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Lecture 8

Lecture 8 - November 7.

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Damian Dupuy

Hypothesis Testing – Hypotheses Two complementary hypotheses of interest – Null Hypothesis 'Ho' (the strawman that we want to knockdown) – Alternate Hypothesis 'Ha' – Generally, the researcher wants to support the alternate hypothesis and reject the null. – Essentially, you are testing the null hypothesis, so you assume it is true, Draw 1 of 2 conclusions – Reject Ho and conclude Ha its true (the hypothesis I gave is true, and the Ho is not) – Fail to reject Ho and Accept Ho as true – Are givent two options – REJECT or FAILTO REJECT Selection of form of Ha, depends on how the hypothesized difference is stated With the null hypothesis, the typical claim is that 'u' (miu) is equal to some hypothesized value of 'u" Ho: u= uH 3 versions of ultimate hypothesis Ha; u =/ uH (not equal) or Ha: u>uH (greater) or Ha: u 2.61 (u is significantly greater than the pph) or Ha: u< 2.61 (pph is significantly greater than the u) Hypothesis testing – ERROR (how significant or not the test is ) – Decision is either to reject or fail to reject the null hypothesis (deteremines how we test) – Based on a single measure, measurable chance of making an incorrect decision. (we cold do everythign right and set up test and completely mess up our interpretation) – In hypothesis testing, 2 sources of error: – Type 1 – Type 2 Type 1 Error – Reject the null hypothesis as false, when in fact it is true – we rejecting Ho , when Ho in fact is true. – The sin of commison (you committing to the fact that your sample is different, and ur population is differe, and ur landing for hypothesis landing is different, when it shouldnt be) – Called alpha (a) error or false positive – Observing a difference when none actually exists – Make sure to Minimize the probability of Type 1 error occuring ***** – In household size example, we would be concluding that there is a significant difference between household size in Toronto and that nationally, when no significant difference actually exists. – One of the serious erros to withdraw. Type 2 error – Fail to reject the null hypothesis, when in fact it is false – The sin of ommision – Called bete (B) error or false negative – Failing to observing a difference when one actually exists – In household size example, we would be concluding that there is no significant difference between household size in Toronto and that nationally, when a significant difference actually exists. Type 1 the most critical of the two errors. ****** Hypothesis Testing – Error Summary - PUT in CHEAT SHEET *** Reality Decision Made Ho is True Ho is False reject Ho a 1-B Fail to Reject Ho 1-a B Total Probability 1 1 Hypothesis Testing - Test Selection – Test used is a function of the research question, and research assumptions – Test will vary according to the number of samples drawn, sampling design, scale of information (determins the test) – One of the most common is the One- Sample means Test
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