Ask any successful data scientists, and they’ll tell you that one of the critical factors to achieving success in the field of data science is having good knowledge about statistics. There are two types of statistical methods, Descriptive and Inferential Statistics. Statistics help data scientists to figure out trends and changes in data by performing mathematical computations. In this guide, we will try to answer the common question, ‘why do we use Inferential Statistics?’ as well as shed some light on the inferential statistics methods, and its use in machine learning programs and Data Science, and various other concepts related to it.
Inferential Statistics allow us to make predictions (inferences) from a given sample data set. The aim of Inferential Statistics is to form interpretations and make a broad statement of the population data beyond the immediate data available.
The definition of Inferential Statistics
What is Inferential Statistics? It is a statistical method that concludes from a small but representative sample the characteristics of a larger similar set of data.
Let’s have a look at an Inferential Statistics example for a better understanding.
Let us suppose that we want to find out the average salary of IT engineers across the country. There are two methods by which we can approach the problem. First, we can go out and meet every IT engineer in the country, ask for their salary and note it down in a datasheet. Then, we can calculate the average salary using the data. Or, we can have a predefined selective number of IT engineers from a particular city, say Mumbai. We can gather data about their salaries much more easily and then use the data to evaluate the average income of IT engineers across the country.
While the second method is much more feasible, consuming less time and resources, it is highly likely that the dataset considered is not truly representative of the entire Indian population. The chances of reaching an outcome that is wayward from the actual average salary are highly likely in this method. So, how can we calculate the average monthly income of IT engineers across the country accurately? The answer to this conundrum is Inferential Statistics.
With Inferential Statistics, you can make conclusions from the available data sample. It also helps in deducing whether a given data sample is similar to the population or not. Inferential Statistics makes use of random samples for testing, and, hence, allows us to have confidence that the sample represents the population.
Flowchart for Inferential Statistics
Little to no information about population sample -> Randomly drawn sample from the population set -> Analysis of the dataset -> More information about the population dataset.
Steps to Performing Inferential Statistics
To perform Inferential Statistics, you need to follow these steps.
Tools Used for Inferential Statistics
The most common tools or Inferential Statistics methods used are hypothesis tests, confidence intervals, and regression analysis. Let us have a look at the types of Inferential Statistics in detail.
Hypothesis tests let us check a sample statistic against a population statistic or statistic of another sample to study any intervention. For instance, if we analyse the consumer’s response to a new flavour of chocolate by comparing the results in different groups, the tests can help us decide whether the new flavour is liked by the sample population or not. After all, we wouldn’t want to launch the new flavour if it is liked by only our sample group. Rather, we need proof that the entire population will like the new flavour. Hypothesis tests enable us to draw these types of inferences about entire populations.
Hypothesis testing can be defined into two broad terms, null hypothesis and alternate hypothesis.
It is a default hypothesis that assumes that the quantity to be measured is zero. It assumes that there is no connection between the two measured events. The null hypothesis can be further divided into four types— simple hypothesis, composite hypothesis, exact hypothesis, and inexact hypothesis.
The alternate hypothesis assumes that there is a statistical relationship between two variables. It is opposite to the null hypothesis. There are three types of alternate hypothesis— left tailed, right-tailed, and two-tailed hypothesis.
One of the primary goals in Inferential Statistics is to estimate the population parameters. The parameters include the unknown values like the mean and deviations of the population. The confidence interval is a type of estimate that gives an extent of values in which the population statistic may lie. It includes uncertainty and sample error. It creates a range of values where the actual population value is likely to fall within. The confidence interval is inversely proportional to the sample size.
This method is used to describe the relationship between a set of dependent and independent variables in a given dataset. The relationship is described by fitting a line to the observed data. The simple linear regression model is typically used in Inferential Statistics.
A burger outlet wanted to perform market research to determine what type of chicken burgers their customers liked. The outlet is researching to figure out the favourite tastes of their customers to provide better services and dishes to the customers. The outlet gathered a customer sample size of a hundred customers in different age groups and regular nearby customers at the outlet.
After applying Inferential Statistics, the outlet was able to determine the most-liked burger types by the customers. About 80% of the customers liked their chicken burgers to be spicy and crispy while the rest liked it non-crunchy and non-spicy. This helped the outlet understand what their customers liked with better accuracy and create better dishes.
In Descriptive Statistics, we need to first choose a dataset that we need to describe. We then measure the subjects in the group. Descriptive statistics is easier to perform when compared to Inferential Statistics. In Inferential Statistics, we first need to define the population dataset. Next, we need to devise a sampling plan that gives a representative sample. Inferential Statistics are more difficult to perform than Descriptive Statistics.
Inferential Statistics are used to predict the results of a general population dataset from the immediate dataset available. There are three main types of Inferential Statistics: hypothesis testing, confidence intervals, and regression analysis. With Inferential Statistics, you can predict the outcome for a large dataset without the need for gathering data from the whole population. If you are interested in learning more about the role of statistics in machine learning or about Data Science, you can check out Jigsaw Academy’s Post Graduate Diploma in Data Science that can help you master Data Science in 11 months. You can master Data Visualisation, Exploratory Data Analysis, Machine Learning and AI and Neural Networks.