Life Expectancy

Introduction

From www.encyclopedia.com, life expectancy is defined as the average number of years remaining for a living being (or the average for a class of living beings) of a given age to live. Life expectancy is also called average life span or mean life span, in distinction to maximum life span. Actually, human life expectancy at various ages and under different circumstances is carefully studied by the insurance and actuarial professions, and is calculated on the basis of historic data as shown on the mortality or annuity table used as a reference. Thus, several studies have been done regarding country’s economic progress and life expectancy. As a measure of economic stability and progress, the analysis of a country’s economic variables (i.e. Population, GNP, Birth Rate, Death Rate, Infant Mortality, Literacy, Energy Consumption and Type of Economy) and the people’s life expectancy appears to be essential. In this report, published data related to the subject matter will be described and analyzed.

Analysis

This report will analyse how life expectancy differs between groups of countries. From recent report of CIA (2006), there are great variations in life expectancy worldwide, mostly caused by differences in public health, medicine and nutrition from country to country. In this regard, this report shows population, GNP, birth rate, death rate, infant mortality, literacy, energy consumption and type of economy of surveyed countries contributes to determinants of country’s life expectancy.

Table 1

The Descriptive Statistics table above provides summary statistics for 148 surveyed countries. Summary statistics include measures of central tendency such as the mean. Based on the table, the average life expectancy of these 148 countries is 55.59 and the common economy type of the surveyed countries is Oil Producing and Exporting economies which was justified by 2.35 mean. On the other hand, the measure of dispersion (spread of the distribution) such as the standard deviation and range was also illustrated (see table 1). And measures of distribution, such as skewness, which indicates how much a distribution varies from a normal distribution. In general, a skewness value greater than one indicates a distribution that differs significantly from a normal, symmetric distribution. And based on the distribution, population, GNP and Energy consumption are variable that differs significantly from a normal, symmetric distribution since the computed skewness value is greater than one.

Apparently, the aim of this report is to identify the relationship between life expectancy and other variables in the given data set and comment on the extent to which life expectancy can be predicted using the other variables. Thus, the following hypothesis was considered:

1. There is a significant difference between Type of economy and life expectancy.

2. There a significant relationship between life expectancy and other variables in the given data set.

Difference between Type of Economy and Life Expectancy

To assess the analysis between the difference of Type of Economy and Life Expectancy, the use of Chi-square and ANOVA analysis was used.

Table 2

The previous table lists the number of cases (both observed and expected) in each category of the variable being analyzed. One option is to have the expected N correspond to all categories having equal frequencies (as in table 2).Alternatively, the expected N can correspond to a user-defined distribution. Here, the distribution in all economies is hypothesized to be equal.

Apparently, the residual lists the difference between what is observed and what is hypothesized. Residuals identify categories which vary from the hypothesized distribution. In our data, the observed number in developing economies and underdeveloped economies with a high life expectancy is higher than expected and the observed number in OPEC economies and developed economies with low life expectancy is lower than expected. Actually, a Chi-Square test can determine if these differences suggest an alternative distribution of life expectancy across economies.

Table 3

This table contains the output of the Chi-Square test. Df equals the number of categories minus one. In this example, type of economy has four categories (developed, underdeveloped, developing and OPEC economies). Small significance values (<.05) indicate that the observed distribution does not conform to the hypothesized distribution. In this data, the significance level is less than .05 for type of economy. The distribution of type of economy differs from the distribution hypothesized.

To verify the findings of Chi-square analysis, the use of ANOVA was also considered. The result of analysis was presented below.

Table 4

The results of the analysis are presented in an ANOVA table. In one-way ANOVA, the total variation is partitioned into two components. Between Groups represents variation of the group means around the overall mean. Within Groups represents variation of the individual scores around their respective group means. Actually, sig indicates the significance level of the F-test. Small significance values (<.05) indicate group differences. In this data, the significance level is less than .05. Meaning to say, at least one of the regions differs from the others. Thus, it true that there is an existing difference among economies with respect to life expectancy.

Relationship between Life Expectancy and Other Variables in the Given Data Set

To determine the appropriate variables that can be used for prediction of life expectancy, correlation analysis should be considered. In appendix, the correlations table displays Pearson correlation coefficients, significance values, and the number of cases with non-missing values. Pearson correlation coefficients assume the data are normally distributed. The Pearson correlation coefficient is a measure of linear association between two variables.

The values of the correlation coefficient range from -1 to 1. The sign of the correlation coefficient indicates the direction of the relationship (positive or negative). The absolute value of the correlation coefficient indicates the strength, with larger absolute values indicating stronger relationships. The correlation coefficients on the main diagonal are always 1.0, because each variable has a perfect positive linear relationship with itself. Correlations above the main diagonal are a mirror image of those below (see Appendix).

The significance of each correlation coefficient is displayed in the correlation table. The significance level (or p-value) is the probability of obtaining results as extreme as the one observed. If the significance level is very small (less than 0.05) then the correlation is significant and the two variables are linearly related. If the significance level is relatively large (for example, 0.50) then the correlation is not significant and the two variables are not linearly related. With respect to life expectancy, the said other variables are linearly correlated except economy type and population variable. Thus, the other variables (i.e. GNP, birth rate, death rate, infant mortality, literacy, and energy consumption) can be use as factors of life expectancy. Using regression analysis we have the following coefficients,

Table 5

Thus, the model to be used in determining life expectancy is

Life Expectancy = 70.545 + 0.0009251(GNP) – 0.173(Birth Rate) – 0.783 (Death Rate) – 0.00249 (infant mortality) + 0.009755 (literacy) – 0.000038 (energy consumption)

Conclusion

The correlation of country’s variable and life expectancy has been confirmed through related report. One of the important learnings obtained from this analysis is the identification of various methodologies directed towards the identification of the relationship between the variables involved. More importantly, this paper had also emphasized the importance of constant studies related life expectancy and other economic factors as well.

References:

CIA (2006) Life Expectancy at Birth, Accessed: March 2006, Available at: http://www.umsl.edu/services/govdocs/wofact2001/fields/life_expectancy_ at_birth.html

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