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1 Table of Information Course ECON1193 – Business Statistics Campus Saigon South Campus Semester Semester A – 2020 Assignment Assignment 2: Individual Case Study Topic Maternal Mortality Ratio Data Set MMR_03 Lecturer Greeni Maheshwari Student Huynh Nhat Dang s3817974 s3817974@rmit.edu.vn Class time Friday – 8:00 A.M Pages Table of Contents Abbreviation I Introduction II Descriptive Statistics and Probabiity Probability a Test of statistical dependence b Country category identification III Descriptive Statistics a Measure of Central Tendency b Measure of Variation .8 c Measure of Shape Confidence Intervals Calculation Assumption for calculation Discussion on confidence intervals result IV Hypothesis Testing 10 Trend of world maternal mortality ratio 10 Hypothesis testing procedure 10 Discussion on hypothesis testing result 11 V Conclusion 12 References 13 Appendice 14 Appendix A Sustainable Development 17 Goals 14 Appendix B Maternal Mortality Ratio Trends by region 15 Appendix C Life time risk of maternal deaths by income group: in X 15 Appendix D Country list of the data set 15 Abbreviation (Notice: Some acronyms are also included with their explanation in the report.) CPD – United Nations Population Division CRVS - Civil Registration and Vital Statistics (CRVS) systems GNI – Gross National Income MMR – Maternal mortality ratio MMRate – Maternal mortality rate SDGs- Sustainable Development Goals UN – United Nations UNFPA – United Nations Population Fund UNICEF – United Nations Children Fund WBG – World Bank Group WHO – World Health Organization I Introduction Sustainable development over decades has become a globally heated topic, with an utmost concern of ensuring human well-being by balancing social, economic and environmental aspects, allowing prosperity for current and future generations (Anbu 2020) Among a wide range of components in sustainability, maternal health, wellbeing and survival remain primary goals and an investment priority in the post-2015 framework for sustainable development strategy, at which social and health experts have adapted many statistical methods to examine performance of healthcare system and global health status for further improvement (WHO 2015) Maternal mortality ratio – one of the most widely used measures to quantify the risk of maternal deaths relative to the number of live births, has become a key performance indicator of the overall health population, of social status of women in the society, and of the functioning of national healthcare system (WHO 2006) In fact, MMR measures the number of maternal deaths during a specific time period per 100,000 births during the same time period, different from a concept of maternal mortality rate (MMRate) – number of maternal deaths divided by women’s personal years ( WHO et al 2015) According to the report of WHO in 2015, a 45% reduction has been witnessed in maternal mortality ratio over the past 25 years, (from 380 deaths/ 100,000 live births in 1990 to 210 deaths/ 100,000 live births in 2015), yet it is far falling short of a global goal Of the global maternal deaths in 2015, developing regions account for approximately 99% (UNICEF 2019); yet, it is targeted that no country should have an MMR greater than 140/100,000 live births as an expectation by 2030 (WHO 2015) Targeting for maternal mortality ratio is vital, but accurate measurement of maternal mortality ratio remains an immense challenge for many reasons: numbers of deaths still go unnoticed and uncounted, a reluctance to report abortion-related health and even a lack of medical atribution and CRVS system (WHO et al 2019) Therefore, it is observed that there has been a signficant progress in maternal deaths reduction; however, there is a plenty of room to improve as well as challenges to tackle in a global world With its aim to promote sustainable development in health service, the United Nations has build up the 2030 Agenda for Sustainable Development with a total of 17 goals (Appendix A – UN 17 goals), at which the goal number aiming at “ensuring healthy lifes and promoting well-being at all ages” with monitoring maternal mortality ratio as one of important elements (UN 2017) The significance of reducing maternal mortality ratio links to an accomplishment of the goal in multiple ways: when reproductive health – a beginning stage of human life is adequately addressed, it quantifies that quality care for women and children is ensured before, during and after childbirth, laying a foundation for future children well-being development (WHO 2018) Also, the majority of death causes are preventable in the case that healthcare systems can ensure equitable equipment and treatment to women, where they can be treated with effective and timely clinical interventions for prenatal care (Jolivet et al 2018) Hence, if nations have successfully