hypothesis testing

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HYPOTHESIS TESTING Bidyadhar (04) Manoj (13) Rashmi (14) Sunil (15) Yash (16) Asha (19)

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INTRODUCTION CHARACTERISTICS OF A HYPOTHESIS CRITERIA FOR HYPOTHESIS CONSTRUCTION STEPS IN HYPOTHESIS TESTING SOURCES OF HYPOTHESIS APPROACHES TO HYPOTHESIS TESTING THE LOGIC OF HYPOTHESIS TESTING TYPES OF ERRORS IN HYPOTHESIS

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  • 1. Bidyadhar (04)Manoj (13)Rashmi (14)Sunil (15)Yash (16)Asha (19)

2. INTRODUCTION CHARACTERISTICS OF A HYPOTHESIS CRITERIA FOR HYPOTHESIS CONSTRUCTION STEPS IN HYPOTHESIS TESTING SOURCES OF HYPOTHESIS APPROCHES TO HYPOTHESIS TESTING THE LOGIC OF HYPOTHESIS TESTING TYPES OF ERRORS IN HYPOTHESIS 3. Dont confuse hypothesis and theory. Theformer is a possible explanation; the latter, thecorrect one. The establishment of theory is the verypurpose of science.- Martin H. Fischer A Hypothesis is :- a mere assumption to be proved or disproved the statement or an assumption about relationshipsbetween variables a tentative explanation for certain behaviors,phenomenon or events that have occurred or will occur a predictive statement capable of being tested by scientificmethods, that relates an independent variable to somedependent variable 4. Hypothesis is a principal instrument inresearch and for researcher its a formal questionthat he intends to resolve Most research is carried out with the deliberateintention of testing hypothesis Decision makers need to test hypothesis to takedecisions regarding alternate courses of action Hypothesis-testing, thus, enables us to makeprobability statements about populationparameters In sum, hypothesis is a proposition which canbe put to test to determine its validity 5. Students who receive counseling will showgreater increase in creativity than students notreceiving counseling; or Car A is performing aswell as Car B Bankers assumed high-income earners aremore profitable than low-income earners. Old clients were more likely to diminish CDbalances by large amounts compared toyounger clients.This was nonintrusive because conventionalwisdom suggested that older clients have alarger portfolio of assets and seek less riskyinvestments 6. o Should be clear and preciseo Should be capable of being testedo Should be limited in scope and be specifico Should be stated in simple termso Should state the relationship between variableso Should be consistent with most known factso Should be amenable to testing within a reasonable timeo Must explain the facts that gave rise to the need forexplanation 7. It should be empirically testable, whether it isright or wrong. It should be specific and precise. The statements in the hypothesis should not becontradictory. It should specify variables between which therelationship is to be established. It should describe one issue only. 8. Theory Main source Observation Through observing the environment Analogies Intuition & personal experience 9. Classical statistics Represents an objectives view of probability in which thedecision making rests totally on an analysis of availablesampling data A hypothesis established, it is rejected or accepted, basedon the sample data collected Bayesian statistics Its extension of classical approach But goes beyond to consider all other availableinformation This additional information consist of subjectiveprobability estimates states in terms of degrees of belief Subjective estimates are based on general experiencerather than on specific collected data 10. In classical tests of significance, two kinds ofhypothesis are used Null hypothesis Alternative hypothesis Two-tailed test One-tailed test 11. Null hypothesis (H0) represents the hypothesis we aretrying to reject and is the one which we wish to disprove: 0 0 0 New Std New Std H Example:1) Suppose a coin is suspected of being biased in favorof heads. The coin is flipped 100 times & the outcome is52 heads. It would not to be correct to jump to theconclusion that the coin is biased simply because morethan the expected number of 50 heads resulted. Thereason is that 52 heads is consistent with thehypothesis that the coin is fair. On the other hand,flipping 85/90 heads in 100 flips would seem tocontradict the hypothesis of a fair coin. In this casethere would be a strong case for a biased coin. 12. Given the test scores of two random samples ofmen and women, does one group differ from theother? A possible null hypothesis is that the meanmale score is the same as the mean female score:H0: 1 = 2where:H0 = the null hypothesis1 = the mean of population 1, and2 = the mean of population 2.A stronger null hypothesis is that the two samplesare drawn from the same population, such that thevariance and shape of the distributions are alsoequal. 13. Alternative Hypothesis (Ha or H1) is usuallythe one which we wish to prove and thealternative hypothesis represents all otherpossibilities.: 0 A New Std H Further, alternative hypothesis it has twotypes are:Two-tailed testOne-tailed test 14. It is non-directional test which considers two possibilities If you are using a significance level of 0.05, a two-tailed testallots half of your alpha to testing the statistical significancein one direction and half of your alpha to testing statisticalsignificance in the other direction. This means that .025 is in each tail of the distribution of yourtest statistic. When using a two-tailed test, regardless of the direction ofthe relationship you hypothesize, you are testing for thepossibility of the relationship in both directions. Example, we may wish to compare the mean of a sample toa given value x using a t-test. Our null hypothesis is that themean is equal to x. A two-tailed test will test both if themean is significantly greater than x and if the meansignificantly less than x. The mean is consideredsignificantly different from x if the test statistic is in the top2.5% or bottom 2.5% of its probability distribution, resultingin a p-value less than 0.05. 15. It is unidirectional test If you are using a significance level of .05, a one-tailed test allots all ofyour alpha to testing the statistical significance in the one direction ofinterest. This means that .05 is in one tail of the distribution of your test statistic. When using a one-tailed test, you are testing for the possibility of therelationship in one direction and completely disregarding the possibilityof a relationship in the other direction. Let's return to our example comparing the mean of a sample to a givenvalue x using a t-test. Our null hypothesis is that the mean is equal to x. A one-tailed test willtest either if the mean is significantly greater than x or if the mean issignificantly less than x, but not both. Then, depending on the chosen tail,the mean is significantly greater than or less than x if the test statistic is inthe top 5% of its probability distribution or bottom 5% of its probabilitydistribution, resulting in a p-value less than 0.05. The one-tailed testprovides more power to detect an effect in one direction by not testing theeffect in the other direction. A discussion of when this is an appropriateoption follows. 16. Types of errors Types of errorsTypes of decision H0true H0 falseReject Type I error(a) Correct decision(1-b)Accept Correct decision(1-a) Type II error(b) 17. Type I Error we may reject the nullhypothesis when it is true; That is, Type I error means rejection of thehypothesis which should have been accepted The value is called level of significance andprobability of rejecting the true Example: the innocent person is unjustlyconvicted 18. Type II Error we may accept the nullhypothesis when in fact the null hypothesis isnot true Type II error means accepting the hypothesiswhich should have been rejected Example: the result is an unjust acquittal, withthe guilty person may go free