Investigate if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years) Essay Example

Investigate if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years) Essay Example Investigate if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years) Essay Investigate if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years) Essay Essay Topic: Life Of Pi My aim is to investigate if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years). The GDP is the gross domestic product or value of all final goods and services produced within a nation in a given year. GDP dollar ($) estimates are derived from purchasing power parity (PPP) calculations. The GDP per capita ($) shows GDP on a purchasing power parity basis divided by population. The life expectancy at birth shows the average number of years to be lived by a group of people born in the same year, if mortality at each age remains constant in the future. It shows the life expectancy on average for the total population for male and females. Life expectancy at birth is also a measure of overall quality of life in a country and summarizes the mortality at all ages. The reason for doing this investigation is that I have seen a lot of documentaries and read a lot of articles in the newspaper which have talked about how the gap between rich and poor has increased. This has led to a poorer quality of life in developing countries. So I wanted to see if there was any link between how rich a country is per person and what on average is the life expectancy for a person is in that country. This will help me get a better understanding of how rich a country is how much it affects the quality of life. This is the reason why I think the investigation is worth doing. Data collection: The data I collected was the GDP per capita using the purchasing power parity ($) and the life expectancy at birth (years). I have collected data for these two variables from the whole world. So my population is defined as the whole world. I obtained the data from the www.CIA.gov and clicked on the world fact book. I got 239 pieces of data originally for both then I had to reject 11 pieces of data for both because some countries did not have any data for the GDP. So from the 228 I used a sampling method of choosing every 4th country on the list until I narrowed my sample to 50 countries. I chose every 4th number because when you divide 228 by 50 and choose the integer number you get 4 this ensures this is a random sampled number which provides the most representative sample from the population. I used a systematic sampling method. The list was in alphabetical order and not in rank order for both variables so by using this method Im not creating any bias. Since the data is from the CI A website I must presume that the data is accurate and reliable. Here is a table of my data which has been systematically sampled to show 50 pairs of data: Country GDP per capita, Purchasing Power Parity ($) Life expectancy at birth (years) American Samoa 8000 75.75 Anguilla 8600 76.7 Armenia 3600 66.68 Bahamas, The 15300 65.71 Barbados 15000 71.84 Benin 1100 51.08 Bolivia 2500 64.78 British Virgin Islands 16000 76.06 Burma 1700 55.79 Cameroon 1700 48.05 Central African Republic 1200 41.71 China 4700 72.22 Congo, Democratic Republic of the 600 48.93 Cote dIvoire 1400 42.65 Djibouti 1300 43.13 East Timor 500 65.2 El Salvador 4600 70.62 Ethiopia 700 41.24 French Guiana 14400 76.69 Gambia, The 1800 54.38 Ghana 2000 56.53 Grenada 5000 64.52 Guatemala 3900 65.23 Guinea-Bissau 700 46.97 Honduras 2500 66.65 India 2600 63.62 Iraq 2400 67.81 Jersey 24800 78.93 Kenya 1100 45.22 Korea, South 19600 75.36 Laos 1800 54.3 Liberia 1000 48.15 Macau 18500 81.87 Malaysia 8800 71.67 Malta 17200 78.43 Martinique 10700 78.72 Mayotte 600 60.6 Monaco 27000 79.27 Morocco 3900 70.04 Nauru 5000 61.95 New Caledonia 14000 73.52 Nigeria 900 51.01 Pakistan 2000 62.2 Papua New Guinea 2100 64.19 Philippines 4600 69.29 Reunion 5600 73.43 Saint Helena 2500 77.38 Saint Pierre and Miquelon 11000 78.11 San Marino 34600 81.43 Saudi Arabia 11400 68.73 Modelling procedures: I am going to do a scatter diagram of GDP per capita against life expectancy at birth for my 50 pairs of data to see if there is any correlation. A scatter diagram is an appropriate modeling procedure as it shows a clear relationship between two random variables. As you can see from the scatter diagram the points form a relationship which appears to be a