developed sustainable development for the aspects of clinical care, they are highly capable of minimizing these maternal risks involved, thus lowering maternal mortality ratio significantly (Child E.W.E 2018) Although maternal mortality is considered a global challenge, a disparity in maternal mortailtiy ratio exists between different nations, according to the World Health Statistics (WHO 2018) The conduct of Girum and Wasie (2017) points out that countries with low and middle income are facing a much higher MMR, pointing out that along with adult literacy rate, GNI per capital are signficantly negatively correlated with MMR In reality, almost of the deaths (99%) occurred in low-and middle income countries, with almost two-thirds (64%) occuring in African Region, followed by Southern Asia (Appendix B, UNICEF), which could be explained by a lack of proper medical care among these nations (WHO 2014) By contrast, high- income countries witness an opposite pattern with rare maternal death occasion - over 5400 lifetime risks (Appendix C, UNICEF) Therefore, the evidence shows that there exists an inverse relationship between two variables - MMR and GNI This following report covers a number of aspects, including an analysis of the maternal mortality ratio among 38 studied countries and thorough investigation into the relationship between MMR and Gross National Income (GNI) Its aim is to figure out what is behind this trend of maternal mortality ratio, at which three methods of descriptitve statistics and a conduct of confidence intervals and hypothesis testing would be respectively applied, interpreted and evaluated in a systematic manner II Descriptive Statistics and Probabiity Probability There are a total of 38 participating countries in the study (Appendix D- country list), which is divided into three categories based on their Gross Domesitc Income: Low-income countries (LI) GNI less than$1000 per capita GNI between $1000 and $12500 per capita Middle-income countries (MI) GNI higher than $12500 per capita High-income countries (HI) Additionally, they are also grouped into two different categories according to their maternal mortality ratio The country would be regarded as having high maternal mortality ratio (H), provided that it happens to have more than 50 death cases per 100,000 live births By contrast, those having equal or fewer than 50 deaths per 100,000 live births are classified as “low maternal mortality ratio” countries (L) Below is a contigency table that has put countries into these multiple categories: Low Maternal Mortality Ratio (L) Total Low-Income Countries (LI) High Maternal Mortality Ratio (H) Middle-Income Countries (MI) High-Income Countries (HI) 17 12 20 12 Total 23 15 38 Table II.1: Contigency Table of each country category on Maternal Mortality Ratio (2015) a Test of statistical dependence With the purpose of determining whether income and maternal mortality ratio are statistically dependent or independent, we use a mathematical evidence by comparing a probability of all countries with a high maternal mortality ratio (H), regarded as P (H), and a conditional probability of countries having high maternal mortality ratio (H) given that they are high-income countries (HI), which is P (H | HI) Here is the result: P (H | HI) = = = P (H) = = = 0.605 P (H | HI) P (H); (0 From the above calculation, the probablity of countries having high maternal mortality ratio P (H) is not equal to the probablity of countries having high maternal mortality ratio given that they are high-income ones, leading to a conclusion that income and maternal mortality ratio are statistically dependent events It also means that the level of country income has an impact on the occurrence of maternal mortality b Country category identification To identify which country category most likely to have a high maternal mortality ratio, we calculate a conditional probability of countries having high maternal mortality ratio given that they belong to each category (low-income, middle-income or high-income): P (H ǀ HI) = = = 0% P (H ǀ MI) = = 0.85 = 85% P (H | LI) > P (H | MI) > P (H | HI) P (H ǀ LI) = = = 100% From the above calculation, low-income country is the category with the greatest likelihood of having high maternal mortality ratio, with the probability of 100% - clearly explained, all countries (6 over 6) in the category have high maternal mortality ratio This indicates that low-income countries are more likely to have high maternal mortality ratio than other country categories Descriptive Statistics Low (LI) Middle (MI) High (HI) Min >, > > Lower Bound -427.125 -123.25 -3.5 Max >, < Upper Bound 1463.875 358.75 22.5 Result No outliers upper outliers No outliers Table II.2: Test of outliers in three country categories (unit: deaths per 100,000 live births) With a view to guarantee an accurate analysis of three measurements in descriptive