ChiSquare Tests. Comments on Projects. Comments on Projects. The Big Picture. Comments on Projects. Population 12/23/2012. Sample and Population


 Candice Heath
 2 years ago
 Views:
Transcription
1 STAT 101 Dr. Kari Lock Morgan 10/30/1 ChiSquare Tests SECTIONS 7.1, 7. Testing the distribution of a single categorical variable : goodness of fit (7.1) Testing for an association between two categorical variables: test for association (7.) Comments on Projects Random sampling is different than convenience sampling Even if your initial sample selected is representative, if people choose not to respond this introduces bias Generally a good idea to present the response rate Comments on Projects Sample is whatever your variable is measured on (rows of your dataset) The type of inference we have learned can only generalize from sample to population (and only if a random sample) We have not learned how to account for uncertainty in the data values themselves Sample and Population Was your sample the same as your population? (Did you have data on all the cases in your population?) a) Yes b) No Comments on Projects The Big Picture If you have data on the whole population, inference is not necessary! Population Sampling Statistical Inference Sample 1
2 Multiple Categories So far, we ve learned how to do inference for categorical variables with only two categories Today, we ll learn how to do hypothesis tests for categorical variables with multiple categories Play a game! (Roshambo) Can we use statistics to help us win? Which did you throw first? a) Rock b) Paper c) Scissors ROCK PAPER SCISSORS How would we test whether all of these categories are equally likely? Hypothesis Testing 1. State Hypotheses. Calculate a statistic, based on your sample data test statistic 3. Create a distribution of this statistic, as it would be observed if the null hypothesis were true 4. Measure how extreme your test statistic from () is, as compared to the distribution generated in (3) Hypotheses Let p i denote the proportion in the i th category. H 0 : All p i s are the same H a : At least one p i differs from the others OR H 0 : Every p i = 1/3 H a : At least one p i 1/3
3 Test Statistic Why can t we use the familiar formula sample statistic null value SE to get the test statistic? More than one sample statistic More than one null value We need something a bit more complicated Observed Counts The observed counts are the actual counts observed in the study ROCK PAPER SCISSORS Observed Expected Counts The counts are the counts if the null hypothesis were true ROCK PAPER SCISSORS Observed Expected For each cell, the count is the sample size (n) times the null proportion, p i = np i ChiSquare Statistic A test statistic is one number, computed from the data, which we can use to assess the null hypothesis The chisquare statistic is a test statistic for categorical variables: observed  ROCK PAPER SCISSORS Observed Expected (368.3)(18.3)(378.3) What Next? We have a test statistic. What else do we need to perform the hypothesis test? A distribution of the test statistic assuming H 0 is true How do we get this? Two options: 1) Simulation ) Distributional Theory 3
4 Simulation Let s see what kind of statistics we would get if rock, paper, and scissors are all equally likely. 1) Take 3 scraps of paper and label them Rock, Paper, Scissors. Fold or crumple them so they are indistinguishable. Choose one at random. ) What did you get? (a) Rock (b) Paper (c) Scissors 3) Calculate the statistic. 4) Form a distribution. 5) How extreme is the actual test statistic? Simulation ChiSquare ( ) Distribution If each of the counts are at least 5, AND if the null hypothesis is true, then the statistic follows a distribution, with degrees of freedom equal to ChiSquare Distribution df = number of categories 1 : df = 3 1 = pvalue using distribution ChiSquare pvalues 1. StatKey simulation or theoretical. RStudio: tail.p( chisquare,stat,df,tail= upper ) 3. TI83: nd DISTR 7: cdf( lower bound, upper bound, df Because the is always positive, the pvalue (the area as extreme or more extreme) is always the upper tail 4
