Psychological Statistics PSY 3204
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This 46 page Class Notes was uploaded by Ms. Beverly Doyle on Wednesday September 23, 2015. The Class Notes belongs to PSY 3204 at University of South Florida taught by Thomas Sanocki in Fall. Since its upload, it has received 18 views. For similar materials see /class/212675/psy-3204-university-of-south-florida in Psychlogy at University of South Florida.
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Date Created: 09/23/15
Dr Thomas Sanocki PSY 3204 quotRegressampCorrKeysquot Use tabs at bottom of this Excel page to change topics Outline Relations between variables between X and Y Regression quotLinear Regressionquot Regression as a line slope and intercept error Predicting with regression Three pitfalls with regression Correlation Correlation is the strength of a relation Pitfalls with correlation Correlation and Error not on exam Multiple Regression Correlation matrix Unique variance of combination Regression ancl Correlation concern relations between two variables X and Y Let39s begin with a typical experiment not RegressionCorrelation Minutes helping in two conditions Relation In an Experiment Control mood 8 10 20 9 16 12 12 g 7 14 13 11 11 15 51 A I wig G v Means 10 13 4 25 5 SD 24 24 Z 0 1 Mood Condition 1V x lt manipulated IV in an experiment A Note 1 Only value of Means are shown 2 Only Two Levels of the X Variable used What if we showed each subject instead of means quotScatterplotquot w each subject 18 H 01 Minutes Helping H H H O N 4 m 00 O N 4 1 2 Mood Value X Control HHHHHH Good mood NNNNNN NEW STUDY Now what if X varied continuously gtgt This is possible with NEW data Regressioncorrelation data X Mood Y Helping minutes Ratings 1 to 7 best Each subject gtgt 4 8 has 2 data points 5 14 x and y gtgt 2 2 6 11 7 22 1 1 2 7 6 19 3 6 Now we can do a real scatterplot Minutes Helping N U39l N O A Typical Scatterplot H U39l H O 0 1 2 3 4 5 Rated Mood X Now the big Regression amp Correlation Question How can we describe the relation between X and Y using a simple math concept Let39s Reg ress X Mood Y Helping minutes Ratings1to7best 4 8 5 14 2 2 6 11 7 22 1 1 2 7 6 19 3 6 Line formula Y mX b orY slopeX intercept m slope how much Y for each unit X b intercept where line starts when X 0 Regression finds the best line to describe data Ie m and b values m slope 314 b intercept 255 25 Minutes Helping H H N 0 U1 0 U1 A Typical Scatterplot Rated Mood X YmXb Y 314x 255 Using regression for prediction Y mX b Y 314X 255 Just plug in X and calculate Y eg X 8 Y 314s 255 Easier example to try Y 1 simple ones on exam Y slope 3 X intercept 1 ifX2 X Mood Y Helping minutes Ratings1to7best 4 7 10 13 16 19 22 lO IU lhWNH Regression line is the set of predicted values Summary Regression is based on best quotlinequot description How much Y for each unit X eg how much helping for each increase in mood Ie m slope b intercept Where does line start X 0 Error is also present what is error Error is how much points depart from line Ie Y predicted Y Minutes Helping H H N N 0 U1 0 U1 U1 Error shown in red it is deviation from predicted Y Note The regression line is the line values of m and b that produces the least error for all points Rated Mood Another example Years in College Lifetime Earnings thousands of dollars 0 1200 2 1450 4 1800 8 2200 What is the relation College and earnings 2500 2000 1500 1000 500 0 2 4 6 8 10 Yea rs of College X b intercept 1220 earnings with no college Most important m slope how earnings Y change per unit ofX year in college m 126 126K more per year of college l For one year How much do ofcollege X earnings Y change Three pitfalls to know about 1 Only linear relations are handled full name is quotLinear Regressionquot 15 10 This ain39t no line yet 10 You do get regression values m slope 45 b intercept 51 Not a great quotfitquot Linear regression should NOT be used here 2 Even if there is a good relation it does not imply causality eg in the mood example maybe people were in a good mood because they had less to do and were able to spend more time helping in the earning example maybe intelligence is the cause more intelligent people take more college and earn more money The Third Variable Problem Athird variable could cause changes in both X and Y 3 Regression does not measure the strength of a relation Minutes Helping Rated Mood These two data sets have the same regression lines dashed lines yet one relation is much stronger How do you measure the strength of a relation Correlation Measures the strength of relation between X and Y Values r range 