statistics, a test of outliers is conducted From an above test table, it is confirmed that there are two existing upper outliers in the middleincome category, which have extremely high maternal mortality ratio compared to others in the same category a Measure of Central Tendency Mean Median Mode High-income 9.75 10 10 Middle-income 184.3 126.5 114 Low-income 544.2 402 - Table II.3: Central Tendency of each country category on Maternal Mortality Ratio (2015) (unit : deaths per 100,000 live births) Since we have calculated that two outliers exist in the data set, the only measure in central tendency not affected by extreme values is Median Therefore, Median is the most suitable tool to be applied in this case As can be seen from Table II.3, the median of low-income countries is the highest with 544.2 deaths per 100,000 births To be more detailed, 50% of low-income countries would have a maternal mortality ratio greater than 544.2 deaths per 100,000 births, which is also the highest number of all categories This is followed by middle-income countries with 184.3 deaths per 100,000 births, and high-income countries appear to have the lowest median with only 9.75 deaths per 100,000 births, nearly sixty-six times smaller than Median of low-income countries Hence, the comparison of Median shows that low-income countries witness a much higher maternal mortality ratio than those with higher income level; and the higher the income level is, the smaller Median and lower maternal mortality ratio b Measure of Variation Range Interquartile Range Standard Deviation Coefficient of Variation High-income 14 6.5 Middle-income 807 120.5 Low-income 1102 472.75 4.025 41.29 % 221.22 120.03% 416.58 76.55 % Table II.4: Measure of variation of each country category on Maternal Mortality Ratio (2015) (unit : deaths per 100,000 live births) Because Means of all three categories are drastically different from one another, the best measure to compare a degree of variation is Coefficient of Variation (CV), which is specifically designed for comparing multiple data sets with distinctive Means From a Table II.4, high-income countries have the lowest CV with 41.29%, meaning that their maternal mortality would concentrate more on an average value 9.75 and less disperse At the same time, Middle-income and low-income countries have higher CVs, especially middle-income category with about 120% These values suggest that two country categories witness a signficant spread of maternal mortality ratio from average values This higher level of variation might become an obstacle to draw an accurate conclusion of statistical patterns in specific category c Measure of Shape Figure II.5: Measure of Shape of each country category on Maternal Mortality Ratio (2015) (unit : deaths) The figure II.5 points out many noticeable differences between box-and-whisker plots of three country categories Firstly, data distribution of high and middle-income countries are left-skewed while that of lowincome countries is opposite with right-skewness, even though both middle and low income countries have a higher Mean compared to the Median It could be explained by the existence of two upper-bound outliers in middle-income country category, making its Mean value become higher than it supposedly is In addition, we can see that middle-income countries has the longest right whisker since it contains extreme values and both middle and low-income countries witness greatly stretched box-and-whisker plots far to the right These skewness patterns indicate that maternal mortality ratio in 50% of low-income countries is likely to concentrate on significant values of the right side while maternal mortality ratio of high and middle-income countries would be more concentrated to the left, with middle-income being more variable III Confidence Intervals Calculation This part aims to calculate confidence interval of the world average maternal mortality ratio (per 100,000 live births) It is supposed that the level of significance (α) is 0.05 Hence, its confidence level is calculated: 1- 0.05 = 0.95 A table of data for confidence interval calculation is attached below: Signficance level α 5% Confidence level (1 - )*100% 95% Population standard deviation unknown Sample standard deviation S 281.89 186 Sample mean Sample size n 38 As the population standard deviation is unknown, we will resort to sample standard deviation S; therefore, Student’s t-table distribution is used instead of z-table: Degree of freedom: d x f = n – = 37 t = 1.6871 Significance level: = 0.05 So, we are 95% confident that the world average maternal mortality ratio in 2015 lies between 108.85 and 263.15 deaths per 100,000 live birth Assumption for calculation In the calculation, although a population standard deviation is unknown, a sample size of the data set is 38, which is higher than 30 – a requirement from the Central Limit