×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

15

0

8

# 224 Class Note for STAT 30100 with Professor Sorola at Purdue

Marketplace > Purdue University > 224 Class Note for STAT 30100 with Professor Sorola at Purdue

No professor available

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
8
WORDS
KARMA
25 ?

## Popular in Department

This 8 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 15 views.

×

## Reviews for 224 Class Note for STAT 30100 with Professor Sorola at Purdue

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15
Chapter 13 TwoWay Analysis of Variance Chapter 7 Twosample comparison of means t tests 1 categorical and 1 quantitative variables Example Are the mean taste ratings of chewy granola bars the same as those for crunchy granola bars if you conduct a taste test Chapter 12 F tests compare the means of several populations 1 categorical and 1 quantitative variables Example Are the mean taste ratings of Quaker Kellogg s and Nature Valley granola bars the same if you conduct a taste test Chapter 13 F tests compare the means of populations that are classi ed in 2 ways 2 categorical and 1 quantitative variables Example Do brand texture chewy vs crunchy andor their interaction make a difference to the mean taste ratings for granola bars What s similar for Two Way ANOVA Just as in One way ANOVA we still 0 We still assume the data are approximately normal 0 The groups must have the same standard deviation even if the means may be different 0 We pool to estimate the standard deviation 0 F statistics are used for the signi cance tests What s different for Two Way ANOVA We can look it each categorical variable separately and we can look at their interaction With oneway ANOVA it was impossible to look at interaction Example from 4 11 edition of M ampM 39 Each of the following situations is a 2way study design For each case identify the response variable and both factors and state the number of levels for each factor I and J and the total number of observations N a b A study of smoking classifies subjects as nonsmokers moderate smokers or heavy smokers Samples of 80 men and 80 women are drawn from each group Each person reports the number of hours of sleep he or she gets on a typical night The strength of concrete depends upon the formula used to prepare it An experiment compares 6 different mixtures Nine specimens of concrete are poured from each mixture Three of these specimens are subjected to 0 cycles offreezing and thawing 3 are subjected to 100 cycles and 3 specimens are subjected to 500 cycles The strength of each specimen is then measured Four methods for teaching sign language are to be compared Sixteen students in special education and sixteen students majoring in other areas are the subjects for the study Within each group they are randomly assigned to the methods Scores on a final exam are compared Example from 4 11 edition of M ampM In the course of a clinical trial of measures to prevent coronary heart disease blood pressure measurements were taken on 12866 men Individuals were classified by age group and race The means for systolic blood pressure are given in the following table 3539 4044 4549 5054 5559 White 131 1323 1352 1394 142 NonWhite 1323 1342 1372 1413 1441 Note that we are not given raw data on these 12 866 men The table above is the mean for each raceage combination This means we can t use ANOVA We 11 just use graphing and marginal means to describe the situation a Plot the means with age on the xaXis and blood pressure on the yaXis For each racial group connect the points for the different ages b Describe the patterns you see Does there appear to be a difference between the 2 racial groups Does diastolic blood pressure appear to vary with age If so how does it vary Is there an interaction between race and age c Compute the marginal means Find the differences between the white and nonwhite mean blood pressures for each age group Use this information to summarize numerically the patterns in the plot category mean white 13598 Nonwhite 13782 3539 13165 4044 13325 4549 1362 5054 14035 5559 14305 How do you know from looking at a means plot whether there is interaction 0 If any lines cross each other then you have an interaction 0 If the lines are all fairly parallel to each other then you do not have an interaction 0 If the lines aren t parallel but don t cross each other either then you might have an interaction If you have 2 factors why not just do 2 separate One Way ANOVAs It is more efficient to study 2 factors simultaneously rather than separately We can reduce the residual variation in a model by including a second factor thought to in uence the response lurking variable We can investigate interactions between the factors If the twoway ANOVA test finds that a main effect is significant then you can go back to doing oneway ANOVA for that factor