5 Goodness of Fit A test for goodness of fit tests whether the distribution of a categorical variable is the same as some null hypothesized distribution The null hypothesized proportions for each category do not have to be the same ChiSquare Test for Goodness of Fit 1. State null hypothesized proportions for each category, p i. Alternative is that at least one of the proportions is different than specified in the null.. Calculate the counts for each cell as np i. Make sure they are all greater than 5 to proceed. 3. Calculate the statistic: observed  4. Compute the pvalue as the area in the tail above the statistic, for a distribution with df = (# of categories 1) 5. Interpret the pvalue in context. In 1866, Gregor Mendel, the father of genetics published the results of his experiments on peas He found that his experimental distribution of peas closely matched the theoretical distribution predicted by his theory of genetics (involving alleles, and dominant and recessive genes) Source: Mendel, Gregor. (1866). Versuche über PflanzenHybriden. Verh. Naturforsch. Ver. Brünn 4: 3 47 (in English in 1901, Experiments in Plant Hybridization, J. R. Hortic. Soc. 6: 1 3) S, Y: Dominant s, y: Recessive Mate SSYY with ssyy: 1 st Generation: all Ss Yy Mate 1 st Generation: nd Generation Second Generation Phenotype Round, Yellow 9/16 Round, Green 3/16 Wrinkled, Yellow 3/16 Wrinkled, Green 1/16 Theoretical Proportion Phenotype Theoretical Proportion Observed Counts Round, Yellow 9/ Round, Green 3/ Wrinkled, Yellow 3/ Wrinkled, Green 1/16 3 Let s test this data against the null hypothesis of each p i equal to the theoretical value, based on genetics H0 : p1 9 /16, p 3/16, p3 3/16, p4 1/16 H : At least one p is not as specified in H a i 0 Phenotype Theoretical Proportion Observed Counts Round, Yellow 9/ Round, Green 3/ Wrinkled, Yellow 3/ Wrinkled, Green 1/16 3 The statistic is made up of 4 components (because there are 4 categories). What is the contribution of the first cell (315)? (a) (b) 1.05 (c) 5.1 (d)
6 Phenotype p i Observed Counts Expected Counts Round, Yellow 9/ /16 = Round, Green 3/ /16 = Wrinkled, Yellow 3/ /16 = Wrinkled, Green 1/ /16 = n 556 = 556 observed = 0.47 Two options: o Simulate a randomization distribution o Compare to a distribution with 4 1 = 3 df pvalue = 0.95 Does this prove Mendel s theory of genetics? Or at least prove that his theoretical proportions for pea phenotypes were correct? a) Yes b) No You can never accept the null hypothesis!!! The null hypothesis can only be rejected with statistically significant results. A high pvalue doesn t let you conclude anything. Two Categorical Variables The statistics behind a test easily extends to two categorical variables A test for association (often called a test for independence) tests for an association between two categorical variables Did reading the example on Rock PaperScissors in the textbook influence the way you play the game? Did you read the example in Section 6.3 of the textbook? a) Yes b) No Rock Paper Scissors Total Read Example Did Not Read Example Total H 0 : Whether or not a person read the example in the textbook is not associated with how a person plays rockpaperscissors H a : Whether or not a person read the example in the textbook is associated with how a person plays rockpaperscissors 6
7 = Expected Counts row total column total sample size ChiSquare Statistic observed  Calculate the count for your cell. Note: Maintains row and column totals, but redistributes the counts as if there were no association = Randomization Test ChiSquare Statistic observed  If the counts are all at least 5, this can be compared to a distribution with (r 1)(c 1) degrees of freedom, where r = number of rows, c = number of columns ChiSquare Distribution df = (r 1)(c 1) = ( 1)(3 1) = ChiSquare Test for Association 1. H 0 : The two variables are not associated H a : The two variables are associated. Calculate the counts for each cell: row total column total = sample size Make sure they are all greater than 5 to proceed. 3. Calculate the statistic: observed  4. Compute the pvalue as the area in the tail above the statistic, for a distribution with df = (r 1) (c 1) 5. Interpret the pvalue in context. 7
8 Metal Tags and Penguins Let s return to the question of whether metal tags are detrimental to penguins. Survived Died Total Metal Tag Electronic Tag Total Is there an association between type of tag and survival? (a) Yes (b) No Source: Saraux, et. al. (011). Reliability of flipperbanded penguins as indicators of climate change, Nature, 469, Metal Tags and Penguins Survived Died Total Metal Tag 33 (47.38) 134 (119.6) 167 Electronic Tag 68 (53.6) 11 (135.38) 189 Total Calculate counts (shown in parentheses). First cell: row total column total sample size 356 Calculate the chisquare statistic: pvalue: df = ( 1) ( 1) = 1 pvalue = Statistics: There strong Unlocking evidence the Power that of metal Data tags are detrimental to penguins. Lock 5 Metal Tags and Penguins Difference in proportions test: z = (we got something slightly different due to rounding) pvalue = (twosided) ChiSquare test: = pvalue = Note: (3.387) = Two Categorical Variables with Two Categories Each When testing two categorical variables with two categories each, the statistic is exactly the square of the zstatistic The distribution with 1 df is exactly the square of the normal distribution Doing a twosided test for difference in proportions or doing a test will produce the exact same pvalue. Summary The test for goodness of fit tests whether one categorical variable differs from a hypothesized distribution The test for association tests whether two categorical variables are associated For both, you calculate counts for each cell, compute the statistic as observed  and find the pvalue as the area above this statistic on a distribution To Do Read Chapter 7 Do Homework 6 (due Tuesday, 11/6) 8
