# Tips for writing a master's statistics final paper with example

A master's statistics final paper can be a hard nut to crack. It not only requires a significant amount of extensive research but also writing of more than 10,000 words. It is usual for any student to find this task daunting. Some challenges most students face are knitting ideas together and putting their findings into words. If you are sailing in the same boat, these tips will get you on the right track and have you writing your master's statistics final paper easily. Here are top tips to help you throughout your writing process:

1) Familiarize and understand your topic

2) Have a precise structure for your paper

3) Write an in-depth literature review

4) Go into detail about your methodology

5) Limit accidental plagiarism

6) Have a powerful conclusion

If you cannot write a research paper alone, consider getting assistance from experts. We have a team of professional writers who can draft an excellent master’s statistics final paper. To clear your doubts and prove our writing prowess, here is an example of a master’s statistics final paper prepared by us. The paper is on discrete choice methods for planning and public policy.

## 1. Introduction

Housing is one of the basic foundation on which living and modern structures thrive. It is impossible for people to survive alone or in group without a functioning, protective and equitable housing stock (Krieger and Hikkins, 2002). In the US wealth is built through homeownership and those who have their homes are richer than those who rent home. Moreover, the wealth from homeownership is intergenerational i.e. there is high probability that people whose parent have their home will also become homeowners than people whose parents rent house (Martinez and Kirchner, 2021).

Historically, home ownership have been denied to people of color. For example, the redlining of black and immigrant neighborhood by the federal government agency “Home Owners Loan Corporation’ which deems neighborhood dominated by black and immigrants as hazardous credit risk made lending institutions to deny mortgages to prospective homebuyers in this neighborhood (Martinez and Kirchner, 2021). However after thirty years of redlining, the federal government introduced the Fair Housing Act of 1968 which make denial of housing loans because of race as illegal.

## Bi-Variate Descriptive Statistics and Frequency Distribution

Table 3 presents the frequency distribution of action taken by ethnicity and race. The result showed the proportion of Hispanic (31.76%) denied loan is greater than that of Non-Hispanic (24%) by 7.6 percentage points. In the same vein, the proportion of non-White (33.31%) that were denied loan is greater than the proportion of White (22.87%) that were denied loan by almost 11 percentage points.

Table 3: Action Taken by Ethicity and Race

 action_taken Hispanic Not Hispa Total Non-White White Loan originated 11,360 68.24 185,939 76 197,299 75 28,978 66.69 168,321 77.13 Application denied 5,286 31.76 59,099 24 64,385 25 14,477 33.31 49,908 22.87

The findings was taken further by considering the disaggregated race. The result showed that American Indian or Native Alaska are the worst hit in terms of denial as about half (49.76%) of their application were denied followed by the black race which have 40% of applications denied. Native Hawaiian have 38.74% of application denied. However, Whites have 22.87% of application denied and only Asian are non-Whites that have relatively low denials at 25%.

Table 5 presents the cross-tabulation of reasons for denial by ethnicity. The result showed that debt-to-income ratio is the major reason for denying both Hispanic (29.44%) and non-Hispanic (28.63%). Credit history is also a major reason of denial for both Hispanic (27.78%) and non-Hispanic (24.19%). In terms of race, it appears that debt-to-income ratio is also the major reason for denial. 28.1% of Whites were denied because of debt-to-income ratio compared to 28.87% among non-Whites. Similarly, 27.61% of Whites and 23.58% of non-Whites were denied due to credit history.

The racial disparities have been entrenched over time as depicted by the cross-tabulation of loan purpose by ethnicity and race. Applying for the purpose of home improvement or refinancing showed that the applicant have a home already. The result showed that proportion of Whites for these two categories are greater than the proportion of non-Whites in these two categories by approximately 4 percentage points for refinancing and almost 3 percentage points for home improvement which suggests that Whites historically have more homes than non-Whites.