1 O 1 0 means no relation close to O is weak closer to 1 or 1 is stronger r 092 Inuitive Formula 1 Get zscores on each measure 2 Calc quotcrossproductsquot for each person 3 Take mean of cp39s to get r r 069 Minutes Helping 34567 Rated Mood r O83 r r 030 Three problems to know as in regression 1 Only linear relations are handled sometimes called quotLinear Correlationquot This ain39t no line yet 9 10 ONb You can get correlation values r 037 2 Even if there is a good relation it does not imply causality The Third Variable Problem A third variable could cause changes in both X and Y 3 Correlation is not equal to regression they are complementary Correlation desribes how strong a relation is Regression describes how Y changes per unit of change in X Correlation and Error Recall that in ANOVA there is quotvariancequot for the IV and for error and that IV Error Total Is there something like this for RegressionCorrelation Yes The correlation value r can be converted to R2 Proportion of variance accounted for R2 r r This the part of the total variance explained by variable X And Error 1 R2 Error is the proportion due to nuisance variables all the other possible variables that could have been used in the correlation SFS Handbook page 1 SFS Handbook Spring 2009 Contents Weekly goals and lab assignments W removed Corrected SFS Pages PSY 3204 SPRING 2009 Professor Thomas Sanocki University of South Florida SFS Handbook page 2 3 10 Week Tuesday Date 16 113 121 127 23 210 217 224 33 310 break 317 324 331 47 414 421 Final 430 Spring 2009 Schedule Topics Problem solving with data Analyzing scores Science Central tendency IV Effect Error frequency Standard Deviation SD Interaction Populations Standard Scores Standard Error Sampling distributions First and easiest exam on Thursday Testing for nothingness aka chance t test Decisions Power effect size and errors Experimental Design Repeated measures t test catch up or get lost ANOVA One Way Multiple Groups ANOVA MULTIFACTOR Multiple IV39s Interaction Working with 2 X 2 s Regression amp correlation Using uniqueness Perspective Which statistic Chi squa re Interaction revisited Partly cumulative Final Thursday April 30th 10AM Noon Reading Start 1 2 7 to p 85 middle 2 226 p85 6 s 4 430 10AM SFS Handbook page 3 TRAIL HEAD Start Here LY IJ39 Statistics is a set of tools for learning about the world and behavior The goal of this course is to gain a basic understanding of what statistics are and how they can be used Statistics is a scary subject for many students but it doesn t have to be Mathematics should not be a challenge in this course because only very basic math is required ie add subtract simple multiplication division squares Exam problems will have simple math Most of the difficulty of statistics is that they are so strange so counterintuitive This makes them difficult to remember They are unlike anything you ve seen or done and this makes it difficult to connect them with anything in your brain Thus statistics go right through However you have a big advantage in this course you This course is designed to help you make statistics meaningful so they will stay in your memory There is one crucial ingredient your effort You must work to make statistics familiar and understandable in your own mind Use this Handbook to help you in the process See the Preface to SFS for more discussion of learning statistics Consult the SFS Appendix if you have difficult with anxiety or test taking and take advantage of your USF Counseling Center if these problems are significant SFS Handbook page 4 The Trail Ahead Learning statistics is like climbing mountains effort is necessary You will get some great views new perspectives understanding at the top But if you don t master the early topics you won t make it To make it to the mountain tops you need the basic concepts that are provided in the first part of this course The first mountain is the basic concept of statistical inference and the t test Along the way up you need to learn some basics about experimentation descriptive statistics and thinking about distributions If you master these topics you will find bridges at the top that make the next topics easy to conquer Get Provisions First Mountain climbing requires lot s of energy and so does statistics Nourish your mind and body with good food and exercise to stave off tension The homeworks and SFS interactive exercises will provide many opportunities to succeed and get a positive start on the trail If reading small type hurts your eyes an essential aid will be inexpensive pair reading glasses to magnify the small print in