{"id":166,"date":"2019-07-30T09:03:02","date_gmt":"2019-07-30T09:03:02","guid":{"rendered":"http:\/\/hsp16.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=166"},"modified":"2019-07-30T09:03:35","modified_gmt":"2019-07-30T09:03:35","slug":"hypothesis-and-variables-meaning-classification-and-uses","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/hsp16\/chapter\/hypothesis-and-variables-meaning-classification-and-uses\/","title":{"rendered":"Hypothesis and Variables – Meaning, Classification and Uses"},"content":{"raw":"
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INTRODUCTION<\/strong><\/p>\r\n \r\n

Today, we are going to see the meaning of the hypothesis, steps involved to write a hypothesis, its characteristics, types and errors in formulating hypothesis. It involves different errors of hypothesis for which we have to identify the variables which will enable the research scholars to justify the area of research and design of the research work under taken by the investigator.<\/p>\r\n \r\n

Hypothesis is usually considered as the principal instrument in research. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate objective of testing hypotheses. Decision-makers often face situations wherein they are interested in testing hypotheses on the basis of available information and then take decisions on the basis of such testing. In social science, where direct knowledge of population parameter(s) is rare, hypothesis testing is often used strategy for deciding whether a sample data offers such support for a hypothesis from which generalization can be made. Thus hypothesis testing enables us to make probability statements about population parameter(s). The hypothesis may not be proved absolutely, but in practice it is accepted if it has withstood a critical testing. Before we explain how hypotheses are tested through different tests meant for this purpose, it will be appropriate to explain clearly the meaning of a hypothesis and the related concepts for better understanding of the hypothesis testing techniques.<\/p>\r\n \r\n

WHAT IS HYPOTHESIS?<\/strong><\/p>\r\n \r\n

Generally, when one talks about hypothesis, one simply means mere assumption or some supposition to be proved or disproved. Thus a hypothesis may be defined as a proposition or a set of proposition set forth as an explanation for the occurrence of some specified group of phenomena either asserted merely as a provisional conjecture to guide some investigation or accepted a highly probable in the light of established facts. Research hypothesis is a predictive\u00a0statement, capable of being tested by scientific methods that relate an independent variable to some dependant variable. For example, consider statement like the following ones:<\/span><\/p>\r\n \r\n

\u201cStudents who receive counseling will show better performance increase in creativity than students not receiving counseling\u201d or<\/span>\u201cthe automobile\u00a0 <\/span>A<\/strong> is performing better than automobile <\/span>B<\/strong>.\u201d<\/span><\/p>\r\n \r\n

The above hypothesis is capable of being objectively verified and tested. It is a proposition which can be put to a test to determine its validity.<\/span><\/p>\r\n \r\n

Here, we are examining the truth or otherwise of the hypothesis (guess, claim or assumptions, etc.) about some feature about one or more populations on the basis of samples drawn from these populations. Testing plays a major role in statistical investigation. Generally, a statistical hypothesis is a statement or a conclusion or an assumption about certain characteristic populations which is drawn on a logical basis and it can be tested based on the sample evidences. Test of hypothesis means either accept or reject the hypothesis under a valid reason. The test of significance enables a researcher to decide either to accept or reject the statistical hypothesis. For example, a manufacturing company producing bolts of different sizes and claims that not more than 2 per cent bolts are defective. In order to verify the claim as true or not, we have to check it on the basis of sample of bolts. A company wants to verify the effectiveness of advertisement given through print media is less effective than audio-visual media or not. There are wide ranges of areas in business where we have to come across situations of arriving at a decision of accepting or rejecting hypothesis. So, it is very much important to have knowledge about the logical basis of such decisions and it is provided by hypothesis testing, which is the objective of this chapter.<\/span><\/p>\r\n \r\n

It is a usual procedure that sample is drawn from the population an estimate of population parameter which is in other words, called sample statistic. Estimate of population parameters thus obtained may or may not exactly match with true values. To take the sample statistic as the estimate of population parameter is involved with risk. So, it is worthwhile to find whether the\u00a0<\/span>difference between the estimated value of the parameter or the true value is significantly different or it could have arisen due to fluctuation of sampling. For this reason only, a hypothesis is formulated and then tested for validity.<\/span><\/p>\r\n \r\n

Meaning of Hypothesis:<\/strong><\/p>\r\n \r\n

Hypothesis simply means a mere assumption to be proved or disproved. But for a researcher hypothesis is a formal question that he intends to resolve. It is a testable statement; hypotheses are generally either derived theory of from direct observation of data<\/span><\/p>\r\n \r\n

Types of Hypothesis<\/strong><\/p>\r\n \r\n

Null hypothesis<\/strong><\/p>\r\n \r\n

Null hypothesis is the statement about the parameters, which is usually a hypothesis of no difference and is denoted by Ho.<\/span><\/p>\r\n \r\n

Alternative Hypothesis<\/strong><\/p>\r\n \r\n

Any hypothesis, which is complementary to the null hypothesis, is called an alternative hypothesis, usually denoted by H1.<\/span><\/p>\r\n \r\n

BASIC CONCEPTS ON TESTING OF HYPOTHESES<\/strong><\/p>\r\n \r\n

a) NULL HYPOTHESIS<\/strong><\/p>\r\n \r\n

In the context of statistical analysis, we often talk about null hypothesis and alternative hypothesis. If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis. The null hypothesis is generally symbolized as Ho and the alternative hypothesis as Ha.<\/span><\/p>\r\n \r\n