Theorem Therefore, Central Limit Theorem is applicable and the simple size is sufficiently large to have an approximately normal distribution, hence no assumption is needed Discussion on confidence intervals result In the case that a population standard deviation is recognized, z-value table would come into use because of having both sufficient sample size and population standard deviation One advantage of utilizing a z-value table for confidence interval calculation is of its standardization from an actual population data ( Educba n.d.), and the mean and sample standard deviation S are likely to vary dramatically from one sample to another in studentt distribution, which generates a greal deal of uncertainty into statistics work (Anderson 2014) Once a degree of uncertainty diminishes, a confidence interval is getting smaller, since confidence interval is a way to show what the uncertainy is with a certain statistic (Moore & McCabe 2002) At the same time, for any given level of confidence, critical z-values are smaller than critical t-values when the sample size is not considerable (McEnvoy 2018) And, when critical values are smaller, confidence intervals width will decrease, supporting our above idea that using a population standard deviation will cause narrower confidence intervals With this decrease in width of confidence intervals, a margin of error (e) – a factor to view a difference of a sample mean from a true population mean will get smaller, ensuring a precise result from the calculation (Bowerman, Duckworth & Froelich 2018) In short, when a population standard deviation is known, confidence interval width gets narrower for higher certainty, leading to a more accurate confidence intervals result IV Hypothesis Testing Trend of world maternal mortality ratio From a calculation in Part III, we are 95% confident that the world average maternal mortality ratio in 2015 is between 108.85 and 263.15 deaths per 100,000 live births According to the report of WHO, the world average maternal mortality ratio in 2014 is 221 deaths per 100,000 live births When comparing this value with a confidence interval calculated above, the average value in the year 2014 – 221 deaths falls between 108.85 and 263.15 deaths, making it unsure to state that whether the maternal mortality ratio will decrease, increase or remain unchanged in the long run Yet, a point estimate of the confidence interval (the sample mean) is 186 deaths, which is seen to be lower than 221 deaths in the 2014 data Therefore, we would make a speculation that the world maternal mortality ratio is expected to decrease in the future A hypothesis testing is conducted to examine our claim Hypothesis testing procedure Signficance level α 5% Confidence level (1 - )*100% 95% Population standard deviation unknown Sample standard deviation S Population mean 281.89 221 Sample mean 186 Sample size n 38 Step Check the distribution: because the sample size n is 38 which is higher than 30, a Central Limit Theorem (CLT) is applicable, satisfying that the sampling distribution of mean is normally distributed Step State null and alternative hypotheses: Null hypothesis H0; < 221 (our claim) Alternative hypothesis H1; 221 Step Choose table: The population standard deviation is unknown and a mean sampling distribution is normally distributed, so we would use a t-table Step Choose rejection region: With the sign of H1 is “”, we would use an upper-tailed test Step Determine critical value (CV): Degree of freedom: d x f = n – = 37 Level of significance: = 0.05 Since it is an upper-tailed test, t is +1.687 10 Step Compute test statistic Step Make a statistical decision Critical value lies in a Non-Rejection region: – 0.765 (t’) < 1.687 (t) Therefore, we not reject the null hypothesis Ho Figure IV.1 t-distribution graph with rejection regions and t-statistics value Step Make a managerial conclusion in the context of real-world As H o is not rejected, hence with 95% of confidence it can be concluded that the world maternal mortality ratio will decrease in the future Step Determine the type of error Since we not reject Ho, it is possible that we might have committed Type II error (β) P (Type II error) = – Power of the test We say that the maternal mortality ratio will decrease in the future, but actually there are chances that maternal mortality ratio might not decrease in the future Type II error could be minimized by increasing the sample size (n) or increasing the significance level ( α), since the higher α means a higher probability of rejecting the null hypothesis when it is actually true Discussion on hypothesis testing result Supposing that the number of countries of the data set will triple, it stands that a degree of freedom (n-1) increases since they are related to each other; it leads to a change in the graph of t-distribution that it will have skinner tails, thus pushing the critical