your textbook Happy trails TS SFS Handbook page 5 The Researcher39s Question U WEEK 1 Introductory Concepts Weekly Learning Goals Learn about how statistics are used with examples Additional lecture material will cover problem solving and science and scales of measurement Read Start Here Preface Chapter 1 Homework Lab assignment HAND 1N BY START OF NEXT LAB Exercises 11 8 Exercises 1 through 8 Chapter 1 of SFS Answer Ch 1 Review questions SFS end of chapter Generate 3 experiments think them up For each describe brie y by writing a a sentence saying what it is about b state the IV and 0 state the DV Turn in the exercises together with your brief descriptions by start of next week s lab At lab start lab Instructors will review correct answers so you can selfcorrect homework SFS Handbook page 6 E 2 I l I Thinking About Influences on Behavior LI WEEK 2 Important foundational concepts of IV and Error Goals Operational de nitions Calculating means brief introduction and MOST IMPORTANT The idea of dividing up individual scores from an experiment into their two parts IV Effect and Error Read Review Chapter 1 Chapter 2 Homework Lab assignment Generate 3 Operational De nitions they could be from your last week s experiments For each provide a sentence that says what is being measured in how it would be measured Chapter 2 Review De nitions write good de nitions Exercises 21 3 4 5 6 9 Table for 26 shows Pounds Lost HINTS 1 Problem 25 requires working backwards 2 Table 22 and section on page 12 and 13 The idea is to put three critical concepts together in a formula quotscores eg the total for one subject the IVE ect and Error The I V E ect is arbitrarily set to 0 for one group the control group This is a way to summarize our understanding We will use these concepts again soon and the arrangement of T able 22 will be replaced by better arrangements and formulas Error is calculated as x Mean where x is the score SFS Handbook page 7 Describing Influences on Behavior WEEK 3 Long week easy but important concepts Goals Learn about two essential tools Measures of central tendency mean median mode Frequency distributions and their graphic presentations Frequency Polygons Master the Standard Deviation learn to calculate it and know its meaning and purpose Read Chapter 3 Homework Lab assignment Chapter 3 Review de nitions Exercises 31 3 5a 5d also make frequency polygons for 31 Week 3 Exercise Graphing Frequency Distributions Make 3 Frequency Histograms including the frequency polygons outlines from things you measure We will go over an example this week in class One histogram could show the frequency of nominal categories at least two should show frequencies of quantitative scores numbers although the numbers can be in categories such as 10 14 15 19 continues next page SFS Handbook page 8 Use the methods taught in class or Chapter 3 also see Stats Calculators to calculate SD of a379 b 299 c 344 5 d 0 4 59 Stats Calculators are on Sanocki s web site Examlnfo page they provide sheets with formats for calculating the statistics Exercises 31 calculate SD for each group 32 35c SD for each group If you should do Exercise 3 7 which is not on the homework here are some corrections to the answers 37a mode there are 2 modes 10 and 11 37a median is 10 SFS Handbook page 9 CHAPTERS 4 amp 5 POPULATIONS amp SAMPLE MEANS we are just starting to climb still easy climbing WEEK 4 Goals Become familiar with samples and populations of scores Learn the further concept of samples of means Learn to generate and graph a sample of means Gauge the accuracy of means 7 how close to the true population mean this is the Standard Error of mean Read Chapters 4 5 See Chapter 5 corrections below amp next pages Homework Chapter 4 Review de nitions Exercises 417 Week 4 Exercise Meaningful Distributions Think up 3 abilities and populations Eg choose one39s you like and excel in eg ability to rollerblade among the population of those 45 and older For each of the 3 draw a standard normal distribution Divide it up into percentages between each standard deviation Add lot39s of labels In the example the low end might have quotcan barely walkquot Put and quotxquot for where you fall In rollerblading I might be almost 2 SD39s up among my carefully defined population Will work through example in class Chapter 5 Review de nitions Exercises 515 Publishertypesetter introduced errors the CORRECTED pages follow p 37 9 lines up from bottom 0 to 21 should be 0 to 1 6 lines up from bottom 11 SD should be 1 SD p 40 12 lines from top 22 SD should be 2 SD next line 22 to 21 SD should be 2 to 1 SD midde of page 1 11 