In the choice of null hypothesis, the following considerations are usually kept in view:<\/strong><\/p>\r\n \r\n

Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. Thus, a null hypothesis represents the hypothesis we are trying to reject, and the alternative hypothesis represents all other possibilities.<\/span><\/p>\r\n \r\n

\u00a0 If the rejection of a certain hypothesis when it actually true involves great risk, it is taken as null hypothesis.<\/span><\/p>\r\n \r\n

Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value.<\/span><\/p>\r\n \r\n

b)\u00a0\u00a0 <\/strong>THE LEVEL OF SIGNIFICANCE<\/strong><\/p>\r\n \r\n

This is a very important concept in the context of hypothesis testing. It is always some percentage (usually 5%) which should be chosen with great care. In case we take the significance level at 5 percent, then this implies that Ho will be rejected when the sampling result (i.e., observed evidence) has a less than 0.05 probability of occurring if Ho is true. In other words, the 5 percent level of significance means that researcher is willing to take as much as 5 percent risk of rejecting the null hypothesis when it (Ho) happens to be true.<\/span><\/p>\r\n \r\n

c) DECISION RULE OF TEST OF HYPOTHESIS<\/strong><\/p>\r\n \r\n

Given a hypothesis Ho and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept Ho (i.e., reject Ha) or reject Ho (i.e., accept Ha).<\/span><\/p>\r\n \r\n

d) TYPE I<\/em> ERROR AND TYPE II<\/em> ERRORS<\/strong><\/p>\r\n \r\n

In the context of testing of hypotheses, there are basically two types of errors. We may reject Ho when Ho is true and we may accept Ho when Ho is not true. The former is known as Type I error and the latter as Type II error. In other words, Type I error means rejection of hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected. Type I error is denoted by \u03b1 (alpha) known as \u03b1 error, also called as the level of significance of test; and Type II error is denoted by \u03b2 (beta) known as \u03b2 error.<\/span><\/p>\r\n \r\n

e) TWO-TAILED AND ONE-TAILED TESTS<\/strong><\/p>\r\n \r\n

In the content of hypothesis testing, these two terms are quite important and must be clearly understood. A two-tailed test rejects the null hypothesis if, say, the sample mean is significantly higher or lower than the hypothesized value of the mean of the population. Such a test is appropriate when the null hypothesis is some specified value and the alternative hypothesis is a value not equal to the specified value of the null hypothesis.<\/span><\/p>\r\n \r\n

ERRORS IN TESTING OF HYPOTHESIS<\/strong><\/p>\r\n \r\n

In the procedure of testing of hypothesis, a decision is taken about the acceptance or rejection of null hypothesis. The possible decisions can be written in a tabular form.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\n\"\"<\/a>\r\n

There is always some possibility of committing the following two types of errors in taking such as decision as<\/p>\r\n \r\n

Type I Error: <\/strong>Reject the null hypothesis Ho when it is true.<\/p>\r\n \r\n

Type II Error: <\/strong>Accept the null hypothesis Ho when it is false.<\/p>\r\n \r\n

Now, we write \u03b1 = Probability of committing Type I error<\/strong><\/p>\r\n \r\n

And \u03b2 = Probability of committing Type II error<\/strong><\/p>\r\n \r\n

The compliment of Type II error is called as the power of the test<\/strong> and is given by (1- \u03b2) and the size of Type I error (\u03b1) is also called as level of significance<\/strong>. The level of significance is\u00a0the quantity of risk, which can be readily tolerated in making a decision Ho. Usually the value of \u03b1, is chosen depending upon the desired degree of precession and it and its value varies between 0.05 (for moderate precision) to 0.01 (for high precision).<\/span><\/p>\r\n \r\n

PROCEDURE FOR HYPOTHESIS TESTING<\/strong><\/p>\r\n \r\n

In hypothesis testing the main question is: whether to accept the null hypothesis or not. Procedure for hypothesis testing refers to all those steps that we undertake for making a choice between the two actions i.e., rejection and acceptance of a null hypothesis.<\/span><\/p>\r\n \r\n

The various steps involved in hypothesis testing are stated below:<\/span><\/p>\r\n

(i)\u00a0<\/strong>Selection of Variables<\/strong><\/p>\r\n \r\n

DEPENDENT VARIABLE<\/strong><\/p>\r\n \r\n

The variable that depends on other factors is called dependent variable. These variables are expected to change a result of an experimental manipulation of the independent variable or variables. The outcome variable measured in each subject, who may be influenced by manipulation of the independent variable, is termed the dependent variable.<\/span><\/p>\r\n \r\n

INDEPENDENT VARIABLE<\/strong><\/p>\r\n \r\n

The variable that is stable and unaffected by other variables is called independent variable. It refers to the condition of an experiment that is systematically manipulated by the investigator. In experimental research, an investigator manipulates one variable and measures the effect of that manipulation on another variable. For example, let\u2019s take a study in which the investigators want to determine how often an exercise must be done to increase strength.<\/span><\/p>\r\n \r\n

Check your progress<\/strong><\/p>\r\n \r\n

Fill in the blanks<\/strong><\/p>\r\n \r\n

F\u00a0 Hypothesis is usually considered as the principal instrument of _________________<\/span><\/p>\r\n

F\u00a0\u00a0 The null hypothesis is generally symbolized as_________<\/span><\/p>\r\n

F\u00a0\u00a0 The variable that depends on other factor is called _____________<\/span>Variable.<\/span><\/p>\r\n \r\n

IDENTIFYING THE KEY VARIABLES FOR ANALYSIS<\/strong><\/p>\r\n\r\n