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Unformatted text preview: Prelim 2 Review D&B Chapters 8, 9, 10, and 12 How are populations characterized?  Mean z Central tendency  Variance z Spread  Standard deviation z Spread (in units of the mean)  Standard error z Variation of the mean How might we see if a population is different from what we might expect?  Compare a mean to some hypothetical value (one sample test)  Compare a mean of one population to the mean of another (two sample test)  Compare several means (ANOVA)  Compare means (predictions) across a range of predictor values (Regression) Possible hypotheses: : : : : : : < = > = = a a a H H H H H H 2 2 2 1 2 2 2 1 1 1 : : : : = = a a H H H H Hypothesis Testing  How confident are we that what we are looking at has not occurred by chance? Hypothesis Testing  Type I Error: z Probability that you think you have a difference when in fact it there is no difference .  Type II Error: z Probability that you think there is no difference when in fact there is a difference . H0 True H1 True Accept H0 Reject H0 H0 True H1 True Probability of false reject if H0 is true H0 True H1 True Probability of false accept if H1 is true H0 True H1 True 1 Power of the Test to Detect Significance H0 True Pvalue = 0.05 Pvalue = 0.01 Pvalue = Probability of obtaining a mean as extreme or more extreme than the sample mean under the null hypothesis Rules of thumb for tests based on a single sample  If sample size > 30 use z z Mean +/ qnorm(.975)*SE  If normal and sample size < 30 use t z Mean +/ qt(.975,df)*SE  If not normal and sample size < 30 use bootstrap hold.means = rep(0, 1000) for(i in 1:1000) { hold.means[i] = mean(sample(data, size = length(data), replace = T)) } sorted.means = sort(hold.means) # 95% Confidence Interval c(sorted.means[25], sorted.means[975]) Two sample ttests  Test hypothesis that variances are equal using Ftest z 2*(1pf(v1/v2,df1,df2)) where v1>v2  If equal, then equal variance ttest  If unequal, then unequal variance ttest Equal variance ttest...
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell University (Engineering School).
 '07
 SULLIVAN,P.

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