Rate or Ratio?

Mortality Rates

Vital Statistics analyzes vital events occurring in the life of an individual. Mortality, fertility and migration are some examples of such vital events. Vital statistics comprises of measures such sex ratio, crude birth rate, crude death rate etc. But terms Rate and Ratio are some what ambiguous. The definition of ratio here doesn't seem to confirm with the traditional mathematical definition which is as follows. A ratio is written as " a to b" or "a:b" and is expressed as quotient of two numbers.  Rate is mathematically defined as quantity measured with respect to another quantity. So rates are always defined in terms of  two units like miles per hour for speed or number per milliliter of water for bacterial growth. 

This ambiguity is illustrated with following example. Sex ratio is defined as number of males per 100 females.  So if sex ratio is 106 means by definition that there are 106 males per 100 females. So sex ratio 106 doesn't confirm with the traditional mathematical definition of ratio. Also if sex ratio is given as 1.06 then one should conclude that  there are 1.06 males per 1 female which is equivalent to the previous statement of 106:100. Now maternal mortality ratio (MMR) is defined as annual number of maternal deaths due to pregnancy related causes per 100,000 live births. But maternal mortality rate (MMR)is also number of maternal deaths per 100, 000 live births. Similarly Crude death rate (CDR) is number of deaths per 1000 people in the population and Infant mortality rates (IMR) number of deaths of infants per 1000 live births.

Intuitive approach is the best possible option for finding a way through this ambiguity. We should not be carried away by these numbers and loose our way in this ambiguity of definition. We should rather link these mathematical figures with country specific scenario. This way we will not loose track of the main objective, which is  getting a clear picture of development status of that country.

.........and one more tip in case of frequent events  like birth and death it is per 1000 and in case of less frequent  events like cause specific death rate it is expressed per 100,000.

Relation between Binomial, Poisson, Geometric and Negative binomial distributions

A small grocery store in a very busy market square

The interrelationship between these distributions is illustrated with following example.

Suppose that there is a small grocery store located in a very busy market square with several big stores and shopping malls. Hundreds of people are walking in this market square in a Saturday morning. Then the number of people entering this store is a random variable following Poisson distribution. Number of people making purchases upon their entry into this shop is a random variable  following Binomial distribution. Number of people making purchases before a person leaves the shop without buying anything is a random variable following geometric distribution. And lastly the number of people entering the shop before third person makes purchases more  Rs. 5, 000/- is also a random variable and follows negative binomial distribution. 

In this example, different random variables governed by probability law of different probability mass functions explain different aspects of a purchase in a small shop.

Statistical Analysis and Modelling of Vital Events

Mortality and Fertility Models for Countries with Limited Data

My book titled " Mortality and Fertility Models for Countries with Limited Data" is available on Amazon.  

It elucidates in a simple manner various methods of data generation, correction, prediction,  analysis  and interpretation. Here  I discuss the statistical analysis of vital events  namely Mortality , Fertility and Migration for countries with limited data like Nepal and India. 

Various techniques of data correction, data analysis and data prediction can be learnt from this book. There are several examples of vital events from Nepal, India and Germany in this book.

Learn various statistical techniques of data correction, analysis and interpretation

Insights into the concept of hypothesis testing (last Part)

When alpha is 0.025(z = 1.96) beta is 0.1866 and when alpha reduces to 0.005 (z = 2.55) beta increases to 0.3538.

When alpha is 0.025

Alpha is 0.025 and Beta is 0.1861

Alpha is 0.005 and Beta is 0.3583

The mathematics mentioned above is explained in this image

Insights into the Concept of Hypothesis Testing (Part 14)

Alpha decreases beta increases

This is continuation to the data on Population 1 and Population 2 given in yesterday’s BLOG. When alpha is 0.025(z = 1.96) beta is 0.1866 and when alpha reduces to 0.005 (z = 2.55) beta increases to 0.3538. This is explained in the diagram. The mathematics behind it will be explained in the next blog which is also the concluding part of the series “Insights into the concept of Hypothesis Testing”.