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Interpreting a p-value given the hypothesis.  Common misconceptions. 

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You are investigating the effect of a {treatment[a]} on {alterperformance[a]}.  You compare the means of your control and experimental groups (with {n} in each sample, and {df} degrees of freedom).  You use a simple independent means t-test at the $\\alpha$=0.05 level, and calculate a p-value of {p}.

Please mark each of the statements below as \"true\" or \"false\".  \"False\" means that the statement does not follow logically from the above premises.

Please note all/several/none of these statements may be true.

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PART A,  PART D, PART E, PART F

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These are really all asking the same thing.  You reject the null hypthesis and accept the alternative hypothesis if the results are significant.

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PART B

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The results are significant if p<$\\alpha$, in this case if p<0.05.

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PART C

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This is highly unlikely to be true (unless the data sets are equal).

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PART G

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You never accept the null hypothesis.  If there is no evidence to reject it then, then we do not reject it, but remember the test was checking for evidence AGAINT the null, rather to evidence FOR the null.  It is more like acquitting a defendant when there is insufficient evidence to secure a conviction.

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PART H

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We were asked for evidence at the 0.05 level, so this is the level we are considering statistically significant.  A p-value less than 0.1 is usually considered a small amount of evidence, so if p is between 0.05 and 0.1 we might claim there is 'some evidence but it is not statistically significant'.

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PART I

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A p-value of less than 0.01 is very strong evidence.

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Your result is significant at the level $\\alpha$=0.05.

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There is no difference between the means of the control and the experimental group.

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You accept the alternative hypthesis.

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You do not reject the null hypthesis.

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There is no evidence to reject the null hypthesis.

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You accept the null hypothesis.

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There is some weak evidence in favour of rejecting the null hypothesis, but it is not statistically significant.

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The evidence in favour of the alternative hypothesis is strong, and statistically significant at the 1% level.

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