SD s should be 1 SD s 2 12 SD s should be 2 SD s MCorrections to answers for 55 55a SE 7 males 0516 SE 7 females 0666 55b SE 7 males 0258 SE 7 females 0333 SFS Handbook page 10 CORRECTED SFS TEXT my original text p 37 Normal Distributions and Standard Normal Distributions A remarkable thing is often discovered when a very large sample of scores a population is measured the scores form a normal distribution For example consider the heights of babies How tall long is the average nine month old girl What is an unusually short size An unusually tall one Try to gure the answer out from the frequency polygon in Figure 41 This is a slightly simpli ed version of the actual population data for female infants Check1 Note the normal shape of the distribution As you learned in the previous chapter it is symmetrical and bellshaped Something else is extremely important The shape can be divided into regularly sized regions that form a pattern that can be used over and over much like a dress pattern can be used over and over The pattern is called the standard normal distribution Let s begin by looking at the pattern The crucial aspect is the vertical bars Note that there is one bar in the middle at the mean In most cases we use the mean as the starting point It is the center of the distribution marked with a 0 on the standard deviation scale From the mean of 70 cm we can go down one standard deviation 1 SD which is 25 cm in the present case This puts us at 675 cm These units are called standard units or z scores Thus a score of 75 would have a zscore of what Checkz Here s a remarkable fact Between the bars marked 0 and 1 about 34 percent of the scores will be in the region That is about 34 percent of the baby heights will be in this range 675 to 70 cm What if we went up from the mean Where would we go to and what percent would be in that region Check the next paragraph Going up we would go from the mean of 70 cm to 725 cm 1 SD Again 34 percent of the scores would be there Mark these percentages in the figure We can then go out one more standard unit to the second standard deviation These occur at 65 and 75 cm Fourteen percent of the scores occur between the first and second standard deviations on each side Beyond the second standard deviations there is about 2 percent of the scores on each side To summarize 1 You should have found the average height to be 70 cm 276 inches Unusually short begins where the left side of the curve gets low somewhere around 65 cm unusually tall begins on the right somewhere around 75 cm If you had problems with this review 2 75 is 2 standard units up or a z score of 2 SFS Handbook page 11 p 40 original correct text Cumulative Distributions It is also helpful to view normal distributions in one other way Instead of looking at them from the middle mean outward which we have done so far you can also look at them from left to right In this view the scores cumulate This is shown in Figure 43 The basic idea is that you begin with the lowest scores at the left and add up the percentages as you go to the right We are now concerned with the percentages of scores under left of a certain score Thus the leftmost tail up to 2 SD is 2 and the next region 2 to 1 SD adds 14 cumulating to 16 What will be the cumulative total up to the mean It would be 50 Finish labeling the distribution Cumulative percentages are usually called percentiles To practice this way of viewing the scores use Figure 43 to answer the questions below What percentage of scores is under 1 SD Remember that this includes all scores under 1SD What percentage of scores is under 2 SD Check your work4 Week 5 get ready for exam SPSS 1 in lab after exam but no new homework Attend lab to be guided through assignment and make SPSS easy SPSS Statistical Package for Social Sciences SPSS 1 Spreadsheets and descriptive statistics 15 points Instructions will be emailed to you Do assignment in lab save results and print them out On printout underline and de ne important concepts by hand neatly for your lab instructor SFS Handbook page 12 CHAPTER 6 Testing for NOTHINGNESS CHANCE climbing gets a bit tougher WEEK 6 Goals Learn to stand on your head think based on the assumption that chance is the only thing that in uences the scores 7 the IV has no effect at all Learn the strange logic of a statistical test Read Chapter 6 3 typos below Homework Chapter 6 Review de nitions Exercises 615 Use our main formula for SEdiff equaln sqrtSDzn SDzn Typo in answers sign of IV Effect is reversed rather than Defme in your own words Type 1 and Type 2 Errors Draw and label own words 2 X 2 decision box