## Estimation Result

Table 6 presents the regression of action taken (approved vs denied) against ethnicity and race using linear probability model (LPM), probit and logit models. The result showed that there is significant difference in approval rate across ethnicity and race. The LPM model showed that the probability of a non-Hispanic getting loan is 0.076 greater than that of Hispanic getting loan while the probit model showed that the probability of a non-Hispanic getting loan is greater than that of Hispanic getting loan by 0.23. The logit mode on the other hand showed that Non-Hispanic have 46% higher odds of getting loans than Hispanic. Comparing Whites and non-Whites, the result showed that Whites have higher probability of having their loans originated than non-Whites by 0.1 in the LPM while in the probit model is 0.31. The logit results showed tha Whites 1.68 times of odds of non-White of securing loan. Looking at the disaggregated race result, with White as the base, the negative significant coefficient showed that all of other race have lower probability of securing loan than all other race. For example, the probability of American Indian assessing loan is 0.269 lower in the LPM model and 0.737 lower in the probit model and the odds of securing loan is 70% lower than that of white. The probability of Asian assessing loan is 0.02 lower in the LPM model and 0.07 lower in the probit model and the odds of securing loan is 12% lower than Whites. Also, the probability of Blacks assessing loan is 0.18 lower in the LPM model and 0.5 lower in the probit model and the odds of securing loan is 56% lower than Whites. Finally, the probability of Native Hawaiian assessing loan is 0.16 lower in the LPM model and 0.46 lower in the probit model and the odds of securing loan is 53% lower than Whites.

The result discussed above is without controls which means it is possible that some uncontrolled factors may bias the results. Therefore, in the next set of analyses, we control for household income, applicant income, loan amount and loan purpose and applicant gender. The result presented in Table 7 showed that even after controlling for these variables, the significant racial difference still persist. For example, in the LPM model, the probability of the loan being originated for White is 0.12 greater than non-white in general while when segregated, the probability of the loan being originated for White is 0.22 greater than that of American Indian, 0.065 greater than that of Asian, 0.163 greater than that of Black and 0.13 greater than that of Native Hawaiian. Similarly, in the probit model, the probability of the loan being originated for White is 0.37 greater than non-white in general while when segregated, the probability of the loan being originated for

White is 0.62 greater than that of American Indian, 0.23 greater than that of Asian, 0.49 greater than that of Black and 0.41 greater than that of Native Hawaiian. All differences are statistically significant. Similarly, in the logit model, the odds of loans being originated for White is 1.88 times that of non-White in general and when segregated, American Indian has 64.3% lower odds of having their loan originated than Whites. Asian applicants has 32.5% lower odds of having their loan originated than Whites, Black has 55.4% lower odds of having their loan originated than Whites and Native Hawaiian have 49.6% lower odds of having their loan originated than Whites. Conversely, in the case of ethnicity, the sign reversed when we control for these variables as non-hispanic now have lower probability and odds of having their loan originated. than Hispanic. This means that the ethnic segregation we observe before may not be real but the racial segregation is real.

## 7. Discussion

The study aims at investigating racial discrimination in housing. The result showed that for loans denied, debt-to-income ratio, credit history and collateral are major reasons while loans were denied for all the groups. The result showed that more Whites have their loan originated than Non-Whites while less Hispanic have their loan originated than non-Hispanic. Moreover, disaggregating the race, the result showed that American Indian have almost half of their application rejected comapared to 22.87% for Whites. Blacks have almost 18 percentage points rejection compared to Whites while if we consider Native Hawaiian, there is 16 percentage points higher rate of denial compared to Whites. The racial segregation seemed to have been entrenched over history as the proportion of non-Whites seeking loan for refinancing or house improvement is lower than that of Whites which depicts that more Whites own homes than non-Whites in the past.

