Business Research MethodologyMBA : 2nd SemesterPresented by :Shantayya.S.G
Basic Concepts in HypothesesTesting Meaning of Hypothesis Testing Null Hypotheses & Alternate Hypotheses Type I & Type II Errors One Tailed & Two Tailed Test Steps in formulating Hypotheses Testing
What is Hypothesis testing Hypothesis is the making an assumption about thepopulation parameter. OR A set of logical and statistical guidelines used to makedecisions from sample statistics to populationcharacteristics.For example:The customer loyalty of brand A is better than brand B.
Null Hypothesis(Ho): The null hypothesis (H0) refers to a hypothesized testingnumerical value or range of values of the populationparameter. Specific statement about a population parameter made forthe purposes of argument. States the assumption to be tested, is a status quo. Is always about a population parameter, not about a samplestatistic.
Example of Ho: In a clinical trial of a new drug, the nullhypothesis might be that the new drug is nobetter, on average, than the current drug. Wewould writeH0: there is no difference between the two drugson an average.
Alternate Hypothesis(HA) An alternatives hypothesis (H1) is the logical oppositeof the null hypothesis. Represents all other possible parameter values exceptthat stated in the null hypothesis. Challenges the status quo. Hypothesis that is believed (or needs to be supported)by the researcher –a research hypothesis.
Example of HAIn the clinical trial of a new drug, the alternativehypothesis might be that the new drug has a differenteffect, on average, compared to that of the current drug.We would writeHA: the two drugs have different effects, on average.orHA: the new drug is better than the current drug, onaverage.The result of a hypothesis test:‘Reject H0 in favour of HA’ OR ‘Do not reject H0’
Type I Error: If the null hypothesis is true and we reject it is calledtype I error. Rejected H0 because the results occurred by chance Conclude that there is a significant effect, even thoughno true effect exists Probabilities of Type 1 error called – alpha ( )Determined in advance, typically 5%
Type II Error: If the null hypothesis is false and we accept it is calledtype II error. Accept H0 even though it is not true Conclude that there is no significant effect, eventhough a true difference exists Probabilities of Type II error called – beta ( )
Type I Error & Type II ErrorAccept H0 Reject H0Correct Decision Type I ErrorType II Error Correct DecisionHo (True)Ho (False)
One Tail Test:Rejection of null hypothesis for significant deviationfrom the specified value Ho in one direction (tail) ofthe curve of sampling distribution is called one tailedtest.For example:Boll pen better then ink pen .
Two Tailed Test:Rejection of null hypothesis for significant deviationfrom the specified value Ho in both the direction (tail)of the curve of sampling distribution is called twotailed test.Foe example:A product is manufactured by a semi-automaticmachine. Now, assume that the same product ismanufactured by the fully automatic machine.This will be two-sided test, because the nullhypothesis is that “the two methods used formanufacturing the product do not differsignificantly.
Steps in Hypotheses Testing1. Formulation of the null and alternate hypothesis2. Definition of a test statistic3. Determination of the distribution of the teststatistic4. Definition of critical region of the test statistic5. Testing whether the calculated value of the teststatistic falls within the acceptance region.
1: Formulation of H0 The Null hypothesis assumes a certain specific valuefor the unknown population parameter. Defined as an inequality – greater than or less than. For example, if the mean of a population isconsidered, then H0: μ ≤ μ0 H0: μ = μ0 H0: μ ≥ μ0
2: Formulation of Ha The alternate hypothesis assigns the values to thepopulation parameter that is not contained in the nullhypothesis. For example, Ha: μ > μ0 Ha: μ ≠ μ0 Ha: μ < μ0 The null hypothesis is accepted or rejected on the basisof the information provided by the sample.
3: Definition of a Test Statistic A test statistic must be defined to test the validity ofthe hypothesis. The test statistic is computed from sampleinformation. A number calculated to represent the match between aset of data and the expectation under the nullhypothesis
4: Determination of thedistribution of the test statistic The probability distribution of the test statisticdepends on the null hypothesis assumed, theparameter to be tested, and the sample size.Commonly used ones are the Normal, “t”, Chi-squareand F-distributions.
5: Definition of the critical regionfor the test statistic The set of values of the test statistic that leads to therejection of H0 in favour of Ha is called the rejectionregion or critical region. Depends upon whether the testing is one-sided ortwo-sided.
6: Decision rule A decision rule is used to accept or reject the null hypothesis. P- valueP < αReject the null hypothesisStatistically significant Test statisticTest statistic (calculated value) < Table value of αAccept H0Statistically insignificant