What is effect size in statistics?

If you were ever fascinated by bar graphs, curves, pie charts & various other ‘data’ depicting representations, you surely are a lover of ‘Statistics’. To make it easier to understand, let us imagine mathematics as a huge Oak tree, which has many branches originating from it What is effect size in statistics?. Mathematical statistics, too, is just one of the branches of this huge structure of an Oak tree, called ‘Mathematics’. 

Let us now try to understand statistics in an easier way. There are many definitions on the internet that try to describe what statistics exactly is, but if we try understanding it in layman’s terms, statistics is basically the collection & representation of data. Statistics is a means of collecting, analysing & presenting the data using forms such as tables, pie charts, graphs. Using statistics, we can have a pictorial representation of the data so that it can be analysed in a better way, making it much easier to understand. 

Why does data matter?

To understand more about data in a better way, let us use an easy example considering a small district in India. 

What is the population of this district in India?

What is the number of people having a bachelor’s degree in that district?

How many people own a smartphone within the district?

What can we try to understand from these questions here? The answer to every single question above is a number. But now the question that lies in front of us is, “What is Data?” 

We’ve not only read but also heard on numerous occasions from stalwarts all across the world that “Data is the new Oil”. With the advent of the ever-increasing use of the internet & social media, roughly 2.5 quintillions of data are being generated by humans every day. With data of this magnitude being generated, it’s really important how do we make this data easier to understand & present it accordingly.

Data, in simple words, is a collection of information. This information can be in the form of facts, figures, words, numbers, etc. Since we are dealing with mathematical statistics here, data in this context will mostly be about numbers. The above examples discuss the demographics of a small district with respect to various parameters where we talk about the population & some other specific requirements, said John O. from twiftnews.

How big a difference can statistics make?

Mathematical statistics, in itself, is a very vast elaboration of how data can be represented in the form of numbers & charts. With huge amounts of data being processed every single day, the medium that we are using to represent & understand the data is really important. Statistics help us to draw conclusions from the data, making it easier to understand for the common people. Statistics is a discipline of study where statisticians are trained to collect, analyse, present & draw conclusions from this data. For example, a complex pie chart depicting the annual sales of various hand sanitizer brands may not be easily understood by a person who is not trained enough to understand this. Statisticians are educated & trained to draw out conclusions, making it easier to make ‘decisions’ based on this data. Rather than saying that a brand ‘X’ sold ‘Y’ number of sanitizers in the following region, we can probably conclude by saying that 4 out of 5 doctors recommend the sanitizer by Brand’ X’, making it easier to understand!

Using statistical concepts to analyse data: 

There are various statistical concepts that are used to analyse the various facets of data. Depending upon the type & size of data, various methods can be used to analyse & draw significant conclusions from it. Some of the widely known concepts that are used to analyse the data are as follows: 

  • Probability
  • Central tendency
  • Regression
  • Variability & their relationship
  • Distribution
  • Testing hypothesis
  • Bayesian statistics

When we talk about the list of concepts in mathematical statistics, the list is very long in order to keep track of it. Each of the concepts has its own significance based on the type of data to be analysed. Earlier, we have seen how data can be used to draw out ‘significant’ conclusions, which effectively can help people & organisations reach a decision. Various important decisions are solely driven by the facts that the data reveals.

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Data-driven decisions using statistics is the future: 

One of the best examples of organisations that have leveraged the use of data effectively is Walmart. Walmart used Big Data Analytics to personalise the shopping experience of users as per their requirements. For example, if someone shopped for a baby product on their visit, by using the sales data, Walmart ran personalised roll-back mobile deals. This not only helped Walmart to increase its customer retention but also helped them to increase their repeat sales. This is just one example where Walmart effectively leveraged the use of data to make decisions, which yielded huge amounts in both sales & profits. 

Analysing the data using statistics has time & again helped organisations take the appropriate decisions to boost the sales, engagement & retention of customers. Here, statistics plays a major role in deciding what decision the company would take, which can either boost the profits or tank the business too! Hence, having the knowledge of statistics can go a long way in helping to make the right decisions. 

Relationship between variables:

As mentioned above, the relationship between the variables is one of the major concepts in itself. The concept of variables & proportionality is extremely important in statistics as to how the variables behave, depending upon the factors in consideration. The statistical relationships between variables are more commonly known as ‘Correlation’. Variables in a data set can be related to each other in many ways, such as the value of one variable may cause or probably depend on the other variable, one variable could be slightly associated with the other one, or even the value of two variables can depend on the third one. 

Depending upon the direction in which the variables move, the correlation can either be positive (same direction) or negative (opposite direction). If the variables are unrelated, the correlation comes out to be neutral. 

The concept of effect size: 

Now that we are aware of the different concepts that are majorly discussed in Statistics, let us jump into a very interesting & fascinating concept of ‘Effect size’. 

Now, before we try to understand it, let us try to understand it using this example. 

A family has two brothers, Zack & Cody. Zack has a good height of 6’1, whereas Cody is comparatively shorter, being 5’4 in height. The difference between the heights of Zack & Cody is called the ‘Effect size’. The greater the difference between their heights, the greater will be the effect size. The effect size generally shows the strength of the relationship between the variables. 

It helps us to determine whether the difference between the variables is real or due to some changes in factors surrounding them. 

The effect size is a very important factor as it tells us about the size of the difference or the impact made. Let us try understanding this in a better way using this example. Let us consider that a person diagnosed with a common cold goes to a doctor, where he is prescribed a medicine for the same. Here, we can measure the ‘effect size’ of the medicine depending upon the healing effect that the medicine has had on him as low, moderate & high. 

Types of effect sizes:

  1. Pearson r correlation.
  2. Cohen’s d effect size
  3. Glass’s Δ method of effect size 
  4. Hedges’ g method of effect size
  5. Cohen’s f2 method of effect size
  6. Cramer’s φ or Cramer’s V method of effect size
  7. Odd ratio

The effect size calculation can be done if you are trying to find out the difference between the assessments of two different results, to check whether they are different from each other. To make it easier to understand, the effect size can be used to assess the difference between the grades of the two tests & how significant the difference is. 

The concept of effect size is very significantly used by teachers & academicians to check the difference in the quality of classes from one class to another. This helps them to assess the effectiveness of their classes & accordingly change their teaching style. 

Statistics is a very broad discipline that deals with concepts that can be applied in real-time applications. Collecting, understanding, analysing & presenting data without statistics is nearly impossible to imagine & understanding concepts like ‘effect size’ make the discipline easier & fascinating to understand. 

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