,929 

HISPANIC 2009 

39,439-26,974=12,465 

(12,465) ²=155,376,225 

TOTAL=693,031,840 

693,031,840/4=173,257,960 

√173,257,960=13,162.7489 

39,439 ± 1.96 x 13,162.7489 

39,439-25,798.9878=13,640.0122 

39,439+25,798.9878=65,237.9878 

ASIAN 1990 

10,439-28,758.4=-18319.4 

(-18,319.4) ²=335,600,416.36 

ASIAN 2000 

23,218-28,758.4=-5540.4 

(-5540.4) ²=30,696,032.16 

ASIAN 2005 

32783-28,758.4=4,024.6 

(4,024.6) ²=16,197,405.16 

ASIAN 2008 

37,408-28758.4=8649.6 

(8649.6) ²=75,815,580.16 

ASIAN 2009 

39944-28,758.4=11,185.6 

(11,185.6) ²=125,117,647.36 

TOTAL = 583,427,081.2 

583,427,081.2/4=145,856,779.3 

√145,856,770.3=12,077.1176 

39,944±1.96 X 12,077.1176

39,944-23,671.15=16,272.85 

39,944+23,671.15=63,615.15 

AMERICAN INDIAN/ALASKA NATIVE 1990 

1090-2829.6=-1739.6                                                             MEAN 

(-1739.6) ²=3,026,208.16                                                       316,574/5=63,314.8  

AMERICAN INDIAN/ALASKA NATIVE 2000 

2246-2829.6=-583.6 

(583.6) ²=340,588.96 

AMERICAN INDIAN/ALASKA NATIVE 2005 

3295-2829.6=928.4 

(465.4) ²=216,597.16 

AMERICAN INDIAN/ALASKA NATIVE 2008 

3758-2829.6=928.4 

(928.4) ²=861,926.56 

AMERICAN INDIAN/ALASKA NATIVE 2009 

3759-2829.6 

(929.4) ²=863,784.36 

TOTAL = 5,309,104.4 

5,309,104.4/4=1327,276.1 

√1,327,276.1=1,152.07 

3759±1.96 X 1152.07 

3759-2258.06=1500.94 

3759+2258.06=6017.06 

NONRESIDENT ALIEN 1990 

35245-63,314.8=-28,069.8                                       MEAN 

(-28069.8) ²=787,913,672.04                                   316,574/5=63,314.8 

NONRESIDENT ALIEN 2000 

55,980-63,314.8=-7334.8 

(7334.8) ²=53,799,291.04 

NONRESIDENT ALIEN 2005 

73223-63,314.8=9908.2 

(9908.2)²=98,172,427.24 

NONRESIDENT ALIEN 2008 

72,682-63,314.8=9367.2 

(9367.2) ²=87,744,435.84 

NONRESIDENT ALIEN 2009 

79,444-63,314.8=16,129.2 

(16,129.2) ²=260,151.092.64 

TOTAL=1,287,780,918.8 

1,287,780,918.8/4=321,945,229.7 

√321,945,229.7=17,942.83 

79444±1.96X17942.83 

79444-35,167.95=44,276.05 

79444+35,167.95=114,611.95 

5b In examining all of the data in section 300, provide a list of conclusions that can be drawn from this data. 

The following is a listing of conclusions that can be drawn from the data of degrees earned by level and race, ethnicity from 1990 to 2009: 

• The majority of degree earners are of white/non-Hispanic ethnicity. 

• Only one American Indian/Alaska Native earned  

• More nonresident alien’s earned Master’s degrees than a combination of black, Hispanic, Asian, and American Indians in 1990. 

• The Master’s degrees earned for nonresident aliens decreased to 72,682 in 2008 from 73,223 in 2005. 

• From the data observed most degree earners had a bachelor’s degree.

Section 302 Group Assignment: C. Foust 

6a.What is the mode for 2009? 

Every value in the distribution contained only one occurrence so there was no mode. 

6b. Using only data from 2005 and 2008, what would you predict, using a 95% confidence interval, to be the number of Bachelor’s degrees earned in the field of Mathematics and Statistics for 2010? 

6c. In examining all of the data in Section 302, provide a list of conclusions that can be drawn from this data. 

The 95% confidence interval used in this problem is equal to 14,771.5 +/- 1.96 (594.67). This equates to a range from 13,605.95 to 15,937.05. Looking at those numbers, it can be said with 95% confidence that the population mean for the number of Bachelor’s degrees earned in the field of Mathematics and Statistics for 2010 will fall between those two scores.

Section 303 Master’s Degree Data and Doctoral Degree Data: K. Johnson 

7a. What is the mode for 2009, Master’s degrees? 

The mode for Master’s degrees earned in 2009 is 178,564 in Education. 

7b. Using only data from 2005, 2008; what would you predict, using a 95% confidence interval to be the number of Master’s degrees earned in the field of Mathematics and Statistics for 2010? 

Prediction; “Prediction is the computation of future outcomes based on the knowledge of present ones”​ (Salkind, 2014)​. I predict the number of Master’s degrees earned in the field of Mathematics and Statistics for 2010 will be higher than of those in 2005 and 2008. This is because the trend for 2005 and 2008 is upward.

