STATISTICAL METHODS I
STATISTICAL METHODS I BIOS 543
Virginia Commonwealth University
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This 4 page Study Guide was uploaded by Priscilla Rau on Wednesday October 28, 2015. The Study Guide belongs to BIOS 543 at Virginia Commonwealth University taught by Staff in Fall. Since its upload, it has received 59 views. For similar materials see /class/230639/bios-543-virginia-commonwealth-university in Biostatistics at Virginia Commonwealth University.
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Date Created: 10/28/15
BIOS 543 Final Review This review is divided into four parts Description Tests of a categorical response variable Tests of a continuous response variable and other topics Descriptive Qtatistim Categorical variable of interest Continuous variable of interest Categorical r Comparing proportions Looking for a relationship p A n Comparing mreans Looking for a relationship Other Methods nda Learning Objectives U A AWL NNN i Ii ni n 0 There is a big picture what is it Descriptive Statistics No matter what hypotheses we test we still have to summarize the data first Data come mainly in two avors categorical and continuous JMP uses modeling type nominal ordinal and continuous to determine which analyses are appropriate See page 1 of the Second Review for more on descriptive statistics See page 3 Writing it up of the Second Review for advice on organizing your results Categorical variable of interest If the variable is categoricalinominal or ordinalithen report frequencies and proportions If the variable is random then perhaps a 95 CI is called for If the variable is fixed by the experimental design then it is not random and a CI is not appropriate See the First Review for more on these topics Continuous variable of interest If the variable is continuous first consider the shape of the distribution Beyond visual inspection of the histogram the primary tool for deciding whether normality is warranted is the normal quantile plot See Estimating with con dence page 68 Don t be too quick to reject normality we have a strong preference for normality Most of the statistics we use are robust to moderate departures from normality In large samples we need a very 14Jan2009 l strong argument to ignore this preference In smaller samples unless there is a strong case against it normality may be justifiable Recall the CLT If normality is justifiable then report the n mean SD and probably 95 CI s If the data are clearly not normal then report the n median and either the IQR or range Inferential Statistics When moving from descriptive statistics to making inference consider the random response variable Is it categorical or continuous If it s categorical then see the subsection below If it s continuous then see the next subsection Categorical Responses All of these topics were covered in the beginning of the course and summarized in the First Review Recall that the categorical response variable is summarized by proportions What s the question Consider the proportions and ask Comparing proportions o Are we comparing an observed random proportion from a single sample to a hypothesized constant proportion Then we re asking whether p p0 see First Review page 3 For large n this involves the calculation of a zstatistic see page 4 o Are we comparing two proportions each arising from a separate independent sample Then we re asking whether p1 p2 See page 5 of the first review The simplest calculation uses JMP to calculate the chisquare statistic o Are we comparing multiple proportions each arising from a separate independent sample Then we re asking whether p1 p2 pk See the first part of Section 4 The analysis of frequencies and the summary on page 14 The chisquare test of equal proportions test of homogeneity is used to make this comparison Looking for a relationship 0 Are we looking for a relationship between two random categorical response variables from a single sample See the second part of Section 4 The analysis of frequencies and the summary on page 14 The chisquare test of independence is used to make this comparison 14Jan2009 2 All of the tests on proportions can be accomplished with the chisquare test Since chisquare calculates the difference between observed and expected frequency counts it s only necessary to understand expectedvalues and then the remainder of the calculation is straightforward Continuous Responses Considering the random response variable and its measurement level the Y and its modeling type if the response is continuous then the methods covered here are appropriate We developed some of these methods using a z statistic but that is rarely used in practice The t statistic for two means or the F statistic for any test is preferred What s the question Next we consider the substantive question Since the response is continuous we re probably interested in means but what about them Questions either refer to comparisons differences or relationships correlations trends lines curves Comparing means You may be interested in differences between your data and an external reference or you may be interested in differences between the groups within your study 0 I have one observed mean is it different than some hypothesized mean If the answer to this question is Yes then use the methods covered in the first pa1t of section 7 handout for One Sample Mean where we compared an observed mean to a single hypothesized value Use the ttest comparison to a specified value 0 I have two paired means from one sample of subjects is there a difference between them If two observations come from the same subject the means are not independent We must use the methods covered in the second part of section 7 Two means from paired measurements Calculate a difference and then use the paired t test comparison to zero 0 I have two independent groups two samples of subjects is there a difference between the two means If the groups are independent then the means in the groups are independent Probably we ll use the equal variance t test see section 8 Hypothesis Testing on Two Sample Means although other considerations may change this like unequal variance or clearly nonnormal data In these three cases we nearly never know the population standard deviation so we nearly never use the z statistic We use one of the tstatistics or a nonparametric test 0 I have more than two independent groups multiple samples of subjects is there a difference between the means 14Jan2009 3 If we have more than two independent groups then we follow a process similar to that used for just two groups Then if the groups are different by the Ftest we track down the differences with Tukey s HSD multiplecomparison procedure See section 12 Comparing multiple means Looking for a relationship Or you may have two random responses and you are interested in whether there is a relationship between the continuous values in these two variables To test for a correlation or straightline fit use the methods of section 10 Correlation and Regression Or if just the rankorder correlation is of interest then the nonparametric methods of section 11 page 6 may be used The following will not be on the exam but if we wanted to transform variables to achieve a straightline or fix other problems then the methods in the last part of section 11 would be used Also higher order curvilinear relationships could also be explored Other Methods We ve done data analysis using all of the above methods This covers a tremendous amount of territory However this map does not cover the whole world For instance we have not covered the following situations Is there a difference between two paired proportions A response variable is measured as a timetoevent like length of survival time These data are often very skewed And not every individual has died yet so we have incomplete information How do I analyze this censored information A response is categorical but the predictor variable is continuous What is the relationship between more than two categorical variables How do I fit an Sshaped curve How to we fit pharmacological models other nonlinear models The response is continuous but we have more than one predictor variable Or some predictors are continuous and some are categorical How do we analyze multiplecorrelation multiple regression data We re interested in testing for agreement Do two tests or raters measure the same thing I m not interested in superiority I m interested in a just as good as or equivalence claim How do we market a generic drug without redoing all the clinical trials that were done on the original drug 14Jan2009 4
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