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# Final Exam Study Guide PubH 6002

GWU

GPA 3.88

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## Popular in Biostatistical Applications of Public Health

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This 10 page Test Prep (MCAT, SAT...) was uploaded by Andie Kelly on Monday January 19, 2015. The Test Prep (MCAT, SAT...) belongs to PubH 6002 at George Washington University taught by Heather Hoffman in Fall2015. Since its upload, it has received 126 views. For similar materials see Biostatistical Applications of Public Health in Public Health at George Washington University.

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Date Created: 01/19/15

Parametric Tests Claims about continuous data regarding a mean of a population with a normal distribution One Sample Tests Sigma Test Test Statistic Margin of Error Known ztest x M E 2a2 x SigmaSqrtn SigmaSqrtn Unknown t test x M E tdfa2 x sSqrtn sSqrtn dfn 1 Two Sample Tests How do population means differ between two populations HoM1M2 Independent s Are Variances Test Test Statistic Variance Equal Known N Paired T test td bar 39Mg ngt30 sdsqrtn f nlt30 assume normal dist dbar mean value of differences from paired sample data 50 SD of differences for paired sample data n of pairs df n1 Y Y 2 Sample z Test BligHMl g SqrtSigma12n1 Sigmazznzn Y N Y 2 Sample Pooled BligHMl g T Test Sqrtsp2n1 sznzn df n1 n22 5102 lil lzj gil gg n1 n22 Y N N Unpooled T Test Blig ml g Sqrt512n1 522n2 df smallest n 1 NonParametric Tests Claims about categorical data Some test claims about a median of a population Do not require any assumptions of the population involved Test Used to Test Wilcoxon Rank Sum Test 2 independent samples H0 Median1Median2 PPN Combine samples Sort lowest to highest Assign rank When values are the same rank assign the mean of the ranks Find the sum of the ranks for either one of the original samples Calculate z R MRSigmaR RSum of the Ranks MR n1n1 212 SigmaRSD of R values Sqrtn1 n2 n1 n2112 Sign Test for Matched Pairs nominal data H0 Mediand0 P P PPN Subtract 2 l vale from 1St value Assign or sign Discard zeros n total of signs x of less frequent signs f sample data contradicts H1 fail to reject Ho f sample data doesn t contradict H1 nlt25 xtest statistic compare to sign test table ngt25 compare x to z 2 x5 n2 Sqrtn2 Wilcoxon Sign Ranked Test for Matched Pairs Continuous Data H0 Mediand0 P P PPN 9 gtl 10 11 Subtract 2 l vale from 1St value Assign or sign Discard zeros Sort lowest to highest Assign rank When values are the same rank assign the mean of the ranks Give each rank the sign of the difference Add absolute value of negative ranks and positive ranks for each sample 2 tnn14 Sqrtnn12n124 t smaller of two sums n number of pairs excluding zeros find test statistic and critical values to test Ho Sign Test for Binomial Distributions nominal Assign or sign Discard zeros data P n total of signs x of less frequent signs If sample data contradicts H1 fail to reject Ho If sample data doesn t contradict H1 nlt25 xtest statistic compare to sign test table ngt25 compare x to z 2 x5n2 Sqrtn2 Kruskal Wallis test ANOVA for gt2 categorical variables PPN 5 Combine samples Sort lowest to highest rank each value For each sample find the sum of the ranks and the sample size Calculate test statistic H12NN1 Rlzn1Rk2nk3N1 Rsum of ranks in sample CV x2 with df k1 Righttailed test Binomial Distribution For discrete dichotomous data outcome of the experiment is a success or a failure Binomial Probability distribution shows outcomes of the binomial experiment and the probability of these outcomes Tests claims about proportions Sampling with replacement independent variables Distribution is approximately normal if np and nq gt5 nfixed of trials x successes in n trials p probability of success in one trial q probability of failure in one trial PXx probability that the random variable takes on the value X nlnxlxl pX qnx Mean np Variance npq SD Sqrtnpq Range rule of thumb 95 of sample values fall within 2 SDs of the mean fSD is unknown minimum usual value mean ZSD maximum usual value meanZSD Continuity correction z x 05M Sigma if determining probability that X is quotat least or quotfewer than x if determining probability that X is quotat most or quotmore than than x X quotis exactly x x05 and x05 phat x n qhat 1D Standard Error One sample sqrtphatqhatn Two sample sqrtphatghatlmll phat2qhat2n2 Eza2SE Test statistic One sample ZMt9 Sqrtpqn Two samples zphatlmmgj gl Sqrtpqn1 pqnz Poisson Distribution Probability distribution of a discrete random variable that represents the count of independent events occurring within a specific unit of time or space time