Class 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationSolutions to Homework 10 Statistics 302 Professor Larget
s to Homework 10 Statistics 302 Professor Larget Textbook Exercises 7.14 RockPaperScissors (Graded for Accurateness) In Data 6.1 on page 367 we see a table, reproduced in the table below that shows the
More informationMendelian Genetics. I. Background
Mendelian Genetics Objectives 1. To understand the Principles of Segregation and Independent Assortment. 2. To understand how Mendel s principles can explain transmission of characters from one generation
More informationAP: LAB 8: THE CHISQUARE TEST. Probability, Random Chance, and Genetics
Ms. Foglia Date AP: LAB 8: THE CHISQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More information2 GENETIC DATA ANALYSIS
2.1 Strategies for learning genetics 2 GENETIC DATA ANALYSIS We will begin this lecture by discussing some strategies for learning genetics. Genetics is different from most other biology courses you have
More informationHypothesis Testing: pvalue
STAT 101 Dr. Kari Lock Morgan Paul the Octopus Hypothesis Testing: SECTION 4.2 andomization distribution http://www.youtube.com/watch?v=3esgpumj9e Hypotheses In 2008, Paul the Octopus predicted 8 World
More informationThe GoodnessofFit Test
on the Lecture 49 Section 14.3 HampdenSydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20
More informationINTRODUCTION TO GENETICS USING TOBACCO (Nicotiana tabacum) SEEDLINGS
INTRODUCTION TO GENETICS USING TOBACCO (Nicotiana tabacum) SEEDLINGS By Dr. Susan Petro Based on a lab by Dr. Elaine Winshell Nicotiana tabacum Objectives To apply Mendel s Law of Segregation To use Punnett
More informationCATEGORICAL DATA ChiSquare Tests for Univariate Data
CATEGORICAL DATA ChiSquare Tests For Univariate Data 1 CATEGORICAL DATA ChiSquare Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.
More informationLAB : THE CHISQUARE TEST. Probability, Random Chance, and Genetics
Period Date LAB : THE CHISQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
More informationChisquare test Fisher s Exact test
Lesson 1 Chisquare test Fisher s Exact test McNemar s Test Lesson 1 Overview Lesson 11 covered two inference methods for categorical data from groups Confidence Intervals for the difference of two proportions
More informationChapter 6: t test for dependent samples
Chapter 6: t test for dependent samples ****This chapter corresponds to chapter 11 of your book ( t(ea) for Two (Again) ). What it is: The t test for dependent samples is used to determine whether the
More informationstatistics Chisquare tests and nonparametric Summary sheet from last time: Hypothesis testing Summary sheet from last time: Confidence intervals
Summary sheet from last time: Confidence intervals Confidence intervals take on the usual form: parameter = statistic ± t crit SE(statistic) parameter SE a s e sqrt(1/n + m x 2 /ss xx ) b s e /sqrt(ss
More informationChapter 23. Two Categorical Variables: The ChiSquare Test
Chapter 23. Two Categorical Variables: The ChiSquare Test 1 Chapter 23. Two Categorical Variables: The ChiSquare Test TwoWay Tables Note. We quickly review twoway tables with an example. Example. Exercise
More informationRecall this chart that showed how most of our course would be organized:
Chapter 4 OneWay ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical
More informationChapter 5. Discrete Probability Distributions
Chapter 5. Discrete Probability Distributions Chapter Problem: Did Mendel s result from plant hybridization experiments contradicts his theory? 1. Mendel s theory says that when there are two inheritable
More informationChapter 19 The ChiSquare Test
Tutorial for the integration of the software R with introductory statistics Copyright c Grethe Hystad Chapter 19 The ChiSquare Test In this chapter, we will discuss the following topics: We will plot
More information11.1 The Work of Gregor Mendel
11.1 The Work of Gregor Mendel Lesson Objectives Describe Mendel s studies and conclusions about inheritance. Describe what happens during segregation. Lesson Summary The Experiments of Gregor Mendel The
More informationOdds ratio, Odds ratio test for independence, chisquared statistic.