Typos p 52 bottom box For each sample we calculate 1 Means M1 and M2 p 59 2quotd line from top replace is like the SD before you squared i with the correct phrase is the SD before you unsquared it ie the SDZ 0r variance p 59 footnote 3 3 not 2 in square root Case A Sediff sqrt23 33 sqrt53 sqrtl67 SFS Handbook page 13 CHAPTER 7 The ttest warning extreme heights WEEK 7 Goals Main Understand how to do the ttest and What it means Also important Understand additional relevant concepts including Degrees of freedom ttable Onetailed versus twotailed tests Type 1 and Type 2 Errors Power and Effect Size Read First read Chapter 7 with emphasis on rst half to p 76 then carefully reread and finish chapter except bottom of p 85 amp p 86 covered week 9 Homework Use textbook method p 72 to obtain t values for the following pairs of samples Sample 1 and Sample 2 Or try Stats Calculators from Sanocki web site similar form a Sample 1 4 6 6 8 Sample 2 8 10 10 12 bS112151618 S216181520 c S1 1 4 16 18 S2 4 6 20 22 Exercises 716 Note SE is SEDifferel lce Also note If you can t nd exact df for critical t in ttable use the next lowest df Chapter 7 Review definitions all Typos 1 important see next page Week 8 no new assignments focus on exam Plan to attend lab Week 9 for SPSS 2 SFS Handbook page 14 IMPORTANT p 71 Formula for t test box bottom replace with as shown quot1 quot2 p 76 rst paragraph the box is on p 77 not 81 p 82 top in formula for Cohen s d both SD s under the square root should be squared SDZ as shown 5022 5022 the SD s are for groups 1 and 2 SFS Handbook page 15 WEEK 9 TRANSITION TO EXPERIMENTAL DESIGN whoa extreme heights Goals This is a very import week gather your wits Attend lab to make SPSS easy see below We will move to a higher level of abstraction 7 experimental design Start to learn about experimental design Independent versus dependent samples from chapter 7 Repeated measures ttest Foundations in design for Analysis of Variance Between groups variance Within groups variance Read Supplements handed out in class Chapter 7 p 8587 Chapter 8 to p 103 Homework Describede ne Independent samples amp generate an example of this type of experiment Dependent samples amp generate an example of this type of experiment Repeated measures ttest amp explain reasons for using repeated measures Between groups variance describe what in uences this Within groups variance describe what in uences this What is the meaning of the Fvalue SPSS 2 15 points ttest Instructions to be emailed Attend lab to be guided through SPSS Hand in printouts with important concepts highlighted and de ned SFS Handbook page 16 WEEK 10 CHAPTERS 8 amp 9 in detail Testing Multiple Groups With ANOVA Goals Map from last weeks concepts to ANOVA Understand what it means to have Multiple levels of one Independent Variable OneWay ANOVA Multiple Factors or Multiple IV s Multifactor ANOVA Learn to calculate OneWay ANOVA Calculate deviations square deviations Use Source Table to summarize F Between Variance Within Variance Read Chapters 8 amp 9 Homework Chapter 8 Review de nitions Exercises 81 2 Fvalue for Exercise 82 is given in answer to 83 Chapter 9 Review de nitions Exercises 91 93 Typo s p 97 Table 83 Mean for Al should be 6 for A2 should be 5 p 98 Table 84 Mean for A2 should be 5 p 116 in Box De nition of Deviations xi should be used not mean of X p 117 last full sentence degrees of freedom in numerator not denominator p 121 just below Fs formula put in place of where a l is the degrees Answers to Exercise 8 la messed up Use next page or replace all 2 s with negative signs Grand mean is 55 93bc In answer source table the MS for errorwithin should be 667 some of the digits were shifted over SFS Handbook page 17 ANSWERS Exercise 81 as originally written these are correct 81 TOT IV BETWEEN ERROR WITHIN a 1 2 Total 3 Total 4 5 IV 6 IV 7 8 9 Error Total IV Error Error Dev Dev Square Dev Dev Square Dev Dev Square 1 755 15 225 655 05 025 76 1 1 2 555 05 025 655 05 025 56 1 1 3 455 15 225 655 05 025 46 2 4 4 855 25 625 655 05 025 86 2 4 Mean A 6 5 355 25 625 555 05 025 35 2 4 6 755 15 225 555 05 025 75 2 4 7 655 05 025 555 05 025 65 1 1 8 455 15 225 555 05 025 45 1 1 Mean B 5 Grand Mean 55 SUM OF SQUARES g g E b Source Sum of Squares Q m F Obtajned w IVBetween 2 211 2 ErrorWithin 20 826 33 F23360 Total 22 7 c Fobtained 60 d Fcrit 599 e Fobtained lt Fcrit therefore accept null The two samples are not signi cantly different SFS Handbook page 18 CHAPTER 10 Testing Multiple IV s With ANOVA WEEK 11 Now we do some extreme climbing 1 Goals Devote quality time to Multifactor thinking Learn 2 X 2 Tables Main