Tests of Significance

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Tests of Significance

• Confidence Intervals are one of the two most
  common types of statistical inference.
• The goal of using a CI is to estimate the
  population parameter.
• The second common type of inference is test of
  significance
• The goal of it is to assess the evidence provided
  by the data about some claim concerning the
  population.

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Tests of Significance

• Example 10.8 Im a great free-throw shooter

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Tests of Significance

• Tests of Significance use elaborate vocabulary,
  but the basic ides is an outcome that would
  rarely happen if a claim were true is good
  evidence that the claim is not true.

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Tests of Significance

• Example 10.9 Sweetening Colas
• The test of significance in this problem is
• Does the sample result xbar1.02 reflect a real
  loss in sweetness OR
• Could we easily get the outcome xbar1.02 just by
  chance?

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Tests of Significance

• A significance statement starts with a statement
  of these alternatives.
• First we must identify the parameter for the
  population we are trying to draw a conclusion
  about.
• Next, we must state the null hypothesis
• The null hypothesis states that there is no
  effect of no change in the population.
• If the null hypothesis is true the sample result
  is just chance at work.

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Tests of Significance

• The null hypothesis in the problems states that
  the cola does not lose any sweetness.
• This is written
• And read H-nought

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Tests of Significance

• The effect we suspect is true, the alternative to
  no effect is called the alternative hypothesis
• This is written
• Suppose there is no loss of sweetness, Is the
  sample xbar1.02 a surprisingly large amount?

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Tests of Significance

• If xbar1.02 is large then that is evidence
  against and in favor of
• Lets compare two samples one have xbar0.3 and
  the other having xbar1.02

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Tests of Significance

• A significance tests works by asking the
  question How likely would the observed outcome
  be if the null hypothesis were really true.
• The final step in tests of significance is to
  assign a number to measure how unlikely our
  observed xbar is.

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Tests of Significance

• The value given to the observations is called the
  P-value.
• P-value tells us the probability of a result
  being at least as far out as the result we got.
• The lower the probability the more surprising the
  result and the stronger the evidence against the
  null hypothesis.

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Tests of Significance

• The P-value for xbar0.3 is .17 which is 17.
• That means that 17 of the samples would have an
  xbar of 0.3 or larger just by chance, when the
  population mean is 0.
• An outcome this likely doesnt give us good
  evidence against the null.

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Tests of Significance

• The P-value for xbar1.02 is .00006.
• Because this pvalue is so small we would think
  that it we are unlikely to a mean of 1.02 when
  the population mean is 0.

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Tests of Significance

• Small P-values give us evidence against the null,
  because they say that it is unlikely to happen by
  chance.
• Large P-values fail to give us evidence against
  the null.
• How big of a P-value is big enough?

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Tests of Significance

• The rule of thumb on P-value is
• If the p-value is less than 0.05 then, there is
  evidence against the null.
• P-values less than 0.05 are called statistically
  significant. Which is just another way of saying
  that this number would rarely occur just by
  chance.

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Tests of Significance

• An outline of what Im supposed to do Please?!
• Describe the effect you are searching for in
  terms of a population parameter.
• Calculate a statistic like an xbar that estimates
  the parameter.
• Observe the P-value and determine how unlikely a
  result is to be true.