Ppt 0000000

Hypothesis testing

Hypothesis • Hypothesis simply means a mere assumption or some supposition to be proved or disproved • For researcher hypothesis is a formal question that he intends to resolve • Hypothesis may be defined as a proposition or a set of proposition forth as an explantion for the occurrence of some specified group of phenomena 12/08/09

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• Research hypothesis is a predictive statement ,capable of being tested by scientific methods

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Characteristics of Hypothesis • Hypothesis should be clear and precise, if not clear and precise inferences drawn on its basis cannot be taken as reliable • Should be capable of being tested • Should state relationship between variables • Should be limited in scope and must be specific

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• Should be stated as far as possible in most simple terms so that the same is easily understandable by all concerned • Should be consistent with most known facts • Must explain the facts that gave rise to the need for explanation 12/08/09

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Basic concepts concerning testing of hypothesis • Null hypothesis and alternate 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, than this assumption is termed as null hypothesis 12/08/09

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• As against this, we may think method A is superior or the method B is inferior ,we are than stating what is termed alternate hypothesis • Null hypothesis h0 • Alternate hypothesis ha

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The level of significance • It is always some percentage which should be chosen with great care ,thought and reason • In case we take significance level at 5 percent ,than this implies that H0 will be rejected when the sampling results has a less than o.o5 probability of occurring if H0 is true 12/08/09

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Test of hypothesis • Given a hypothesis H0 and an alternate hypothesis Ha ,we make a rule which is known as decision rule according to which we accept H0 or reject H0

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Type 1 and type 2 errors • We may reject H0 when H0 id true and we may accept H0 when in fact H0 is not true • The former is known as type 1 error and letter as type 2 error

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Two tailed and one-tailed tests • A two tailed test rejects the null hypothesis ,if the sample mean is significantly higher or lower than the hypothesized value of the mean of the population • One tailed test would be used when we are to test, whether population mean is either lower than or higher than some hypothesized value 12/08/09

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Procedure for hypothesis testing • Making a formal statement • The formulation of hypothesis is an important step which must be accomplished with due care in accordance with the object and nature of the problem under consideration also indicates whether we should use a one tailed test or two tailed test 12/08/09

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Selecting a significance level • The hypothesis are tested on a predetermined level of significance and as such the same should be specifdied • Generally 5%level or 1% level is adopted for the purpose • Factors affecting level of significance • Magnitude of the difference between sample means

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• Size of the samples • Variability of measurements within samples • Whether hypothesis is directional or non-directional

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Deciding the distribution to use • Choice remains between normal distribution and t-distribution

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Selecting a random sample and comting an appropriate value

• Sample to furnish empirical data

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Calculation of probability • The sample result would diverge as widely as it has from expectations

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Comparing the probability • Calculated with the specified value for

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Flow diagram for Hypothesis testing

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Test of hypothesis • Hypothesis testing determines the validity of the assumption with a view to choose between two conflicting hypothesis about the value of a population parameter

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• Parametric tests or standard tests of hypothesis • Non-parametric test or distribution free test of hypothesis

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• Parametric tests usually assume certain properties of the parent population from which we draw samples • Assumptions like observations come from a normal population ,sample size is large ,assumptions about the population parameters like mean,variance etc • Must hold good before parametric tests can be used

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Non parametric tests • Because such tests do not depend on any assumption about the parameters of the parent population • Non-parametric tests need more observations than parametric tests to achieve the same size of type 1 and type 2 errors

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Limitations of the tests of hypothesis • Tests should not be used in a mechanical fashion. testing is not decision making itself; tests are only useful aids for decision making • Tests do not explain the reasons as to why does differences exist • Results of significance tests are based on probabilities 12/08/09

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• Statistical inferenses based on the significant tests cannot be said to be entirely correct evidenses concerning the truth of the hypothesis • Inference techniques must be combined with adequate knowledge of the subject matter along with the ability of good judgement 12/08/09

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QUESTIONS

Thank you

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