effect A Main effect B Interaction Learn multifactor ANOVA formula deviations Learn to identify interactions Interaction means in uence of one IV depends on the level of other IV interaction mean effects of IV s are not additive Read Chapter 10 Homework Chapter 10 Review defmitions Exercises 101 3 5a Typo s p 133 Lines 7 amp 8 from top correct text is Underlining is good for history and bad for math Whereas outlining is a little better for math instead of Outlining is good for history p 137 First formula 10 lines down Interaction these are all means bar for mean ofA is missing that is the second term For 101c there are errors in the Error row because the 4 and 2 were shifted Instead ofno df and MS 2 and F 2 it should read df 4 MS 2 SFS Handbook page 19 CHAPTER 10 Interpreting 2 X 2 s keep pushing up the mountain puf puf 1 WEEK 12 Goals Consolidate understanding of 2Way ANOVA Master 2 X 2 Tables Main effect A Main effect B Interaction Master interactions Interaction means in uence of one IV depends on the level of other IV interaction mean effects of IV s are not additive Read Review Chapter 10 Homework Find the Interaction Exercise to be handed out Make up 3 2 X 2 5 IV s produce possible data and interpret the effects state main effects and Whether interaction occurs verbally describe What is happening At least one of these examples should be interactive Additional Homework Assignment SPSS 3 15 points SPSS 3 Running a MultiFactor ANOVA to be emailed Hand in printouts With important concepts highlighted and defined SFS Handbook page 20 CHAPTER 11 Correlation amp Regression Concepts Using Uniqueness WEEK 13 Goals Learn the concepts of Regression Slope Intercept linearity Learn concept of Correlation Review Zscores Correlation mean of the crossproducts of 2 s Read Chapter 11 to p 162 Homework First 12 Chapter 11 Review de nitions through Cross Product Correlation Regression Exercise next page Typo in rst ve step Method step 3 Correct For m sum the X Y column then divide by sum of X2 column instead of sum the X Y column then divide by sum of XY SFS Handbook page 21 Correlation Regression Exercise For each of the two problem sets below H Make a scatterplot by hand Calculate the correlation using the z score cross product formula you are taking the mean of the cross products SFS p 159 161 Use the means and SD39s given to convert scores to z scores for each subject calculate cross product of 239s by multiplying them sum cross products and divide by n to get correlation r value Fit a regression line by eye and hand intuitively to scatterplot Calculate the slope of the regression line Pick two points along the X axis Estimate the Y values by eye and hand Calculate slope Difference in Y Difference in X for the pairs of points Estimate the intercept the value of Y when X is zero Using your slopes and intercepts estimate the value of Y when X is 8 N Ab U39l z score mean SD Problem Set 1 Humanb w 4 M39s 4 25 SD39s 212 1079 Problem Set 2 l de O b H 4 M39s 4 14 SD39s 212 255 SFS Handbook page 22 CHAPTER 11 Multiple Regression and then CHAPTER 13 Perspective Which statistic when WEEK 14 Goals Consolidate Correlation amp Regression Optional if time Multiple Regression through lecture example Step back and gain perspective on the statistics Learn differences between statistics and understand when to use each based on the type of research design and the type of data IMPORTANT FOR FINAL EXAM Read Chapter 11 review all Chapter 13 learn basic concepts Homework All Chapter 11 Review de nitions ALL yes some repetition Exercises 111 3 4 5 Chapter 13 Exercises 1 7 9 IMPORTANT FOR FINAL EXAM SFS Handbook page 23 CHAPTER 12 Analyzing How Often an Event Occurs Chi Square WEEK 15 Goals This is a fairly simple statistic one last hill before parking lot Understand concepts relevant to ChiSquare frequency of occurrence categories distribution by change Calculate simple ChiSquare Understand Contingency Tables intuitively no CT calculations on exam Read Chapter 12 Homework Chapter 12 Review definitions More problems a A coin is tossed 10 times and comes up Heads 8 times and Tails 2 Is it fair b What ifit came up 91 73 c Test if this 6sided die is fair It was rolled 20 times frequencies are Value 1 2 3 4 Frequency 2 3 2 3 2 8 Exercises 121 3 ChiSquare Contingency Tables covered in last lecture LAB INSTRUCTOR WILL TELL YOU WHENW HERE TO HAND IN SFS Handbook page 24 OLD EXAMS LEARN HOW TO ANSWER QUESTIONS No longer available many studenm were unwilling to learn to get answers and instead expected answers to be given to em
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