distance volume area Often used to describe the behavior of rare events Often used to approximate a binomial distribution when ngt100 nplt10 x occurrences in an interval PXx Mxe39M x SigmasqrtM Multinomial Experiments discrete categorical data Independent variables All Outcomes are categorized into exactly one of several different categories ChiSquared Distribution distribution is skewed but comes closed to the normal curve as degrees of freedom increase Only has non negative variables Degrees of Freedom Relate to the number of categories for each variable 0 Observed frequency E Expected frequency if equal Enk if unequal Enp for each category Egt5 for each category k of outcomes n of Trials Test of Variables Description Goodness of 1 Does the distribution X2 Sum Fit Test follow the expected E oneway distribution table df k l H0 OE ALWAYS A RIG HTTAILED TEST Test of 2 Is one variable contingent X2 Sum independence on another E two way H0 row and column contingency variables are independent E row totalcolumn total tables Grand total dfr1c1 Test of 2 Used in experiments with X2 Sum homogeneity predetermined sample E two way sizes contingency E row totalcolumn total tables Grand total dfr1c1 McNemar s Matched Pairs Rows and columns will X2 absvalueb c 12 Test have the same headers bc H0 frequencies b and c occur in the same proportion are concordant pairs Fisher s Exact Test Small Expected Cell Counts Frequency for a particular category expected under the claimed distribution More than 20 of cell counts Elt5 SAS output provides exact p value 2 sided Prgtp Odds Ratio Ratio of odds for those adbc exposed to risk factor to odds of those unexposed odds exposed ab to risk factor odds unexposed cd H0OR1 OR1 or if CI contains 1 there is no difference in odds for exposed and unexposed groups ORgt1 odds of disease is higher in exposed group ORlt1 odds of disease is lower in exposed group Relative risk Ratio of risk of disease for aabl those exposed to the risk ccd factor to risk of disease for those unexposed to risk factor H0 RR1 RR1 or if CI contains 1 there is no difference in risk for exposed and unexposed groups RRgt1 probability of disease is higher in exposed group RRlt1 probability of disease is lower in exposed group Tests of Association Test Dependent Variable Independent Variable Null va othesis Notes Correlation Con nuous 1 Continuous Rho 0 Pearson coefficient measure of strength of linear correlation Rhopopulation rsample FALLS BTWN 1 AND 1 Coefficient of determination r2 Proportion of variation that can be explained by the linear association If no association r0 1 Test statisticr Critical value Pearson correlation coefficient table If absvaluergtcv reject H0 2 trsqrt1r2n 2 dfn2 f absvaluetgtcv reject H0 Simple Linear Regression Con nuous 1 Continuous Bi 0 Test statistic t value k1 Degrees of freedom Model k Errorn k1 Totaln 1 ymxb Multiple Linear Regression Con nuous gt1 Continuous Omnibus null BlBZBkO Partial tests Bi 0 Bk0 K dependent variables F value tests omnibus null hypothesis T value test statistic for partial tests Yb0b1x1b2x2 1way ANOVA Con nuous 1 Categorical M1M2Mk Sample data separated into groups based on one factor F test tests for significant differences when variances are unknown Degrees of freedom Model k l ErrorN k TotalN 1 Yb0b1x1bk1xk1 Multiple comparison procedures Bonferroni test pairwise comparisons of each group to each other Tukey Kramer Test each grouping is assigned a letter means with the same letter are not significantly different 2 Way Continuous 2 Categorical Omnibus Sample data separated into groups based ANOVA null on more than one factor BlBZBkO Yb0b1x1bklxk1Bkzlbl1zl1 Partial tests Bl0 Bk0 BOoverall mean ANCOVA Continuous Mix of Omnibus Dummy variable x1 Continuous null 1 if occurs and BlB2Bk0 2 if does not occur Categorical Variables Partial tests Yb0b1x1b22b3xlz Bl0 Bk0 X1 categorical independent variable 2 continuous control variable Xlz interaction Degrees of freedom Model k l ErrorN k TotalN 1 Simple Categorical 1 can be a Omnibus Used to predict probability of an event Logistic combination null odds of event plp Regression BlB2Bk0 Partial tests Bl0 Bk0 nodds b0b1x1kak e b0b1x1kak Dummy variable ORe39 1 Continuous variable ORe Confidence interval e39w39l3996 SE b12122 Multiple Categorical gt1 can be a Logistic combination Regression Analysis of Variance Table Sum of Squares R2 Explained variation Unexplained variation Mean Square Sum of SquaresDegrees of freedom F value MSMMSE Variance between samples MSM Explained nsybar2 Variance within samples MSE Unexplained 2 Sp mean of varIances Standard Error of the Estimate Root MSE Hic mean Overall sample mean

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