What is Estimation?

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

What is the Need for Estimation?

Estimation falls under the category of statistical hypothesis tests. The main use of these tests is for analyzing two samples, and determining whether or not a random chance differentiates the two samples with respect to time. However, the difference in size between the samples cannot be precisely interpreted.

Apart from the p-value methods, these new techniques are used for quantifying the effect magnitudes, and for fining out the uncertainty level of the values that are to be estimated. Hence, we mainly use estimation in statistics as an alternative way for testing the statistical hypothesis. Word estimation is used for solving simple problems.

What are the Uses for Estimation?

Estimation in statistics is highly useful for the following methods-

• For finding out the difference or association that exists between two given samples.
• When point estimations are considered, the uncertainty around them can be quantified with estimation.
• In the case of multiple independent studies which are similar in nature, the magnitude of their effect can be quantified.

What are the Problems Involving Hypothesis Testing?

When we use statistical hypothesis testing, we mainly do it so that we can find out the p-values. This is one of the most popular ways in which the results are interpreted. Other methods also exist like the student’s t-test. This is a general method in which the distribution between two samples can be evaluated to be the same or not. As a result, the nature of the difference between the samples can be figured out. They can either be randomly generated, or they can be real.

Even when these methods are used on such a wide scale, there exist some problems with these traditional testing methods. They are-

• Whenever the p-values are calculated, the results are mostly misunderstood. As a result, it leads to misuse of the samples or the data inferred from them.
• If two samples are considered, there exists a difference between them in all cases, no matter how small the difference is.

As a result, the usage of p-values for interpreting and analyzing results has been gradually discouraged in the last 10 to 20 years. In research or presentation, and even in fields such as psychology or medicine, it has been declared that they need methods with even better understanding and clear interpretation power. As a result, the result presentations have gradually started using estimation methods in statistics for the same purpose.

How does Estimation in Statistics Work?

The main usage of estimation methods in statistics is to use various methods that can help in quantification or determining the relationship between the data that has been inferred or found out. It is a broader term, and it comprises many things. For example, when a particular result or outcome is considered, the uncertainty amount that lies in it, or the effect size that the particular outcome can generate is calculated.

What are the Types of Estimation?

Usually, the process of estimation in statistics can help in describing three different classes. These method classes can help in estimating any given data as per the desired result. The classes are as follows-

• Effect Size – When an effect is intervened, or treatment is provided, then the size of the effect is calculated with this method.
• Interval Estimation – Every value holds an uncertainty amount. This method helps to quantify that specific amount.
• Meta-Analysis – When multiple studies which are similar in nature are carried out, then the findings across them are quantified with this method.

Since these methods are the modern techniques in which researches are carried out instead of hypothesis tests, these are called new statistics. Even though these methods are not new, the easier method of interpretation and analysing data has been a major hit to deal with all new research questions. As a result, the claims that can be made from analyzing the results are much meaningful and are easily understandable as well.

The major difference between statistical hypothesis and estimation is that in estimation, the size of the difference and its confidence can be easily stated and described. Hence, differentiating between two sets of data or methods can be done easily.

These methods are discussed in detail further below.

What is Effect Size?

By effect size, we mean the estimation procedure in statistics that can help to determine the magnitude of difference that exists between multiple samples. Their various treatment methods can be differentiated as well.

If we do a hypothesis test, we can know the nature of the difference between different samples, whether they are real, or they are created randomly. In contrast to this, effect size helps in stating the difference between the samples by putting a number. The size of an effect needs to be measured, and it has various applications in advanced research levels.

For quantification of the magnitude that the effects hold, we generally use two techniques. They are as follows-

• Association – It states the degree up to which the change occurs in both the samples together.
• Difference – It states the degree up to which the difference exists between the two samples.

For instance, if we consider correlation calculations, it falls under the category of association in effect size. As correlation states how the change in one sample affects the other, this is an association class. On the other hand, if we consider Cohen’s d-statistic methods, it states the difference between the two means of the samples. It mainly deals with people and their population. With time, the word sample of the people population changes. Their difference is what is measured across time. Hence, it falls under the difference class of effect size.

What is Interval Estimation?

By interval estimation, we mean the method in statistics by which an observation’s uncertainty can be quantified. The main use of this estimation method is for describing a range that is made by transforming a point estimate. This range helps in measuring its precision. Hence, interpretation and comparison become much easier.

Interval estimation is mainly classified into three different types. They are-

• Tolerance Interval – It states when a distribution proportion is described with its coverage or bounds, which has a particular confidence level.
• Confidence Interval – For a population parameter, it states the estimation bounds.
• Prediction Interval – When a single observation is considered, this interval estimates its bounds.

What is Meta-Analysis?

By meta-analysis, we mean the usage of multiple studies which are similar in nature and weighing on them. This is done so that the quantification can be done with the effect of cross-study in a broader sense.

This type of study is extremely helpful when multiple studies that are small in size but similar in nature are performed with findings that are conflicting in nature and are noisy. Here, the study conclusions are not taken at their face value. Instead, the combination of multiple findings is done with the help of statistical methods. This helps in creating stronger findings.

Practice Problem

If in the roll of a die, event A suggests that a single role will produce a score of 3 or more, and event B suggests that a single role will produce a score of 2 or less, find the better estimate.

⇒ In a die, we know there are six possible scores, that is, {1, 2, 3, 4, 5, 6}

For event A, the possible outcomes are {3, 4, 5, 6}, and for event B, the possible outcomes are {1, 2}

$\begin{array}{l}\therefore \text{ P}\left(\text{A}\right)=\frac{4}{6}=\frac{2}{3}\\ \text{and, P}\left(\text{B}\right)=\frac{2}{6}=\frac{1}{3}\end{array}$

Here, A is estimated to have a possibility of 66.67% and B is estimated to have a possibility of 33.33%. Hence, A has a better estimate, or A has a higher chance of occurring.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelor of Science
• Master of Science
• Bachelor of Arts