value t closer to the Mean, a Non- rejecion region in this case (Kerr et.al 2002) At the same time, the sample mean also moves to a closer position to an actual population Mean and the data distribution is less variable, making a standard deviation S become smaller (Salkind 2011) With a smaller S and a larger n, a test statistic t’ would go up as its formula is t = , moving t’ closer to a Rejection region With both t and t’ moving towards each other, it is possible that there is a change in final decision if these two values are relatively close to each other However, when looking into our case, a test statistic point is notably far from a critical value (Figure IV.1), making a test statistic point hard to cross a Rejection region even with such changes Therefore, it could be said that the statistical decision will remain unchanged In fact, an increasing sample size boosts higher accuracy Since sample size (n) is a denominator of the standard error formula e = , with the standard error being inversely proportional to the sample size (Rumsey 2016), a tripling increase in sample size will cause a decrease in standard error With this decrease in error, the statistic result becomes more accurate as the smaller the standard error gets, the more representative the sample is for an entire population (Kenton 2019) Holmes et al (2017) also stated that increasing the sample size can increase the Power of the Test (1- β), with a larger sample size means more information we have and our uncertainty reduces, thus lowering a 5% chance of committing Type II error 11 V Conclusion To sum up, this report on available data of 38 countries regarding their maternal mortality ratio has overall indicated that MMR and Gross National Income (GNI) have a negatively correlated relationship, strongly confirmed in Probability and Descriptive Statistics sections Moreover, the maternal mortality ratio is estimated to experience a downward trend in the future, as stated in Hypothesis Testing Many key findings of this paper are consequently pointed out in the following paragraph: The first finding is based on Probability section, that GNI and MMR are two statistically dependent events, meaning that the probability of countries having high MMR depends on its gross national income It is explained with a contigency table, suggesting that the probability of all country having high MMR is different from the probability of countries with high MMR given that they are high-income In particular, countries with low level of income are more likely to have a high maternal mortality ratio, supported by the probability of countries having high MMR given that they are low-income being the highest A strongly inverse relationship between MMR and GNI is the second finding with an application of three measures in descriptive statistics: central tendency, variation and shape The median deaths are falling significantly from 545 deaths to only nearly 10 deaths per 100,000 live births when GNI level decreases, suggesting that the higher gross national income is, the lower maternal mortality ratio its country has Also, the signficant difference in maternal mortality ratio between high-income countries and middle-to-low income countries is remarkably highlighted in two measures: co-efficiency of variation as well as a box-whisker plot It comes to a final conclusion that high-income countries have the lowest MMR, noticeably so with a comparatively negligible number of maternal deaths, as stated in Part 2, Appendix C; while middle and low-income countries account for the largest MMR, thus strengthening a claim of strongly negative relationship between MMR and GNI The final finding is drawn from a confidence interval and hypothesis testing part It is calculated that an average MMR in 2015 is between 108.85 and 261.15 deaths per 100,000 live births, with the point estimate being lower than average data in previous year After conducting a hypothesis testing in Part 4, we are 95% confident that the world maternal mortality ratio will decrease in the future, but actually the world maternal mortality ratio might not decrease in the future In consideration of the above, these findings could become valuable assets for strategic-planning of reaching global SDG target 3: once a relationship between MMR and GNI is thoroughly addressed, experts now realize a need to go beyond just a sole focus on mortality, linking it to further and broader facets – socio-economic issues They could deeply concentrate on these country and regional challenges including health system, family planning or women’s social status and education, meanwhile observing developed healthcare function among high-income countries for further research From that point, appropriate measures would be taken to help lowincome countries prevent maternal deaths References Anbu, S 2020, ‘Sustainable Development: The Balance between