curve so to try to establish a more linear relationship. I am going to do this by first logging my data for the GDP per capita and not logging the life expectancy data and then do a scatter diagram of this data. I am then going to log the life expectancy data but not the GDP per capita data and do a scatter diagram of this data. Then finally I am going to log both my data for GDP per capita and the life expectancy at birth and do a scatter diagram. I am going to check which scatter diagram gives the strongest linear correlation and thats the data Im going to chose. Country Life expectancy at birth (years) Log of GDP per capita, Purchasing Power Parity ($) American Samoa 75.75 3.903089987 Anguilla 76.7 3.934498451 Armenia 66.68 3.556302501 Bahamas, The 65.71 4.184691431 Barbados 71.84 4.176091259 Benin 51.08 3.041392685 Bolivia 64.78 3.397940009 British Virgin Islands 76.06 4.204119983 Burma 55.79 3.230448921 Cameroon 48.05 3.230448921 Central African Republic 41.71 3.079181246 China 72.22 3.672097858 Congo, Democratic Republic of the 48.93 2.77815125 Cote dIvoire 42.65 3.146128036 Djibouti 43.13 3.113943352 East Timor 65.2 2.698970004 El Salvador 70.62 3.662757832 Ethiopia 41.24 2.84509804 French Guiana 76.69 4.158362492 Gambia, The 54.38 3.255272505 Ghana 56.53 3.301029996 Grenada 64.52 3.698970004 Guatemala 65.23 3.591064607 Guinea-Bissau 46.97 2.84509804 Honduras 66.65 3.397940009 India 63.62 3.414973348 Iraq 67.81 3.380211242 Jersey 78.93 4.394451681 Kenya 45.22 3.041392685 Korea, South 75.36 4.292256071 Laos 54.3 3.255272505 Liberia 48.15 3 Macau 81.87 4.267171728 Malaysia 71.67 3.944482672 Malta 78.43 4.235528447 Martinique 78.72 4.029383778 Mayotte 60.6 2.77815125 Monaco 79.27 4.431363764 Morocco 70.04 3.591064607 Nauru 61.95 3.698970004 New Caledonia 73.52 4.146128036 Nigeria 51.01 2.954242509 Pakistan 62.2 3.301029996 Papua New Guinea 64.19 3.322219295 Philippines 69.29 3.662757832 Reunion 73.43 3.748188027 Saint Helena 77.38 3.397940009 Saint Pierre and Miquelon 78.11 4.041392685 San Marino 81.43 4.539076099 Saudi Arabia 68.73 4.056904851 Country GDP per capita, Purchasing Power Parity ($) Log of Life expectancy at birth Log (years) American Samoa 8000 1.879382637 Anguilla 8600 1.884795364 Armenia 3600 1.823995591 Bahamas, The 15300 1.817631467 Barbados 15000 1.856366324 Benin 1100 1.708250889 Bolivia 2500 1.811440944 British Virgin Islands 16000 1.881156321 Burma 1700 1.746556361 Cameroon 1700 1.681693392 Central African Republic 1200 1.62024019 China 4700 1.858657484 Congo, Democratic Republic of the 600 1.689575216 Cote dIvoire 1400 1.629919036 Djibouti 1300 1.634779458 East Timor 500 1.814247596 El Salvador 4600 1.848927713 Ethiopia 700 1.615318657 French Guiana 14400 1.884738738 Gambia, The 1800 1.735439203 Ghana 2000 1.752278985 Grenada 5000 1.809694359 Guatemala 3900 1.814447379 Guinea-Bissau 700 1.67182056 Honduras 2500 1.823800154 India 2600 1.803593665 Iraq 2400 1.831293744 Jersey 24800 1.897242103 Kenya 1100 1.655330558 Korea, South 19600 1.87714089 Laos 1800 1.73479983 Liberia 1000 1.682596291 Macau 18500 1.91312479 Malaysia 8800 1.855337404 Malta 17200 1.894482215 Martinique 10700 1.896085085 Mayotte 600 1.782472624 Monaco 27000 1.899108858 Morocco 3900 1.845346137 Nauru 5000 1.792041311 New Caledonia 14000 1.866405498 Nigeria 900 1.707655324 Pakistan 2000 1.793790385 Papua New Guinea 2100 1.807467376 Philippines 4600 1.840670561 Reunion 5600 1.865873528 Saint Helena 2500 1.888628725 Saint Pierre and Miquelon 11000 1.892706638 San Marino 34600 1.910784435 Saudi Arabia 11400 1.837146344 Country Log of GDP per capita, Purchasing Power Parity Log ($) Log of Life expectancy at birth Log (years) American Samoa 3.903089987 1.879382637 Anguilla 3.934498451 1.884795364 Armenia 3.556302501 1.823995591 Bahamas, The 4.184691431 1.817631467 Barbados 4.176091259 1.856366324 Benin 3.041392685 1.708250889 Bolivia 3.397940009 1.811440944 British Virgin Islands 4.204119983 1.881156321 Burma 3.230448921 1.746556361 Cameroon 3.230448921 1.681693392 Central African Republic 3.079181246 1.62024019 China 3.672097858 1.858657484 Congo, Democratic Republic of the 2.77815125 1.689575216 Cote dIvoire 3.146128036 1.629919036 Djibouti 3.113943352 1.634779458 East Timor 2.698970004 1.814247596 El Salvador 3.662757832 1.848927713 Ethiopia 2.84509804 1.615318657 French Guiana 4.158362492 1.884738738 Gambia, The 3.255272505 1.735439203 Ghana 3.301029996 1.752278985 Grenada 3.698970004 