10. Defining Research Problems and Hypothesis Formulation

Introduction:

The first step in research is to identify the problem area in which the study will be conducted. The first question a researcher analyzes should be what the problem is. A researcher must find the problem and formulate it so that it is liable for research. Defining the research problem and developing the hypothesis is the most challenging step in any research process.

Let us understand what a research problem is.

In general terms, a research problem refers to some difficulty that a researcher experiences in the context of either a theoretical or practical situation and wants to obtain a solution for.

A research problem requires –

• Finding the best solution to the problem.
• Opting for the best course of action to attain the objective optimally in the given environment.

Thus, we can state the components of research problems in a nutshell as follows:

1. There must be an individual or group with some problem to solve.
2. There must be some objective to be attained.
3. There must be an alternative course of action.
4. There must be an answer to the question about the selection of alternatives.
5. There must be some environment in which the difficulty exists.

As it is rightly said that a problem properly defined is half solved, the researcher should determine which course of action can achieve the objective and find the best solution for the given problem.

Defining Research Problems:

The problem to be investigated must be clearly defined, which will help distinguish relevant data from irrelevant ones.

Questions like:

• What data are to be collected?
• What characteristics of data are relevant and need to be studied?
• What relationships are to be explored?
• What techniques are to be used?

The researcher should consider some similar questions so that he can plan his strategy to define a research problem well. Hence, the formulation of a problem is more essential than its solution.

The steps involved in defining a research problem are:

1. Identification of research problem:

The first step in research is to identify the problem area on which the research will be conducted. What the problem is should be the first question a researcher analyzes. Based on the objective, the research problem could be in any of the following three areas:

1. Exploratory: – gathering information that may help define the problem and suggest a hypothesis. It emphasises the discovery of ideas.
2. Descriptive: – This may describe customers’ buying behaviour, market potential, demographics, etc.
3. Causal: – This is helpful to test hypotheses about cause-and-effect relationships.
4. Selection of research problem:

The selection of the research problem must be carefully done. The researcher can use a research guide to select a research problem. After identifying two or more issues or opportunities, the selection should be based on priority, availability of finance, and time constraints. It should be based on resource availability, which gives the research maximum net value. The researcher should also examine the available literature while selecting the research problem. However, the following points must be considered by a researcher in choosing a research problem:

– Search for new features and not the subjects that have already been overdone.

– Avoid subjects that are too narrow, controversial, or vague.

-The subject selected should be feasible and family-friendly so that research materials or sources can be easily accessed.

– Before the final selection of the problem research paper, consider these questions to get an affirmative answer and, based on that, select the problem

1. Is he well equipped with all the resources to carry out research?
2. Is there any financial constraint that may be a hurdle in the research study?
3. Will cooperation be necessary from those who must participate in the research as subjects?

– A brief feasibility study must always be undertaken for problems that are very new and lack well-developed techniques and records.

The process of research problem definition:

– Determine the decision maker’s objective.

-Understand the context of the problem.

-Recognize the problem rather than its symptoms.

-Regulate the unit of analysis.

-Determine the suitable variables.

-State the research hypothesis and Research objective.

Techniques Involved in Defining a Problem:

The task of defining a research problem must be intelligently done. The research problem should be defined systematically, and it should be conducted with a predetermined objective. It must give due weight to all the related points. As it is a crucial part of a research study, it should not be conducted hurriedly.

The techniques involved in undertaking the research problem are as follows:

– Statement of a problem in a broad general way:

The problem should be stated in a broad, general way, considering the practical, intellectual, and scientific aspects.

In the case of social research, the researcher must undertake a preliminary survey, i.e., a Pilot survey.

– The researcher must state the problem or get guidance from some subject expert to accomplish the tasks.

The feasibility of a solution should be considered by stating the problems.

1. Understanding the nature or origin of the problem:

The researcher must clearly understand the nature of the problem and the origin from which it has occurred. If the researcher has stated the problem, he should consider all the relevant factors. Before making a general statement concerning the issue, If the researcher has not raised the problem, he should discuss it with those who have raised it or find out how it was initially created. Whoever understands the nature and origin of the problem, the researcher must always keep in mind the objective of the research.