Conserving Environmental Resources and Economic Development’, National Seminar on Climate change, Environment and Agricultural Development, Madurai, 27-28th March 2014, p.p 2-3 Anderson, A 2014, Business statistics for dummies, John Wiley & Sons, Inc., NJ 12 Bowerman, B.L., Duckworth, W M & Froelich, A 2018, Business statistics and analytics in practice, 9th edn, McGraw-Hill Education, NY Child E.W.E 2016, Indicator and Monitoring Framework for the Global Strategy for Women's, Children's and Adolescents' Health (2016-2030), WHO, USA Educba n.d., ‘Z score vs T score’, Educba, viewed 25 April 2020, < https://www.educba.com/z-score-vs-tscore/> Holmes, A., Susan, D, Barbara, I & Kevin, H 2017, Introductory Business Statistics, 1st edn, Openstax.org Jolivet, R., Moran, A., O’Connor, M., Chou, D., Bhardwaj, N., Newby, H., Requejo, J Schaaf, M., Say, L & Langer, A 2018, Ending preventable maternal mortality: Phase II of a multi-step process to develop a monitoring framework, 2016-2030 BMC Pregnancy and Childbirth, USA Kenton, W 2019, ‘Standard Error’, Investopedia, viewed 25 April 2020, Kerr, A.W., Hall, H.K & Kozub, S.A., 2002, Doing statistics with SPSS, Sage Publication, GB, pp 68-71 10 McEvoy, D M., 2018, Guide to Business Statistics John Wiley & Sons, Inc., USA 11 Moore, D.S & McCabe G., 2002, Introduction to the Practice of Statistics, 4e, CD & SPSS Manual, 4th edn, Freeman, UK 12 RMIT University Vietnam 2020, Maternal Mortality Ratio Dataset, RMIT University Vietnam, accessed 25 April 2020 13 Rumsey, D 2016, Statistics for dummies, 2nd edn, Wiley Publishing, Inc., IN 14 Salkind, N., J., 2011, Statistics for people who (think they) hate statistics, Thousand Oaks Publication, CA 15 UN 2017, The Sustainable Development Goals Report 2017, Department of Economic and Social Affairs (DESA), UN, United Nations Publications, USA 16 UNICEF 2019, ‘Maternal mortality declined by 38 percent between 2000 and 2017’, UNICEF, viewed 27 April 2020, < https://data.unicef.org/topic/maternal-health/maternal-mortality/> 17 WHO 2006, Reproductive Health Indicators: Guidelines for Their Generation, Interpretation and Analysis for Global Monitoring, World Health Organization 18 WHO 2014, Maternal Mortality Fact Sheets, WHO, viewed 27 April 2020, < https://www.who.int/en/newsroom/fact-sheets/detail/maternal-mortality> 19 WHO 2015, Strategies toward ending preventable maternal mortality (EPMM), WHO, viewed 26 April 2020, 20 WHO 2018, World Health Statistics 2018: Monitoring Health for the SDGs Sustainable Development Goals, WHO Publications, LU 21 WHO, UNICEF, UNFPA, WBG, CPD 2015, Trends in maternal mortality: 1990 to 2015: estimates by WHO, UNICEF, UNFPA, World Bank Group and the United Nations Population Division, WHO, viewed 26 April 2020, 13 22 WHO, UNICEF, UNFPA, WBG, CPD 2019, Trends in maternal mortality: 2000 to 2017: estimates by WHO, UNICEF, UNFPA, World Bank Group and the United Nations Population Division, WHO, viewed 28 April 2020, < https://www.unfpa.org/featured-publication/trends-maternal-mortality-2000-2017> Appendice Appendix A Sustainable Development 17 Goals Reproduced from United Nations n.d 14 Appendix B Maternal Mortality Ratio Trends by region Reproduced from UNICEF 2019 Appendix C Life time risk of maternal deaths by income group: in X Reproduced from UNICEF 2019 Appendix D Country list of the data set 15 Country Name Maternal mortality ratio (modeled estimate, per 100,000 live births) GNI per capita, Atlas method (current US$) High-Income Norway Qatar Singapore Netherlands New Zealand Saudi Arabia Slovenia Portugal Puerto Rico Oman Slovak Republic Poland 93050 75660 54020 49030 40270 23810 22240 20440 19430 18150 17580 13340 13 10 11 12 10 14 17 11480 9530 7280 6160 6070 5540 5320 4210 4070 3520 3020 2850 2780 2020 1950 1920 1690 1430 1190 1020 94 31 68 138 17 265 132 51 114 121 814 215 150 54 114 156 178 178 789 980 740 710 580 550 390 315 258 290 489 1360 553 Middle-income Panama Romania Montenegro Peru South Africa Serbia Namibia Paraguay Samoa Philippines Morocco Nigeria Papua New Guinea Nicaragua Vietnam Solomon Islands Sao Tome and Principe Pakistan Myanmar South Sudan Low-income Senegal Nepal Rwanda Mozambique Sierra Leone Niger Reproduced from RMIT University Vietnam 2020 16 17 ... manner II Descriptive Statistics and Probabiity Probability There are a total of 38 participating countries in the study (Appendix D- country list), which is divided into three categories based... sample size and population standard deviation One advantage of utilizing a z-value table for confidence interval calculation is of its standardization from an actual population data ( Educba... n .d .), and the mean and sample standard deviation S are likely to vary dramatically from one sample to another in studentt distribution, which generates a greal deal of uncertainty into statistics
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