STATISTICAL METHODS I
STATISTICAL METHODS I BIOS 543
Virginia Commonwealth University
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This 3 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 Alvin Best in Fall. Since its upload, it has received 48 views. For similar materials see /class/230637/bios-543-virginia-commonwealth-university in Biostatistics at Virginia Commonwealth University.
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Date Created: 10/28/15
BIOS 543 Second Review The second midterm will cover the material on comparing the means of continuous variables and on looking for relationships between continuous variables Sections 5710 Continuous Responses Which statistical method should I use As we discussed in the rst review which covered how to answer this question if the response is categorical begin by considering the random response variable and its measurement level the Y and its modeling type Descriptive Statistics No matter what hypotheses we test we still have to summarize the data rst If the variable to be summarized is continuous rst 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 Don t be too quick to reject normality we have a strong preference for normality Most of the statistics we use are robust and can handle moderate departures from normality In large samples we need a very strong argument to ignore this preference In smaller samples unless there is a strong case against it normality may be justi able Recall the CLT Use the recommendations on Section 5 pages 1718 to guide you If normality is justi able then report the n mean SD and perhaps 95 CI s If the data are clearly not normal then report the n median and either the IQR or range Note also that even if the main focus is on the continuous response variable there may also be categorical variables that you need to describe For instance if you are comparing two groups e g males and females then describe the groups Continuous Y Categorical responses were covered earlier That is qualitative response variables with nominal measurement level Recall the rst question 0 Is the response categorical If the answer is No it s continuousl then the methods covered here are appropriate 1 Continuous variables are variables where taking an average makes some sense They must therefore be numeric In addition the rank ordering of values may also be considered here using nonparametric methods Copyright Al Best 14 January 2009 All rights reserved Rev 21 BIOS 543 Second Review If the answer is yes then go back to the first review Next the most difficult question 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 or relationships Looking to make a comparison If you are interested in comparing your observed mean to something then 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 Ihave an observed mean is it different than some hypothesized mean If the answer to this question is Yes then use the methods covered in the section 7 handout for One Sample Mean where we compared an observed mean to a single hypothesized value 0 I have two paired means 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 section 7 Two means from paired measurements 0 I have two independent groups is there a difference between the means If the subjects in the groups are independent then the means in the groups are independent Probably we ll use the equal variance ttest see section 8 Two sample means although other considerations may change this like unequal variance or clearly nonnormal data Note that we almost never know the population standard deviation so we rarely use the z J 1 statistic We use one of the tstatistics or a J ic test A J on ourJ39 as described in section 8 page 18 o I have two independent groups is there a difference between the standard deviations 0r variances Use the Brown Forsythe test to compare variances see section 8 pages 12 13 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 The step by step approach to answering these questions is given in section 10 sta1ting on page 22 Note If you are comparing the means of more than two groups use the ANOVA methods covered in Section 12 which we have NOT covered yet Copyright Al Best 14 January 2009 All rights reserved Rev 22 BIOS 543 Second Review See the example writeups that begin on page 26 in section 10 Note that these methods are only appropriate if a straightline t is reasonable If not then the methods in section 11 should be considered but these methods will NOT be on the second mid term Writing it up Remember the overarching teachingmethod of this course is that students will take real data go thru the steps of statistical decision making and write up their understanding The overarching goal of this course is the last part writing up your understanding Be complete yet concise When writing up your result in real life and in this course you will want to use the conventional IMRD style And you ll want to make sure that you ve been clear on the 4phases we ve repeatedly emphasized o lDescribe the data 0 2State the question 0 3Answer the question 0 4Communicate your understanding When stating the question you may choose to use the traditional null and altemativehypothesis approach but that is NOT required Many authors simply state the question as a researchhypothesis eg a statement looking for differences looking for relationships When answering the question it should be clear how you answered the question ie what statistical method did you use State your answer to the question in English and provide statistical support for your conclusion And nally if you have a signi cant result then tell the story Don t just say the groups are different or that there is a relationship What is the direction and magnitude of the difference What is the direction and strength of the relationship You want to be complete yet concise does NOT mean that you want to write up all possible analyses in the hopes that one of them will be right Choose your analysis method based on the question the distribution of the data and the defensibility of the method by assessing the assumptions Choose one method and write it up Do NOT write up the process of analysis write up your conclusions Nobody publishes residual plots Normal quantile plots and the various diagnostic tools that we use in the process of deciding on the appropriate analysis Your reader will assume that you followed a defensible process that s why this is a required course for many programs You only need to comment on any outof theordinary aspects of the analysis Be clear Be organized Follow the traditional style Tell your story Copyright Al Best 14 January 2009 All rights reserved Rev 23
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