Kin 304 Inferential Statistics

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Kin 304Inferential Statistics

• Probability Level for Acceptance
• Type I and II Errors
• One and Two-Tailed tests
• Critical value of the test statistic

Statistics means never having to say you're
certain
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Inferential Statistics

• As the name suggests Inferential Statistics allow
  us to make inferences about the population, based
  upon the sample, with a specified degree of
  confidence

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The Scientific Method

• Select a sample representative of the population.
  The method of sample selection is crucial to this
  process along with the sample size being large
  enough to allow appropriate probability testing.
• Calculate the appropriate test statistic. The
  test statistic used is determined by the
  hypothesis being tested and the research design
  as a whole.
• Test the Null hypothesis. Compare the calculated
  test statistic to its critical value at the
  predetermined level of acceptance.

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Setting a Probability Level for Acceptance

• Prior to analysis the researcher must decide upon
  their level of acceptance.
• Tests of significance are conducted at
  pre-selected probability levels, symbolized by p
  or a.
• The vast majority of the time the probability
  level of 0.05, is used.
• A p of .05 means that if you reject the null
  hypothesis, then you expect to find a result of
  this magnitude by chance only 5 in 100 times. Or
  conversely, if you carried out the experiment 100
  times you would expect to find a result of this
  magnitude 95 times. You therefore have 95
  confidence in your result. A more stringent test
  would be one where the p 0.01, which translates
  to 99 confidence in the result.

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No Rubber Yard Sticks

• Either the researcher should pre-select one level
  of acceptance and stick to it, or do away with a
  set level of acceptance all together and simply
  report the exact probability of each test
  statistic.
• If for instance, you had calculated a t statistic
  and it had an associated probability of p
  0.032, you could either say the probability is
  lower than the pre-set acceptance level of 0.05
  therefore a significant difference at the 95
  level of confidence or simply talk about 0.032 as
  a percentage confidence (96.8)

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Type I and II Errors

• type I error reject a true null hypothesis
• type II error accept a false null hypothesis
• If you selected 0.01 instead of 0.05 as your
  acceptance level you would reduce the likelihood
  of committing a type I error, but unfortunately
  increase the chance of committing a type II
  error.
• If you are more concerned about committing a type
  I error than a type II then set a stringent
  acceptance level such as p 0.01 or even p
  0.001. This might be done because the
  consequences of a type I error are more profound,
  such as medical research where life and death may
  be at stake.
• Most commonly an acceptance level of p 0.05 is
  selected, which seems to represent the best
  balance between committing the two types of
  errors.

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One and Two-Tailed tests

• Most tests of significance are two-tailed. This
  means that rejection of the null hypothesis
  occurs regardless of the direction of the
  deviations.
• A one- tailed test of significance is used when
  the researcher is sure that differences or
  relationship can occur only in one direction

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Significance of Statistical Tests

• The test statistic is calculated
• The critical value of the test statistic is
  determined
• based upon sample size and probability acceptance
  level (found in a table at the back of a stats
  book or part of the EXCEL t-test report, or SPSS
  output)
• The calculated test statistics must be greater
  than the critical value of the test statistic to
  accept a significant difference or relationship

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