Rm   3   Hypothesis
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Rm 3 Hypothesis

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Rm   3   Hypothesis Rm 3 Hypothesis Presentation Transcript

  • Hypothesis
    • Hypothesis is a principal instrument in research
    • Most research is carried out with the deliberate intention of testing hypothesis
    • Decision makers need to test hypothesis to take decisions regarding alternate courses of action
    • In Social Sciences, hypothesis testing is often used for deciding whether a sample data offers support for certain generalizations
    • Hypothesis-testing, thus, enables us to make probability statements about population parameters
  • Meaning of Hypothesis
    • Simply, a mere assumption to be proved or disproved
    • But for a researcher, hypothesis is a formal question that he intends to resolve
    • 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”
  • Meaning of Hypothesis
    • Often hypothesis is a predictive statement capable of being tested by scientific methods, that relates an independent variable to some dependent variable
    • 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
    • In sum, hypothesis is a proposition which can be put to test to determine its validity
  • Characteristics of a Hypothesis
    • Should be clear and precise
    • Should be capable of being tested
    • Should be limited in scope and be specific
    • Should be stated in simple terms
    • Should state the relationship between variables
    • Should be consistent with most known facts
    • Should be amenable to testing within a reasonable time
    • Must explain the facts that gave rise to the need for explanation
  • Basic Concepts of Hypothesis
    • Null Hypothesis and Alternative Hypothesis
    • The Level of Significance
    • Type I and Type II Errors
  • 1. Null Hypothesis and Alternative Hypothesis
    • In the context of statistical analysis:
    • 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
    • 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
  • Null Hypothesis and Alternative Hypothesis…
    • Alternative Hypothesis is usually the one which we wish to prove and the Null hypothesis is the one which we wish to disprove
    • Thus, a null hypothesis represents the hypothesis we are trying to reject, and the alternative hypothesis represents all other possibilities
  • 2. The Level of Significance
    • In the context of hypothesis-testing, the level of significance is an important concept
    • It is always some percentage (usually 5%)
    • 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
    • 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
  • 3. Type I and Type II Errors
    • Basically two types of errors are possible:
    • Type I Error – we may reject the null hypothesis when it is true; and
    • Type II Error – we may accept the null hypothesis when in fact the null hypothesis is not true
    • 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
  • Steps in Hypothesis-testing
    • To test a hypothesis means to state (on the basis of data the researcher has collected) whether or not the hypothesis seems valid
    • In hypothesis testing the main question is – whether to accept the null hypothesis or not to accept the null hypothesis?
    • Steps for hypothesis testing refer to all the steps we take for making a choice between rejection and acceptance of the null hypothesis
  • Steps in Hypothesis-testing…
    • Making a formal statement
    • Selecting a significance level
    • Deciding the distribution to use
    • Selecting a random sample
    • Calculation of the probability
    • Comparing the probability
  • Making a Formal Statement
    • Consists in making a formal statement of the null hypothesis and also the alternative hypothesis
    • 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.
    • Hypothesis may be stated as follows:
    • Null hypothesis: population mean = 80
    • Alternative hypothesis: population mean is not equal to 80
  • Selecting a Significance Level
    • The hypothesis are tested on predetermined level of significance and should be specified
    • Generally, either 5% level (0.05) or 1% level (0.01) is adopted
  • Deciding the distribution to use
    • The next step is to determine the appropriate sampling distribution
    • Generally, follow the principles of Normal Distribution
  • Selecting the Random Sample
    • Select the random sample and compute an appropriate value
    • The sample should furnish the empirical data
  • Calculation of the Probability
    • 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
  • Comparing the Probability
    • The next step is to compare the probability thus calculated with the specified value (the significance level)
    • 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
  • Statistical Tests of Hypothesis
    • Tests of hypothesis are also known as tests of significance
    • They are classified as:
    • Parametric Tests or Standard Tests – ex. are z-test, t-test, F-test etc. and are based on the assumption of normality
    • Non-Parametric Tests or Distribution-free tests of hypothesis