2. Surveying the available literature:

The researcher must devote sufficient time to reviewing the research on related problems. Researchers must be well conversant with the theories in the field, reports, and records. Being well-known with the available data will help narrow the problem and suggest the proper technique. The researcher can analyse certain aspects of the theory, which will help him overcome them during his research study.

3. Developing the idea through discussion:

A researcher can adopt the experience survey method to conduct the research. In this method, he can discuss the problems with his colleagues and others who have enough experience in the same area or are working on similar issues. This will help the researcher develop ideas through discussion to help him focus on formulating the problem and finding solutions.

4. Rephrasing the research problem:

Once the researcher understands the nature and origin of the problem, the environment, and the available literature, rephrasing the problem into analytical or operational terms is not complex. Rephrasing helps the storage structure to put the research problem in a specific term so that it may become operationally viable. Get me help in developing a working hypothesis.

In addition to the above points, the following points must also be considered while defining a research problem:

– Provide a clear definition of the technical terms, words, and phrases used in the statement of the problem.

– Any assumptions or postulates related to the research problem should be clearly stated.

– The criteria for the selection of the problem should be mentioned.

The researcher must consider factors such as period and source of data availability when defining the problem.

– The scope of the investigation to which the problem is to be studied must be mentioned while defining a research problem.

Formulation of Hypothesis:

A hypothesis is a tentative assumption that a researcher wants to test for its logical or empirical consequences. Simply put, a hypothesis is a mere assumption or supposition that must be proved or disproved. From the researcher’s point of view, a hypothesis is a formal question that the researcher intends to resolve.

The hypothesis may be defined as “a proposition or a set of propositions set forth as an explanation for the occurrence of some specified group of phenomena asserted merely as a provisional conjecture to guide some investigation or accepted as highly probable in the light of fact.”

A research hypothesis has specific qualities, such as:

– It is a predictive statement.

– It is capable of being tested by scientific methods.

– It relates an independent variable to a dependent variable.

Characteristics of hypothesis:

1. Clear and precise:

Hypothesis should be clear and precise; if it is not clear and accurate, the inferences drawn on its basis cannot be taken as reliable.

2. Testable:

The hypothesis should be testable; it is testable if other deductions can be made from 8, which can be confirmed if the order is approved by observation.

3. Relationship:

Hypothesis should state the relationship between the variables, that is, between the dependent variables and the independent variables.

4. Specific:

The Scope of the hypothesis should be limited and specific; narrower hypotheses are generally more testable by the researcher.

5. Easily understandable:

A hypothesis should be stated in simple terms that are easily understandable by all concerned.

6. Consistent:

The hypothesis should be consistent with the body of facts.

7. Timing:

Factors should be considered while testing the hypothesis; it should be tested reasonably to reach a reliable conclusion.

8. Empirical reference:

The hypothesis must explain the facts that can reduce the original problem condition. It explains what it claims to explain.

Hypothesis Testing:

Introduction

Based on sample data, hypothesis testing must decide whether the hypothesis is likely true or false. For testing hypotheses, statisticians have developed software tests of hypotheses, also known as tests of significance. The test of the hypothesis can be classified as follows:

– Parametric test or standard test of hypothesis

– Non-parametric test of distribution-free test of hypothesis

A parametric or standard hypothesis test generally assumes specific properties of the parent population from which samples are drawn. Other options include observations from an average population, population parameters like mean-variance, etc., and sample size. It must be good before the parametric test can be used. However, you cannot make such assumptions when the researcher does not want to. In such situations, statistical methods for testing hypotheses are used. These are called non-parametric tests. Please tell us not to depend on any other option about the parameters of the current population. More observation than a parametric test is needed to achieve the exact size of Type I and Type II errors.

Basic Concepts Concerning Testing of Hypothesis:

1) Null hypothesis and Alternative hypothesis:

NULL HYPOTHESIS	ALTERNATIVE HYPOTHESIS
When methods A and B are compared regarding superiority, and it is assumed that both methods are equally good, this assumption is termed a null Hypothesis. Rejecting a null hypothesis is known as the alternative hypothesis.	When method A and method B are compared regarding superiority and it is assumed that method A is superior to method B, this assumption is termed the Alternative Hypothesis. In other words, the set of alternatives to the null hypothesis is called the alternative hypothesis.
The null hypothesis is symbolised by	Alternative hypothesis is symbolised by

 Before drawing the sample, the null hypothesis and alternative hypothesis are chosen. Hypothesis testing proceeds based on the null hypothesis, considering the alternative hypothesis. Suppose we assume that the null hypothesis is true. The probabilities can be assigned to different possible sample results. This cannot be done if we proceed with an alternative hypothesis. A null hypothesis is called a statistical hypothesis, which is frequently used.

