Sometimes we must make decisions based on a limited set of data. For example, we would like to know the operating characteristics, such as fuel efficiency measured by miles per gallon, of sport utility vehicles (SUVs) currently in use. If we spent a lot of time, money, and effort, all the owners of SUVs could be surveyed. In this case, our goal would be to survey the population of SUV owners.
However, based on inferential statistics, we can survey a limited number of SUV owners and collect a sample from the population. Samples often are used to obtain reliable estimates of population parameters. In the process, we make trade-offs between the time, money, and effort to collect the data and the error of estimating a population parameter.
The process of sampling from a population with the objective of estimating the properties of a population is called inferential statistics. We now list some of the advantages and disadvantages of inferential statistics.
Advantages of Inferential Statistics:
- It allows us to save time and money since we can make an inference about the whole population on the basis of a small sample size. For example, in order to estimate the average male height of a district it is much more efficient to consider a small sample of individuals rather than studying the entire male population of the particular district.
- In the above example it was theoretically possible to study the entire population. Sometimes it is impossible to study the entire population. For example, if we want to find the mean life of bulbs produced by a particular factory we clearly cannot test each bulb that the factory produces. A representative sample needs to be taken in such cases.
- We can compare two different populations by testing whether their means are equal or not. This can be done by carrying the two sample Z test and the paired T test.
- The methods of inferential statistics such as linear regression allow us to make predictions of future values taken by a dependent variable on the basis of past values. This is important in real life such as business where we might be interested in predicting the expected annual sales in order to decide how many products to manufacture.
- There exists non-parametric tests which can be used for testing of hypothesis. This is useful since most parametric tests can be used only if the parent population is normally distributed.
- The various tests of hypothesis are very easy to carry out with the help of statistical software such as R software, SPSS, etc.
Disadvantages of Inferential Statistics:
- The estimates and conclusion obtained on the basis of a sample are not 100% accurate. Since we are not studying the entire population there is always a degree of uncertainity invovlved.
- During testing of hypothesis, we come of across two types of errors – Type 1 and Type 2 errors. Unfortunately both errors cannot be minimised simultaneously since trying to minimise the Type 1 error too much can lead to an increase in type two error and vice versa.
- Most hypothesis tests for equality of means and variance are based on the assumption that the parent population follows normal distribution. This assumption need not be true. We need to check the assumption of normality every time before applying the test.
- Predictive techniques like linear regression can only be applied under the assumption that there is a linear relationship between the dependent and the independent variable.