7 HP Lecture Slides March 9

# 7 HP Lecture Slides March 9 - Chapter 12 HP350 Spring 2010...

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1 Chapter 12 HP350 Spring 2010

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2 Statistical Testing Null hypothesis significance testing (NHST) is the procedure used decide whether an observed difference between the groups,( e.g., control vs. experimental), is due to chance or the results of a “real” difference between the groups. A statistical test is a set of rules whereby a decision about the hypothesis is reached.
3 Null Hypothesis (H 0 ) for difference Null hypothesis is that there is “no difference between groups, that is, any observed differences between means is due to random chance. Null hypothesis is represented by H 0 . Common null hypotheses, where y 1 : mean of group 1, y 2 : mean of group 2 H 0 : y 1 = y 2 H 0 : y 1 - y 2 = 0

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4 Null Hypothesis (H 0 ) for correlation Null hypothesis is that the correlation between two variables is zero , that is, any observed difference from zero is due to random chance. Null hypothesis is represented by H 0 . Common null hypotheses, where r xy : correlation between x and y H 0 : r xy = 0
5 Alternative Hypothesis (H 1 ) Alternative hypothesis is the hypothesis of “some difference,” that is, any observed differences between means (or between correlation coefficient and zero) is due to some factor other than random chance. Alternative hypothesis is represented by H 1 . Common null hypotheses, where y 1 : mean of group 1, y 2 : mean of group 2 H 1 : y 1 y 2 r xy : correlation between x and y H : r 0

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6 Test Is a coin biased? H 0 (null hypothesis): probability of heads equals tails, i.e., coin is fair. H 1 (alternative hypothesis): probability of heads is not equal to probability of tails, i.e., coin is biased. Hypotheses must be mutually exclusive, that is, when one hypothesis is true, the other must be false.
7 Probability 2 coin tosses: Probability of 0 heads = .25 Probability of 1 head   = .5 Probability of 2 heads = .25 Total probability: .25 + .5 + .25 = 1.0

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8 Probability Number of Heads 10 coin tosses: Probability of 5 heads = .25 Probability of 8 heads = .05 Total probability  under curve = 1.0
9 p = .95 p=.025 p =.025 Probability .025 + .95 + .025 = 1.0

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10 p value To determine whether to reject a null hypothesis ( H 0 ), a level of probability is needed to serve as the basis of rejection. It is known as p value , which refers to the probability of rejecting a null hypothesis when it is true. p value symbolized as p or α (alpha) . A commonly used value is .05 , which is generally good protection against falsely rejecting H 0 when it is true.
11 p value Compute a test statistic and examine the associated p value. If p < .05, reject H 0 and accept H 1 ,i.e., coin is biased. If p > .05, accept H 0 ,i.e., coin is fair.

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12 One-tailed vs. two-tailed p values Two-tailed p values are used when the alternative hypothesis (H 1 ) does not predict which side or tail of the probability distribution the significance will be detected.
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7 HP Lecture Slides March 9 - Chapter 12 HP350 Spring 2010...

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