to find which levels are significantly different from each other Two Way ANOVA Table Source Sum of Degrees of Mean square F df df Pvalue Squares Freedom A SSA DFA Il SSA MSA Main effect 7 A f A DFA MSE 0 DFA DFE B SSB DFBJl M 39 ff t MSB SSB FB MSB feign e ec DFB MSE 0 DFB DFE AB SSAB DFAB SSAB MSAB Interaction IlJ1 MSAB 713F143 FAB iMSE ofA and B DFAB DFE E SSE DFE rror MSE SSE N IJ DFE T t l SST N l o a MST SST DF T The hypothesis tests are H0 main effect A 0 Use Pvalue from F A H0 main effect B 0 Use Pvalue from F B H0 interaction of A and B0 Use Pvalue from interaction of A and B Example Exercise 1320 One way to repair serious wounds is to insert some material as a scaffold for the body s repair cells to use as a template for new tissue Scaffolds made from extracellular material ECM are particularly promising for this purpose Because they are made from biological material they serve as an effective scaffold and are then reabsorbed One study compared 6 types of scaffold material Three of these ECMs and the other three were made of inert materials There were 3 mice used per scaffold type The response measure was the of glucose phosphated isomerase Gpi cells in the region of the wound A large value is good indicating that there are many bone marrow cells sent by the body to repair the tissue Here are the data for 2 weeks 4 weeks and 8 weeks after the repair Material Gpi 2 weeks 4 weeks 8 weeks ECM 70 55 60 75 70 65 65 70 65 ECM2 60 60 60 65 65 70 70 65 60 ECM3 80 75 70 60 70 80 75 75 70 MAT 50 20 15 45 25 25 50 25 25 MAT2 5 5 10 10 10 5 15 5 5 MAT3 30 10 5 25 15 15 25 10 10 Using SPSS Analyze 9 General Linear Model 9 Univariate Move Gpi into Dependent Variable box Move Time anal Material into FixealFactors box To get a means plot click Plots box move Material into the Horizontal Axis box Move Time into the Separate Lines box Click Aalal anal Continue To get summary statistics click Options box Move Material anal Time into the DisplayMeans box Click Descriptive Statistics box anal click Continue Click OK Make a table giving the sample size mean and standard deviation for each of the materialbytime combinations Is it reasonable to pool the variances Because the sample sizes in this experiment are very small we expect a large amount of variability in the sample standard deviations Although they vary more than we would prefer we will proceed with the ANOVA Descriptive Statistics Dependent Variable GPI Material Time Mean Std Deviation N ECM1 2 7000 5000 3 4 6500 8660 3 8 6333 2887 3 Total 6611 6009 9 ECM2 2 6667 7638 3 4 6333 2887 3 8 6333 5774 3 Total 6444 5270 9 ECM3 2 7167 10408 3 4 7333 2887 3 8 7333 5774 3 Total 7278 6180 9 MAT1 2 4833 2887 3 4 2333 2887 3 8 2167 5774 3 Total 3111 13411 9 MAT2 2 1000 5000 3 4 667 2887 3 8 667 2887 3 Total 778 3632 9 MAT3 2 2667 2887 3 4 1167 2887 3 8 1000 5000 3 Total 1611 8580 9 Total 2 4889 24648 18 4 4056 28330 18 8 3972 28619 18 Total 4306 27064 54 Maieiiei ECM3 4ECMW iECMZ 4MATW 4MAT3 MATZ b Make a plot othe means othe Combinations Describe the main features of Lheplot Estimated Marginal Means ofGPl aa a E i in E 1 a a 5 sea in o o o n i i i 2 4 a Time c Makeambleothesamplesizeandmeanforeachtypeofmatmal Makea plot othe means othemaienais Give a shortsummary ofthe n Crpl depends on the type ofmatenal 1 Material Dependent Vanabie GPi 95 Cun dence iniewai Maieiiai Mean Sid Enai LDWEY Humid UppEv Humid ECW 3111 1742 EZ 578 BB i344 EcM2 EA 444 i 742 an 911 E7 978 ECM3 72 77E 1 742 BB 245 7B 31 i MAN 31 m i 742 27 57B 34 E44 MATZ 7 77E 1 742 4 245 ii 311 mm mm 1742 12578 19544 d Make a table ofthe sample size mean and standard error for each time period Make a plot of the means of the times Give a short summary of the Crpi depends on the timeperiod 2 Tlme 0333mm variable 6P1 95 03nr133n331ntewai Time Mean Sm Ermr Luwer 333n3 Upper333n3 2 43 339 1232 46 391 51337 4 43 556 1 232 33 357 43 354 E 39 722 1232 37 224 42 221 e Run the analysis ofvariance Report the F statistics and Pvalues for the main effects and the interaction What are the hypotheses you are testing What do you conclude Write a short paragraph summarizing the results ofyour analysi s 73sts 31 33tw33n 3331333 Weds 33333333twrr3313 cpl 733331333 33333 33335 31 333 33333 F 33 33333133733331 27327533 17 2225725 31435 333 lat3rc33t 133134137 133134137 3334331 333 1113331 25373322 7174137 232347 333 rrrr3 325333 432533 13322 333 Mst3rrsi rrrre 1341337 13 134137 2314 331 Ellvr 333333 33 27315 mil 123325 333 54 33333133 7331 23323 322 52 3 3 333333 375 4313333 3 333333 33 H3 main effect material 0 H main effect material 3 0 F PvaluP conclusion Hg main effect time 0 H main effect time 3 0 F PvaluP conclusion Hg interaction 0 H interaction 0 F PvaluP conclusion

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Janice Dongeun University of Washington

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com