MIT 9 07 - Single sample hypothesis testing (71 pages)

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Single sample hypothesis testing



Previewing pages 1, 2, 3, 4, 5, 33, 34, 35, 36, 67, 68, 69, 70, 71 of actual document.

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Single sample hypothesis testing

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Pages:
71
School:
Massachusetts Institute of Technology
Course:
9 07 - Statistical Methods in Brain and Cognitive Science

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Single sample hypothesis testing II 9 07 3 02 2004 Outline Very brief review One tailed vs two tailed tests Small sample testing Significance multiple tests II Data snooping What do our results mean Decision theory and power Brief review Null and alternative hypothesis Null only chance effects Alternative systematic chance effects Assume the null is true Given this assumption how likely is it that we d see values at least as extreme as the ones we got If it s highly unlikely reject the null hypothesis and say the results are statistically significant The results are due to a combination of chance and a systematic effect Key Concepts H0 and Ha are contradictory mutually exclusive Support for Ha can only be obtained indirectly by rejecting H0 Rationale We can never prove anything true but we can prove something false We know the value of the parameter given H0 but not given Ha Why bother with Ha at all The alternative hypothesis describes the condition that is contrary to the null hypothesis and this can be directional or non directional Directional The effect only occurs in a specific direction increases or decreases Non directional The effect may be greater or less than a population parameter Outline Very brief review One tailed vs two tailed tests Small sample testing Significance multiple tests II Data snooping What do our results mean Decision theory and power A Tale of Two Tails Directional hypotheses are called one tailed We are only interested in deviations at one tail of the distribution Non directional hypotheses are called twotailed We are interested in any significant deviations from H0 The p value for a test of Ho o against Ha o is prob z Ha o is prob z Ha o is prob z Figure by MIT OCW How do you decide to use a one or two tailed approach A one tailed approach is more liberal it is more likely to declare a result significant tcrit 1 69 tcrit 2 03 5 one tailed 5 two tailed There s no one right answer as to which test to use People will debate this point p



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