Week 5 Hypothesis Testing

Week 5 Hypothesis Testing - Engr9397 Week5...

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Engr 9397 – Week 5 Analysis
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Hypothesis testing Statistical hypothesis ( H ) : a statement about population parameter values These statements are tested by sampling the population to determine if the statement should be accepted or rejected These tests are performed by using an appropriate test statistic and decision rule
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Hypothesis Testing –Step by Step Step 1: Formulate hypotheses H o : The null hypothesis, (ex. observations are result of chance) H 1 : The alternative hypothesis (ex. observations are the result of a real effect, plus chance variation. Step 2: Identify an appropriate test statistic that will assess the evidence against the null hypothesis Step 3: Determine the p value Step 4: Compare the p value to a fixed significance level, acts as a cut off point, if the p value alpha, then we rule out H o and an effect is agreed to be statistically significant
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Example – Hypothesis Testing method
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Hypothesis Testing Decision Theory In hypothesis testing, two kinds of random errors can occur: Type I error: initial hypothesis is true, but test rejects it Reject hypothesis too easily, is too large, as increases, the incidence of Type I error increases Type II error: initial hypothesis is false, but test accepts it is set too low, as decreases incidence of Type II error increases Accept H 0 Reject H 0 H 0 true Correct decision Type I error H 0 false Type II error Correct decision
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Types of Hypothesis Tests One sample test comparing with a known value Two sample test comparing two samples Several sample test more than two samples (ANOVA used for testing several sample means) Goodness of fit tests checking the fit of theoretical distributions to data Correlation test for linear association between 2 random variables Regression analysis testing if data can be fitted by a line
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Hypothesis formulation There are only 3 alternative questions that one can ask: Is there a change or not? /+ 2 tail test (ex. H 1 :  0 ) Is it greater or not? /+ 1 tail test (ex. H 1 : > 0 ) Is it lower or not? /+ 1
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Week 5 Hypothesis Testing - Engr9397 Week5...

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