Hypothesis & Calculations 

Null Hypothesis:  There will be no difference in the number of Master’s degrees in Mathematics and Statistics in 2010 than in the combined mean of years 2005 and 2008. 

Research Hypothesis:  There will be a difference in the number of Master’s degrees in Mathematics and Statistics in 2010 than in the combined mean of years 2005 and 2008. 

However, I must accept the null hypothesis since my obtained values of -0.71 and 0.71 do not exceed the critical value of 26.11, therefore the mean population of mathematical and statistical Master’s Degrees will not change for the year 2010. 

7c. In examining all of the data in section 302 Master’s degree data, provide a list of conclusions that can be drawn from this data. 

• Despite the drop between 1980 and1990, I conclude that other than the following, most Master’s degrees categories will increase within their respective degree field. 

• Physical Science and Science technologies may not increase. 

• Philosophy and Religious Studies may slightly increase or decrease. 

• Liberal arts may stay the same. 

• Health Professions will greatly increase. 

• Foreign Languages, Literatures, and Linguistics will remain basically unchanged. 

• Area, Ethnic, Cultural, and Gender Studies will not increase. 

8a. What is the mode for 2009, Doctoral degrees? 

The mode for the 2009 Doctoral degrees is 12,112 in Health professions and related clinical sciences. 

8b. Using only data from 2005 and 2008, what would you predict, using a 95% confidence interval, to be the number of Doctoral degrees earned in the field of Mathematics and Statistics for 2010? I predict, following the calculations which incurred during 7b. That there will not be a difference in Doctoral degrees earned in the field of Mathematics and Statistics that is statistically significant. 

Another definition for prediction is” predictive modeling as the process of applying a statistical model or data mining algorithm to data for the purpose of predicting new or future observations”​ (Shmueli, 2010)​ And hypothesis is more than general predictions, “One model states that hypotheses are used to generate predictions. Thus, hypotheses tend to be general, whereas predictions tend to be concrete. Hypotheses provide possible answers to the motivating research question, whereas predictions pertain to the expected outcomes of the current studies being presented”​ (Anglim, 2009)​. 

Assumptions:  As sample size becomes large the sampling distribution approaches the normal distribution, even if the original population is not normal; assumption is that σX is known, assumption of a simple random sample is not known.​ (Newsome, 2014)​.

Hypothesis & Calculations 

Null Hypothesis:  There will be no difference in the number of Doctoral degrees in Mathematics and Statistics in 2010 than in the combined mean of years 2005 and 2008. 

Research Hypothesis:  There will be a difference in the number of Doctoral degrees in Mathematics and Statistics in 2010 than in the combined mean of years 2005 and 2008. 

Statistically speaking, I predict at a confidence level of 96% that the mean population of Mathematical and Statistical Doctoral graduates will fall between 1013 and 1523. However, since the critical valve of 26.11 exceeds the obtained values of -0.71 and 0.71, I reject the null hypothesis finding that the mean of the 2010 Doctoral degrees will not be a change that is statistically significant. 

8c. in examining all of the data in Section 302 Doctoral degree data, provide a list of conclusions that can be drawn from this data. 

There are not likely any statistically significant changes that will be made within the Doctoral degree data, however I have provided the following conclusions: 

• Doctoral degrees in general will not increase significantly. 

• Engineering and Engineering Technologies are at risk of decreasing. 

• Security and Protective Services may be at risk of becoming obsolete. 

• Mathematics and Statistics will probably rise. 

• Health Professionals and Related Clinical Services will Rise Significantly. 

• Area, Ethnic, Cultural, and Gender Services has the probability of going either higher or lower. 

• I conclude that Liberal Arts will decrease. 

CONCLUSION 

In closing, the 2012 statistical abstract data concerning education has proven to be an essential tool for retrieving educational statistics.  The degrees earned was just the icing on the cake!  The statistical data in this report has shown, who is and the what, about earning a degree!  Women, men, black or white every group is moving forward to receive a higher education.  The 95% confidence intervals are overwhelmingly surprising.  Group Three can proudly say that our statistical conclusions haven been proven valid.   

Appendix A: By Nunaphat Smykla-Haruansan 

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For this article:

I wanted to take a moment to express my heartfelt gratitude for your invaluable contributions throughout our journey to achieving master’s degree. This course assignment designed to encouraged, our collaboration, and our expertise played a crucial role in making this accomplishment possible.

Team knowledge and guidance truly made a difference. I deeply appreciate the time and effort our team invested, whether it was through brainstorming sessions, & reviewing my work.

Graduating with this degree is not just a personal achievement but also a testament to the collective efforts of those who supported me along the way. I am incredibly grateful to have had you as a teammate/classmate and am inspired by all dedication and commitment in our master's degree of Environmental Health class.

Thank you once again for being such an essential part of this success. I look forward to continuing our work together and am excited about the future opportunities we can pursue as a team.

Warmest regards,

Nuna S.