In the world where knowledge is power and time is priceless, it is essential to make quick and informed decisions in order to not to be left behind. This is where a discipline named inferential statistics comes to the rescue. Its techniques help to understand general trends with only a limited set of data to analyze.
Inferential statistics is focused on analysing chosen parameters of sample groups (such as average student marks or animal behavior probabilities) and comparing differences between these groups based on these values. The results can be used for making assumptions about broader groups – such as, all students in a country or the entire animal species.
Main Aspects of Inferential Statistics
Direct measurements performed over a data sample – that is, a limited group of specimens that are available to a researcher – provide results describing that specific sample and its qualities. Of course, this is not enough to describe the qualities of all other such groups, so a researcher has to make assumptions about them, more or less precise. Inferential statistics includes special methods for making such assumptions and ensuring their precision is high enough to be accepted.
The following major components are used for that:
- Hypothesis: initial guess which will be estimated later through statistical methods. Typically this is about a factor making some influence: e.g. people with less physical activity are likely to contract a disease.
- Statistical significance: a parameter indicating the likelihood that the finding is due to chance rather than a true observation
- Confidence intervals: selected ranges of values that are likely to include the parameter which is estimated. The probability level is calculated for each interval: e.g. the number of students in a class to get all As will be among 5 and 10 with a 95% probability and will be out of that range with a 5% probability.
- Correlation: likeliness of connection between different parameters. E.g., we can say that low physical activity correlates with a disease if it is observed that less active people are often catching it. But we cannot say that it causes this disease unless we have a solid proof for that.
- False positive and false negative: percentage of risk to accept a wrong assumption or to reject a right one, accordingly.
Initial assumption that leads to the creation of a hypothesis depends on a researcher’s own experience and intuition in a great deal. Significant knowledge about a specific field is necessary in order to come up with a valid idea. Wild guessing is hardly an option here: in most cases it will result in a wrong hypothesis which will be rejected afterwards, and a new one should be made.
So the general order of inferential statistical operations is as follows:
- Preliminary research
- Making a hypothesis
- Testing the hypothesis
- Making a conclusion based on an accepted hypothesis
- Estimating the risk of an error and its possible consequences.
Where Should You Apply Inferential Statistics
As mentioned above, such operations are needed when you attempt to understand a big group when only a small part of it is available for you to examine directly. In fact, this is common for situations when there is too much data and too little time to process it.
Predicting spread of illnesses, understanding risk factors of the population and developing countermeasures on beforehand are key elements of modern medical science. Inferential statistics methods are widely used for that, as medical researchers have to make prognosis based on the examination of limited groups of patients.
Estimating the efficiency of new teaching methods is a big deal whenever any changes are made within a school. Besides that, it is useful to understand factors influencing students’ success (or failure) on a mass scale. All these activities require statistical analysis.
National and global markets are heavily influenced by ever-changing demand, taxes & quotas, currency rates and many other dynamic factors. And this system gradually becomes even more complicated! Inferential statistics helps businesses and governments to make better forecasts and thus to maintain their positions in this difficult situation.
Wildlife researches are all about understanding the life of bigger groups by examining a few specimens in the captivity (or observing some small groups in their natural habitats, though such observation is limited of course). It is always difficult to tell a unique behavior trait from a common behavior of a species which is why zoologists have to rely upon statistics.
It is important to remember that inferential statistics gives answers with a certain portion of probability. It cannot give you solid facts because you have to make assumptions about bigger groups that were not measured directly. However it attempts to mitigate this problem by estimating the probability of mistake for every hypothesis that is accepted. Another limitation is the necessity of making the first guess prior to performing most inferential tests. This first step brings some uncertainty into the process – that is why the preliminary research or some experience in the field of research is important.
The power of inferential statistical methods comes from utilizing proven methods of approving or rejecting assumptions which takes it to another level compared to wild guessing. In real life we often make intuitive guesses: some of them turn out right, while some appear wrong. Adding a proper analytical method to this can boost our ability to understand the processes and trends around us and consequently to improve our life.