The following points should be considered while choosing the null hypothesis:

– A null hypothesis represents the hypothesis we are trying to reject, and an alternative hypothesis represents all other possibilities.

– Null hypothesis should always be a specific hypothesis photo.

– Suppose rejecting a specific true hypothesis involves excellent risk; it is the null hypothesis. This is because the probability of dismissing it when it is true is minimal (level of significance).

An alternative hypothesis is one that one wishes to prove, and a null hypothesis is one that one wishes to disprove.

2) Level of significance:

The level of significance is determined in advance before testing the hypothesis. The significance level is the maximum value of the probability of rejecting when it is true. The level of significance is a fundamental concept in hypothesis testing. It should be chosen with great thought and reason. It is always some percentage, usually 5%. For example, it will be rejected when the sampling result has less than a 0.05 probability of occurring if it is true. If we take the significance level at 5%, researches willing to take as much as 5% risk of rejecting a null hypothesis when it happens to be true.

 3) Decision rule or test of hypothesis:

The decision rule is made based on the given hypothesis and alternative hypothesis.

The rule is made according to which we accept  that we are rejecting

Or

We reject  that if we are accepting

 

   4) Type I and Type II errors:

 

The null hypothesis is either accepted or rejected. There is a chance of error when accepting or rejecting the hypothesis because it is impossible to be sure whether the decision is correct. Two types of error may occur: Type I Error and Type II Error.

• When a True hypothesis is Rejected Type I error occurs. It is also known as a “false positive” finding or conclusion.
• When a False hypothesis is Accepted Type II error occurs. It is also known as a “false negative” finding or conclusion.

Tabularised relations between truth/falseness of the null hypothesis and outcomes of the test:

 

Table of error types		Null hypothesis (H0) is
		True	False
Decision about null hypothesis (H0)	Don’t reject	Correct inference (true negative)(probability = 1 – α)	Type II error (false negative) (probability = β)
	Reject	Type I error (false positive)(probability = α)	Correct inference (true positive)(probability = 1 – β)

 

Error rate:

• A perfect test would have zero false positives and zero false negatives
• Considering the nature of statistics science, all statistical hypothesis tests will likely make type I and II errors.
• The type I error rate or significance level is the probability of rejecting the null hypothesis, given that it is true. It is denoted by the Greek letter α (alpha), also called the alpha level.
• Usually, the significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the true null hypothesis.
• The rate of the type II error is denoted by the Greek letter β (beta) and related to the power of a test, which equals 1−β.
• These two error rates are traded off against each other: for any given sample set, reducing one type of error generally increases the different types of error.

5) Two-tailed and One-tailed tests:

  -Two-tailed hypothesis test

 A two-tailed test rejects the null hypothesis if the sample mean is considerably higher or lower than the hypothesized population mean. The two-tailed test is appropriate when the null hypothesis and alternative hypothesis values are equal to the specified null hypothesis value. Two-tailed hypothesis tests are nondirectional and two-sided tests because we can test for effects in both directions.

Symbolically, it can be expressed as:

: µ = µ   and : µ ≠ µ

which means

µ > µ  or  µ < µ

In a two-tailed test, there are two rejection regions, one on each tail of the curve. The two shaded regions cover the two tails of the distribution.

While performing a two-tailed test, the significance level percentage is split between both tails of the distribution.

For example, Alpha is 5%, and the distribution has two 2.5% shaded regions (2 * 2.5% = 5%).

 

 

 

 

 

 

 

 

 

 

 

When a test statistic falls in either critical region, the sample data are sufficiently incompatible with the null hypothesis that we can reject it for the population.

In a two-tailed test, the generic null and alternative hypotheses are the following:

• Null: The effect equals zero.
• Alternative:  The effect does not equal zero.

