Unit 3 Hypothesis

Meaning Tentative solutions proposed by the researcher Intelligent and logical guesses about possible differences, relationships, causes and solutions These may or may not be real solutions to the problem Whether they are or not is to be tested by the researcher A predictive statement , capable of being tested by scientific methods that relates an independent variable to dependent variable

Definition A tentative generalization, the validity of which remains to be tested. In most elementary stage hypothesis may be any guess, hunch , imaginative idea which becomes the basis for action or investigation

Characteristics of Hypothesis Clarity Empirically testable Specific Simple to understand Consistency Time bound Consider all aspects of a problem

Importance of Hypothesis Provides definite focus Spells out the difference between precision and haphazardness Suggests the type of research Suggests the type of analysis Helps to develop theory

Types of Hypothesis Null and Alternative hypothesis Null 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 Null hypothesis Symbolized as Ho Alternative Hypothesis We may think that method A is superior and method B is inferior, then this assumption is Alternative hypothesis Symbolized as Ha

Null and Alternative Hypothesis Suppose we assume that the mean attendance of a class is 70. Null hypothesis H0 :µ= µ H0 =70 (Null hypothesis is that the mean attendance of a class is 70) Alternative Hypothesis Ha : µ≠ µ H0 (The alternative hypothesis is that mean attendance of class is not equal to 70. It may be more or less than 70) Ha : µ> µ H0 (The alternative hypothesis is that mean attendance of class is greater than 70) Ha : µ< µ H0 (The alternative hypothesis is that mean attendance of class is less than 70)

Null hypothesis and Alternative hyothesis Alternative hypothesis is usually the one which one wishes to prove and null hypothesis is the one which one wishes to disprove Null hypothesis represents the hypothesis we are trying to reject and alternative hypothesis represents all other possibilities

Level of Significance Usually taken as 5% or sometimes 1% 5% level of significance means Ho will be rejected when the result has less than 5%(.05) probability of occurring if Ho is true Researcher is willing to take as much as 5% risk of rejecting Ho when it happens to be true Level of significance is the maximum level of the probability of rejecting null hypothesis when it is true. Usually determined in advance

Decision Rule Given a hypothesis Ho and an alternative hypothesis Ha, we make a rule called decision rule according to which we accept Ho or reject Ho If Ho is that a student is punctual( he/she is never late for the class) and Ha is that the student is not punctual ( he/she is usually late for the class), then we must decide the number of times to be tested and the criterion for accepting or rejecting H0. We might test in 20 classes and plan our decision saying that if the student is on time up to 18 times we accept Ho else reject Ho.

Type 1 and Type 2 Errors Type 1 Error Type 2 Error Rejecting Ho when Ho is true Denoted by α (alpha) Also called level of significance of test Type 2 Error Accepting Ho when Ho is false Denoted by β

Type 1 and Type 2 Errors

Two tailed and One tailed tests A two tailed test rejects null hypothesis if sample mean is significantly higher or lower than the hypothesized mean It is appropriate when null hypothesis is some specified value and alternative hypothesis is not equal to the null hypothesis value. Symbolically, two tailed test is appropriate when H0 :µ= µ H0 and Ha : µ≠ µ H0

Two tailed test

One tailed test A one tailed test is appropriate if we are to test whether sample mean is either significantly higher or lower than the hypothesized mean It is appropriate when null hypothesis is some specified value and alternative hypothesis is either greater than or less than the null hypothesis value Symbolically, two tailed test is appropriate when H0 :µ= µ H0 and Ha : µ> µ H0 (Right tailed test) OR H0 :µ= µ H0 and Ha : µ< µ H0 (Left tailed test)

One tailed tests Right tailed test Left tailed test

Procedure for Hypothesis testing Steps undertaken to make a choice between accepting or rejecting null hypothesis Making a formal statement Both null and alternative hypothesis clearly stated Selecting a significance level Generally 5% or 1%

Procedure for Hypothesis testing Deciding the distribution to use T-distribution or normal distribution Compute statistics Calculate probability that sample result would diverge as widely as it has from expectations Compare probability with specified level of significance If calculated probability < α in one tailed or α/2 in two tailed test, reject Ho If calculated probability > α in one tailed or α/2 in two tailed test, accept Ho

Tests of Hypothesis Parametric tests Non parametric tests Used with normal distribution Z-test, t-test, chi-square test, f-test Non parametric tests Distribution free Sign test , Fisher-Irwin test, Signed rank test, rank sum tests etc. Correlation Analysis Finding out if there is a relationship between two or more variables Regression Analysis To establish cause and effect relationship between two variables

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