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Hypothesis <ul><li>Hypothesis is a principal instrument in research </li></ul><ul><li>Most research is carried out with the deliberate intention of testing hypothesis </li></ul><ul><li>Decision makers need to test hypothesis to take decisions regarding alternate courses of action </li></ul><ul><li>In Social Sciences, hypothesis testing is often used for deciding whether a sample data offers support for certain generalizations </li></ul><ul><li>Hypothesis-testing, thus, enables us to make probability statements about population parameters </li></ul>
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Meaning of Hypothesis <ul><li>Simply, a mere assumption to be proved or disproved </li></ul><ul><li>But for a researcher, hypothesis is a formal question that he intends to resolve </li></ul><ul><li>Definition: “A proposition or a set of propositions, set forth as an explanation for the occurrence of some specified group of phenomena asserted merely as a provisional conjecture to guide some investigation or accepted as highly probable in the light of established facts” </li></ul>
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Meaning of Hypothesis <ul><li>Often hypothesis is a predictive statement capable of being tested by scientific methods, that relates an independent variable to some dependent variable </li></ul><ul><li>Ex: students who receive counseling will show greater increase in creativity than students not receiving counseling; or Car A is performing as well as Car B </li></ul><ul><li>In sum, hypothesis is a proposition which can be put to test to determine its validity </li></ul>
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Characteristics of a Hypothesis <ul><li>Should be clear and precise </li></ul><ul><li>Should be capable of being tested </li></ul><ul><li>Should be limited in scope and be specific </li></ul><ul><li>Should be stated in simple terms </li></ul><ul><li>Should state the relationship between variables </li></ul><ul><li>Should be consistent with most known facts </li></ul><ul><li>Should be amenable to testing within a reasonable time </li></ul><ul><li>Must explain the facts that gave rise to the need for explanation </li></ul>
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Basic Concepts of Hypothesis <ul><li>Null Hypothesis and Alternative Hypothesis </li></ul><ul><li>The Level of Significance </li></ul><ul><li>Type I and Type II Errors </li></ul>
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1. Null Hypothesis and Alternative Hypothesis <ul><li>In the context of statistical analysis: </li></ul><ul><li>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 </li></ul><ul><li>As against the above, we may think that the Method A is superior or that the Method B is inferior, we are then stating what is termed as Alternative Hypothesis </li></ul>
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Null Hypothesis and Alternative Hypothesis… <ul><li>Alternative Hypothesis is usually the one which we wish to prove and the Null hypothesis is the one which we wish to disprove </li></ul><ul><li>Thus, a null hypothesis represents the hypothesis we are trying to reject, and the alternative hypothesis represents all other possibilities </li></ul>
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2. The Level of Significance <ul><li>In the context of hypothesis-testing, the level of significance is an important concept </li></ul><ul><li>It is always some percentage (usually 5%) </li></ul><ul><li>This implies that the null hypothesis will be rejected, when the sampling result (observed evidence) has less than 0.05 probability of occurring if the null hypothesis is true </li></ul><ul><li>That is, the 5% level of significance means that the researcher is willing to take as much as a 5% risk of rejecting the null hypothesis when it happens to be true </li></ul>
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3. Type I and Type II Errors <ul><li>Basically two types of errors are possible: </li></ul><ul><li>Type I Error – we may reject the null hypothesis when it is true; and </li></ul><ul><li>Type II Error – we may accept the null hypothesis when in fact the null hypothesis is not true </li></ul><ul><li>That is, Type I error means rejection of the hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected </li></ul>
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Steps in Hypothesis-testing <ul><li>To test a hypothesis means to state (on the basis of data the researcher has collected) whether or not the hypothesis seems valid </li></ul><ul><li>In hypothesis testing the main question is – whether to accept the null hypothesis or not to accept the null hypothesis? </li></ul><ul><li>Steps for hypothesis testing refer to all the steps we take for making a choice between rejection and acceptance of the null hypothesis </li></ul>
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Steps in Hypothesis-testing… <ul><li>Making a formal statement </li></ul><ul><li>Selecting a significance level </li></ul><ul><li>Deciding the distribution to use </li></ul><ul><li>Selecting a random sample </li></ul><ul><li>Calculation of the probability </li></ul><ul><li>Comparing the probability </li></ul>
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Making a Formal Statement <ul><li>Consists in making a formal statement of the null hypothesis and also the alternative hypothesis </li></ul><ul><li>Ex: The average score in an aptitude test at the national level is 80. To evaluate a state’s education system, the average score of 100 of the state’s students selected on random basis is 75. The state wants to know if there is a significant difference between the state’s scores and the national scores. </li></ul><ul><li>Hypothesis may be stated as follows: </li></ul><ul><li>Null hypothesis: population mean = 80 </li></ul><ul><li>Alternative hypothesis: population mean is not equal to 80 </li></ul>
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Selecting a Significance Level <ul><li>The hypothesis are tested on predetermined level of significance and should be specified </li></ul><ul><li>Generally, either 5% level (0.05) or 1% level (0.01) is adopted </li></ul>
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Deciding the distribution to use <ul><li>The next step is to determine the appropriate sampling distribution </li></ul><ul><li>Generally, follow the principles of Normal Distribution </li></ul>
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Selecting the Random Sample <ul><li>Select the random sample and compute an appropriate value </li></ul><ul><li>The sample should furnish the empirical data </li></ul>
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Calculation of the Probability <ul><li>The next step is to calculate the probability that the sample result would diverge as it has from expectations, if the null hypothesis were in fact true </li></ul>
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Comparing the Probability <ul><li>The next step is to compare the probability thus calculated with the specified value (the significance level) </li></ul><ul><li>If the calculated probability is equal to or smaller than the significance level, then reject the null hypothesis (i.e. accept the alternative hypothesis); but if the calculated probability is greater, then accept the null hypothesis </li></ul>
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Statistical Tests of Hypothesis <ul><li>Tests of hypothesis are also known as tests of significance </li></ul><ul><li>They are classified as: </li></ul><ul><li>Parametric Tests or Standard Tests – ex. are z-test, t-test, F-test etc. and are based on the assumption of normality </li></ul><ul><li>Non-Parametric Tests or Distribution-free tests of hypothesis </li></ul>
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