 

 

 

 

 

 

 

 

 

 

Advantages of two-tailed hypothesis tests

1. Both positive and negative effects can be detected.
2. Two-tailed tests are standard in scientific research.

One-Tailed Hypothesis Test

One-tailed hypothesis tests are also known as directional and one-sided tests. In one-tailed tests, the test for effects is in only one direction. In one-tailed tests, the entire significance level percentage goes into the extreme end of one tail of the distribution.

For example, we take an alpha of 5%. Each distribution has one shaded region of 5%. While performing a one-tailed test, we must define whether the critical region is in the left or right. The test can detect an effect only in the direction that has the vital area. It has absolutely no capacity to detect an effect in the other direction.

We can choose either of the following sets of generic hypotheses:

• Null: The effect is less than or equal to zero.
• Alternative: The effect is more significant than zero.

Or

• Null: The effect is greater than or equal to zero.
• Alternative: The effect is less than zero.

 

 

 

 

 

 

 

 

 

 

 

Advantages of one-tailed hypothesis tests

• One-tailed tests have more statistical power to detect an effect in one direction than a two-tailed test with the same design and significance level.
• One-tailed tests occur most frequently for studies where one of the following is true:
• Effects can exist in only one direction.
• Effects can exist in both directions, but the researchers only care about an impact in one direction.
• There is no drawback to failing to detect an effect in the other direction. which is not recommended.

The disadvantage of one-tailed tests

• It has no statistical power to detect an effect in the other direction.

Critical Regions in a Hypothesis Test

• In hypothesis tests, critical regions are ranges of the distributions where the values represent statistically significant results.
• Analysts define the size and location of the critical regions by specifying both the significance level (alpha) and whether the test is one-tailed or two-tailed.
• Consider the following two facts:
• The significance level is the probability of rejecting a correct null hypothesis.
• The sampling distribution for a test statistic assumes that the null hypothesis is correct.

Procedure For Hypothesis Testing:

 The main question in hypothesis testing is whether to accept the null hypothesis or not to accept the null hypothesis.

The procedure for hypothesis testing refers to the steps that are undertaken to make a choice between rejecting and accepting a null hypothesis.

The various steps involved in hypothesis testing are stated below:

1. The hypothesis should be clearly stated, considering the nature of the research problem. A formal statement of null hypothesis should be made. The decision on using one-tailed test or two-tailed tests should also be made at this step.

– If it is of the type greater than the power of the kind lesser, then we use a tailed test.

– If it is of the type, whether greater or smaller, we use a two-tailed test.

 

2. The selection of a significance level must be adequate based on the purpose and nature of the research. Generally, either a 5% or 1% level is adopted for research purposes.

3. The next step is to determine the appropriate sampling distribution. The rule for selecting the current distribution is generally between the normal distribution and the t-distribution.

 

1. The next episode will draw a sample to furnish empirical data and compute an appropriate value.

2. A probability is calculated After selecting a random sample and computing the appropriate value. The probability is calculated that the sample result would diverge as widely as it has from expectations if the null hypothesis were true.

 

1. The next step is to compare the probability calculated with a specified value for the significant level.

2. A) –If the probability is equal to or smaller than the value in the case of a tailed test.

And

– If it is  /2 in the case of a two-tailed test

Then

Reject the null hypothesis, i.e. Accept the alternative hypothesis.

But

– Accept the null hypothesis if the calculated probability is more significant.

3. B) -If you reject the significance level at most, there is a risk of committing a Type I error.

But,

– If we accept it, we risk committing a Type II error.

Review Questions:

1. What is the importance of identifying the problem area in research, and how does it contribute to the research process?
2. Define a research problem and explain the essential requirements for a research problem.
3. Explain the different types of research problems and provide examples of each (Exploratory, Descriptive, Causal).
4. What factors should a researcher consider when selecting a research problem?
5. Describe the process of defining a research problem and explain why it is crucial for the success of a research study.
6. Discuss the steps involved in the identification of a research problem.
7. Explain a preliminary or pilot survey’s role in the problem identification.
8. How can a researcher develop ideas through discussion, and why is this important for formulating a research problem?
9. What are the key characteristics of a good hypothesis, and why are they important?
10. Describe the process of hypothesis testing and explain the significance of null and alternative hypotheses in this context.