The regression models showed that for LPM, probit and logit models, without controlling for other factors, there is significant difference across ethnicity and race. The result showed that Hispanic have lesser chance of getting loans than non-Hispanic and non-Whites in general have lower chance of getting loans than Whites. If we seggreagate race, the result showed that American Indian have the lowest chance of securing mortgage loans followed by Black/African American then by Native Hawaiian and finally by Asian applicants. However, when variables like loan amount, applicants income, gender, household income and loan purpose were controlled for, the result showed that there is reversal for Hispanic and non-Hispanic which means after controlling for these variables, Hispanic now have higher probability of securing loan than non-Hispanic. This means that there is no ethnic segregation in loans and the difference found in the simple model is due to factors not controlled for. However, even after adding the control variables for race and disaggregated race, the result still remain the same which means that there is sufficient evidence that there is racial segregation in assessing mortgage loan in New York. The result supports the first hypothesis that loan originators consider race when deciding to originate loans or deny loans while there is no support for the second hypothesis that loan originators consider ethnicity (being Hispanic or not) when deciding to originate loans or deny loans. The result support the findings of (Krieger and Hikkins, 2002, Martinez and Kirchner, 2021, Williams, 2020; Ray et al., 2021) who also found significant racial segregation in mortgage loans.

## 7.0. Conclusion

This study investigates the presence of racial and ethnic segregation in mortgage loans in New York using the Home Mortgage Disclosure Data for the state of New York for the year 2015. The hypothesis was that loan originators consider ethnicity and race when deciding to originate loans or deny loans. descriptive statistics and binary models like linear probability model, logit model and probit model were used to compare findings. While the study provide evidence for the presence of racial segregation, no evidence was found for ethnic segregation. Therefore, despite the introduction of the Fair Housing Act of 1968 to erase racial discrimination in housing, the act have not had desired effect as racial segregation still persisits and there is need for stakeholders to take urgent step to attack this menace so that no American will live as a second-class citizen in the land of their fathers.

## References

Baert, S and Pauw, A (2014). Is Ethnic Discrimination Due to Distaste or Statistics?" Economics Letters. 125 (2): 270–273.

Bayer P., Ferreira F., Ross S.L. (2014). Race, Ethnicity and High-Cost Mortgage Lending Working Paper. National Bureau of Economic Research; 2014.

Been V, Ellen IG, Madar J. (2009) The High Cost of Segregation: Exploring Racial Disparities in High-Cost Lending. Fordham Urban Law

Brancaccio, D and Conlon, R. (2021). How Mortgage Algorithms Perpetuate Racial Disparity in Home Lending. Available at https://www.marketplace.org/2021/08/25/housing-mortgage-algorithms-racial-disparities-bias-home-lending/ [retrieved 12 Jan 2022]

Hanck, C., Arnold, M., Gerber, A., and Schmelzer, M. (2021). Introduction to Econometrics with R. Open Review

Krieger J, Higgins DL (2002) Housing and Health: Time Again For Public Health Action. Am J Public Health. 2002 May; 92(5):758-68.

Krueger, Alan B. (2002-12-12). Economic Scene; Sticks and Stones Can Break Bones, But The Wrong Name Can Make A Job Hard To Find. The New York Times.

Martinez, E and Kirchner, L. (2021). How We Investigated Racial Disparities in Federal Mortgage Data. Available at https://themarkup.org/show-your-work/2021/08/25/how-we-investigated-racial-disparities-in-federal-mortgage-data [retrieved 12 Jan 2022]

Perrallion, M.C. (2019). Week 12: Linear Probability Models, Logistic and Probit. University of Colorado Anschutz Medical Campus

Perry, A.M. (2021). How Racial Disparities in Home Prices Reveal Widespread Discrimination. Available at https://www.brookings.edu/testimonies/how-racial-disparities-in-home-prices-reveal-widespread-discrimination/ [retrieved 12 Jan 2022]

Ray, R., Perry, A.M., Harshbarger, D., Elizondo, S. and Gibbons, A. (2021). Homeownership, Racial Segregation, and Policy Solutions To Racial Wealth Equity. Available at https://www.brookings.edu/essay/homeownership-racial-segregation-and-policies-for-racial-wealth-equity/ [retrieved 12 Jan 2022]