1.809694359 Guatemala 3.591064607 1.814447379 Guinea-Bissau 2.84509804 1.67182056 Honduras 3.397940009 1.823800154 India 3.414973348 1.803593665 Iraq 3.380211242 1.831293744 Jersey 4.394451681 1.897242103 Kenya 3.041392685 1.655330558 Korea, South 4.292256071 1.87714089 Laos 3.255272505 1.73479983 Liberia 3 1.682596291 Macau 4.267171728 1.91312479 Malaysia 3.944482672 1.855337404 Malta 4.235528447 1.894482215 Martinique 4.029383778 1.896085085 Mayotte 2.77815125 1.782472624 Monaco 4.431363764 1.899108858 Morocco 3.591064607 1.845346137 Nauru 3.698970004 1.792041311 New Caledonia 4.146128036 1.866405498 Nigeria 2.954242509 1.707655324 Pakistan 3.301029996 1.793790385 Papua New Guinea 3.322219295 1.807467376 Philippines 3.662757832 1.840670561 Reunion 3.748188027 1.865873528 Saint Helena 3.397940009 1.888628725 Saint Pierre and Miquelon 4.041392685 1.892706638 San Marino 4.539076099 1.910784435 Saudi Arabia 4.056904851 1.837146344 You can see from the scatter diagrams that the log of GDP per capita against the life expectancy shows the strongest linear correlation so that is the one I am going to choose. Therefore this means that I am going to use the data for log of GDP per capita and the life expectancy at birth. From the scatter diagram I can see that there is a positive correlation between the two variables. From looking at the scatter diagram I can see that the data takes an elliptical shape. Since the ellipse appears to be quite narrow it implies that there is a good positive correlation i.e. as one variable increases, so does the other. Therefore the data shows a clear linear relationship. Another technique that I am going to use is a histogram because you are able to see the distribution clearly and able to determine whether I can use Pearsons product moment correlation (PMCC) or Spearmans coefficient of rank order. I am going to draw a histogram for each variable and if the distribution is not normally distributed I shall use Spearmans and if it is I shall use PMCC. As the histograms roughly show a normal distribution I am going to use PMCC method. Analysis: Now I am going to calculate the PMCC with the help of Microsoft Excel. x y x2 y2 XY 75.75 3.903089987 5738.063 15.23411 295.6591 76.7 3.934498451 5882.89 15.48028 301.776 66.68 3.556302501 4446.222 12.64729 237.1343 65.71 4.184691431 4317.804 17.51164 274.9761 71.84 4.176091259 5160.986 17.43974 300.0104 51.08 3.041392685 2609.166 9.250069 155.3543 64.78 3.397940009 4196.448 11.546 220.1186 76.06 4.204119983 5785.124 17.67462 319.7654 55.79 3.230448921 3112.524 10.4358 180.2267 48.05 3.230448921 2308.803 10.4358 155.2231 41.71 3.079181246 1739.724 9.481357 128.4326 72.22 3.672097858 5215.728 13.4843 265.1989 48.93 2.77815125 2394.145 7.718124 135.9349 42.65 3.146128036 1819.023 9.898122 134.1824 43.13 3.113943352 1860.197 9.696643 134.3044 65.2 2.698970004 4251.04 7.284439 175.9728 70.62 3.662757832 4987.184 13.41579 258.664 41.24 2.84509804 1700.738 8.094583 117.3318 76.69 4.158362492 5881.356 17.29198 318.9048 54.38 3.255272505 2957.184 10.5968 177.0217 56.53 3.301029996 3195.641 10.8968 186.6072 64.52 3.698970004 4162.83 13.68238 238.6575 65.23 3.591064607 4254.953 12.89575 234.2451 46.97 2.84509804 2206.181 8.094583 133.6343 66.65 3.397940009 4442.223 11.546 226.4727 63.62 3.414973348 4047.504 11.66204 217.2606 67.81 3.380211242 4598.196 11.42583 229.2121 78.93 4.394451681 6229.945 19.31121 346.8541 45.22 3.041392685 2044.848 9.250069 137.5318 75.36 4.292256071 5679.13 18.42346 323.4644 54.3 3.255272505 2948.49 10.5968 176.7613 48.15 3 2318.423 9 144.45 81.87 4.267171728 6702.697 18.20875 349.3533 71.67 3.944482672 5136.589 15.55894 282.7011 78.43 4.235528447 6151.265 17.9397 332.1925 78.72 4.029383778 6196.838 16.23593 317.1931 60.6 2.77815125 3672.36 7.718124 168.356 79.27 4.431363764 6283.733 19.63698 351.2742 70.04 3.591064607 4905.602 12.89575 251.5182 61.95 3.698970004 3837.803 13.68238 229.1512 73.52 4.146128036 5405.19 17.19038 304.8233 51.01 2.954242509 2602.02 8.727549 150.6959 62.2 3.301029996 3868.84 10.8968 205.3241 64.19 3.322219295 4120.356 11.03714 213.2533 69.29 3.662757832 4801.104 13.41579 253.7925 73.43 3.748188027 5391.965 14.04891 275.2294 77.38 3.397940009 5987.664 11.546 262.9326 78.11 4.041392685 6101.172 16.33285 315.6732 81.43 4.539076099 6630.845 20.60321 369.617 68.73 4.056904851 4723.813 16.45848 278.8311 Totals 3224.34 179.0276425 215012.6 653.5361 11793.26 This shows that my variables have a good positive correlation. I am now going to carry out a hypothesis test on the correlation coefficient to see if there is enough evidence from my sample to conclude that there is correlation in the whole population. : ? = 0 (There is no correlation between the two variables in all the countries in the world) : ? 