Hypothesis Testing

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Hypothesis Testing

• 2007-03-21

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Purpose of a Hypothesis Test

• To corroborate theory by testing ideas against
  facts
• Corroboration involves making predictions about
  how social phenomena works
• We accept a theory only after it is corroborated
  by empirical predictions

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Statistical Inference

• Entails drawing conclusions about a population on
  the basis of sample statistics
• Awareness of sampling error is important in
  making a statistical inference

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Statistical Purpose of a Hypothesis Test

• To determine whether statistical effects computed
  from a sample indicate
• (1) real effects in the population or
• (2) sampling error
• How likely is this to have happened by chance?
• Deciding whether to accept or reject a statement
  on the basis of data

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Hypothesis Test Preparation

• State the research question
• Determine which variables to use
• Define the population under study
• Define the sample and sample size
• Select the statistical test
• Draw a conceptual diagram

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Six Steps of Statistical Inference

• State the null hypothesis
• Describe the sampling distribution
• State the chosen level of significance
• Observe the actual sample
• Make the rejection decision
• Interpret and apply the results

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Hypothetical Framework forHypothesis Testing

• Let us imagine for a moment
• Provide a measuring stick against which to
  compare our actual results
• In steps 1-4 we say
• Hold this thought. If the hypothesis is true,
  here is what happens in repeated sampling
• Only in step 5 do we firm up the decision and
  decide what we really believe is true

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Focus on p-Values

• p-Value is a measurement of the unusualness of a
  sample outcome when the hypothesis is true
• Tells us how often in repeated sampling we are
  likely to obtain the difference between the
  observed and what is expected

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Level of Significance

• Specifies the critical probability at which we
  are no longer willing to say that out sample
  outcome resulted from random sampling error
• Level of confidence
• (1 level of significance)

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Possible Results ofRejection Decisions
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Test Direction

• One-tailed
• direction of the effect is know
• stronger test
• easier to reject Ho
• Two-tailed
• things are different

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Selecting the Right Statistical Test

• This is the easy part
• See handout