0 (Positive Correlation) N= 50 I will be doing a one tail test at the 5% significant level So the critical value = 0.2353 So 0.833872644 0.2353 Therefore I can conclude that there is enough evidence from the sample to say that I accept that there is a positive correlation. Regression line The equation of the regression line is: As you can see on the page here is my scatter diagram with the regression line drawn on it which was all done in excel. This is Y upon X regression line. Interpretation: From the investigation that I have carried out I have discovered that that there is a positive correlation between my two sets of data which is shown on my graph and regression line. The aim of my investigation was to see if there is any correlation between the GDP per capita ($) of a country and the life expectancy at birth (years). I can now confidently say that I have achieved my aim as there is a positive correlation as predicted. The sample that I took is of the whole world and is a good representation of the whole population. By using the correlation results I can predict if there was a country with a low GDP then it is expected that they have a low average life expectancy. This trend would be expected for every country in a similar position but some countries may incur lower life expectancies than normal due to some external factor e.g. war, outbreak of a new disease or some sort of natural disaster. But regardless of these exceptions they shall not affect the overall correlation. I think that this data was worth investigating and collecting because I now realise how important the GDP per capita of a country is in affecting how long a person lives and how the higher the GDP the better the quality of life is for a person. This investigation has shown that people living in developing countries are more likely to die at a young age and will not have such a high quality of life as we enjoy in a country like the UK. I also think this investigation will act as very good evidence to try and convince richer nations to help poorer ones. This data should be given to an organisation like the United Nations to try an act as a catalyst to convince them to do something about this before it is too late. Accuracy and refinements: One possible source of error was that the data may have been displayed incorrectly on the website or I may have copied it incorrectly. I would improve this by comparing data from a number of different sources to ensure accurate and reliable results. The sampling method that I used could have been a possible source of error. This is because my systematic sample only included every 4th so for example every 3rd did not have a chance to be chosen. I could have improved my sampling method by using simple random sampling instead of systematic sampling. Simple random sampling ensures that every item of data has an equal chance of being chosen. This is a very important factor in ensuring the reliability of my work. Even though the data is very reliable there are some improvements that could be made. First of all the data was only collected for a given year in my case it was for 2003. For more accurate data I could have used data over five years to see if there is actually a difference and to see if for example at that given years there may have been a low life expectancy due to an external factor like war or disease. Also the sample was only from 228 countries and there are more countries in the world so a more fair representation would be to random sample from every country in the world. This was not possible because my source did not include some of these countries due to political reasons and from lack of information for those countries. In my investigation I had to reject 11 statistics for 11 countries this reduced the randomness of my sample. I would improve this by making sure that data was available for every item in the parent population. Overall I am very happy with the accuracy and reliability of my data because I got it from a very reliable source which was www.CIA.gov. Having a reliable source for my data enables me to achieve my aim of a positive correlation.