Odds ratio, Odds ratio test for independence, chisquared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
More informationMendelian Inheritance & Probability
Mendelian Inheritance & Probability (CHAPTER 2 Brooker Text) January 31 & Feb 2, 2006 BIO 184 Dr. Tom Peavy Problem Solving TtYy x ttyy What is the expected phenotypic ratio among offspring? Tt RR x Tt
More informationCalculating PValues. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating PValues Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating PValues" (2014). A with Honors Projects.
More informationLecture 42 Section 14.3. Tue, Apr 8, 2008
the Lecture 42 Section 14.3 HampdenSydney College Tue, Apr 8, 2008 Outline the 1 2 the 3 4 5 the The will compute χ 2 areas, but not χ 2 percentiles. (That s ok.) After performing the χ 2 test by hand,
More informationExtending Hypothesis Testing. pvalues & confidence intervals
Extending Hypothesis Testing pvalues & confidence intervals So far: how to state a question in the form of two hypotheses (null and alternative), how to assess the data, how to answer the question by
More information112 Goodness of Fit Test
112 Goodness of Fit Test In This section we consider sample data consisting of observed frequency counts arranged in a single row or column (called a oneway frequency table). We will use a hypothesis
More informationAllele Frequencies and Hardy Weinberg Equilibrium
Allele Frequencies and Hardy Weinberg Equilibrium Summer Institute in Statistical Genetics 013 Module 8 Topic Allele Frequencies and Genotype Frequencies How do allele frequencies relate to genotype frequencies
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationSection 12 Part 2. Chisquare test
Section 12 Part 2 Chisquare test McNemar s Test Section 12 Part 2 Overview Section 12, Part 1 covered two inference methods for categorical data from 2 groups Confidence Intervals for the difference of
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationCHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS
CHAPTER IV FINDINGS AND CONCURRENT DISCUSSIONS Hypothesis 1: People are resistant to the technological change in the security system of the organization. Hypothesis 2: information hacked and misused. Lack
More informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationChapter 7 Part 2. Hypothesis testing Power
Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23  Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300minute
More informationChapter 8 Introduction to Hypothesis Testing
Chapter 8 Student Lecture Notes 81 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationTesting Research and Statistical Hypotheses
Testing Research and Statistical Hypotheses Introduction In the last lab we analyzed metric artifact attributes such as thickness or width/thickness ratio. Those were continuous variables, which as you
More informationComparing Multiple Proportions, Test of Independence and Goodness of Fit
Comparing Multiple Proportions, Test of Independence and Goodness of Fit Content Testing the Equality of Population Proportions for Three or More Populations Test of Independence Goodness of Fit Test 2
More informationSydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.
Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under
More informationHypothesis Testing for a Proportion
Math 122 Intro to Stats Chapter 6 Semester II, 201516 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving
More informationHomework 5 Solutions
Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces
More informationCHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY
CHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples
More informationLesson Lesson Outline Outline
Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and
More informationPRACTICE PROBLEMS  PEDIGREES AND PROBABILITIES
PRACTICE PROBLEMS  PEDIGREES AND PROBABILITIES 1. Margaret has just learned that she has adult polycystic kidney disease. Her mother also has the disease, as did her maternal grandfather and his younger
More informationRecommend Continued CPS Monitoring. 63 (a) 17 (b) 10 (c) 90. 35 (d) 20 (e) 25 (f) 80. Totals/Marginal 98 37 35 170
Work Sheet 2: Calculating a Chi Square Table 1: Substance Abuse Level by ation Total/Marginal 63 (a) 17 (b) 10 (c) 90 35 (d) 20 (e) 25 (f) 80 Totals/Marginal 98 37 35 170 Step 1: Label Your Table. Label
More informationThe ChiSquare Test. STAT E50 Introduction to Statistics
STAT 50 Introduction to Statistics The ChiSquare Test The Chisquare test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed
More informationHypothesis testing  Steps
Hypothesis testing  Steps Steps to do a twotailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =
More informationMultiple random variables
Multiple random variables Multiple random variables We essentially always consider multiple random variables at once. The key concepts: Joint, conditional and marginal distributions, and independence of
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More informationPASS Sample Size Software
Chapter 250 Introduction The Chisquare test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationTwosample ttests.  Independent samples  Pooled standard devation  The equal variance assumption
Twosample ttests.  Independent samples  Pooled standard devation  The equal variance assumption Last time, we used the mean of one sample to test against the hypothesis that the true mean was a particular
More informationp ˆ (sample mean and sample
Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationDEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS. Posc/Uapp 816 CONTINGENCY TABLES
DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 816 CONTINGENCY TABLES I. AGENDA: A. Crossclassifications 1. Twobytwo and R by C tables 2. Statistical independence 3. The interpretation
More informationStats for Strategy Exam 1 InClass Practice Questions DIRECTIONS
Stats for Strategy Exam 1 InClass Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check
More informationA trait is a variation of a particular character (e.g. color, height). Traits are passed from parents to offspring through genes.
1 Biology Chapter 10 Study Guide Trait A trait is a variation of a particular character (e.g. color, height). Traits are passed from parents to offspring through genes. Genes Genes are located on chromosomes
More informationHypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam
Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationSPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS)
SPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One
More informationChapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion
Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative
More informationLAB 11 Natural Selection (version 2)
LAB 11 Natural Selection (version 2) Overview In this laboratory you will demonstrate the process of evolution by natural selection by carrying out a predator/prey simulation. Through this exercise you
More informationHardyWeinberg Equilibrium Problems
HardyWeinberg Equilibrium Problems 1. The frequency of two alleles in a gene pool is 0.19 (A) and 0.81(a). Assume that the population is in HardyWeinberg equilibrium. (a) Calculate the percentage of
More informationCHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES
CHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES The chisquare distribution was discussed in Chapter 4. We now turn to some applications of this distribution. As previously discussed, chisquare is
More information7A The Origin of Modern Genetics
Life Science Chapter 7 Genetics of Organisms 7A The Origin of Modern Genetics Genetics the study of inheritance (the study of how traits are inherited through the interactions of alleles) Heredity: the
More informationTopic 8. Chi Square Tests
BE540W Chi Square Tests Page 1 of 5 Topic 8 Chi Square Tests Topics 1. Introduction to Contingency Tables. Introduction to the Contingency Table Hypothesis Test of No Association.. 3. The Chi Square Test
More informationIs it statistically significant? The chisquare test
UAS Conference Series 2013/14 Is it statistically significant? The chisquare test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chisquare? Tests whether two categorical
More information11. Chi Square. Go to Data/Weight Cases and select Freq as the weights. Select Analyze/Nonparametric Tests/Chi Square.
11. Chi Square Objectives Calculate goodness of fit Chi Square Calculate Chi Square for contingency tables Calculate effect size Save data entry time by weighting cases A Chi Square is used to analyze
More informationGoodness of Fit Goodness of fit  2 classes
Goodness of Fit Goodness of fit  2 classes A B 78 22 Do these data correspond reasonably to the proportions 3:1? We previously discussed options for testing p A =0.75! Exact pvalue Exact confidence interval
More informationSimulating ChiSquare Test Using Excel
Simulating ChiSquare Test Using Excel Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 524 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu
More informationWhat about two traits? Dihybrid Crosses
What about two traits? Dihybrid Crosses! Consider two traits for pea: Color: Y (yellow) and y (green) Shape: R (round) and r (wrinkled)! Each dihybrid plant produces 4 gamete types of equal frequency.
More informationChapter 14: 16, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution?
Chapter 14: 16, 9, 1; Chapter 15: 8 Solutions 141 When is it appropriate to use the normal approximation to the binomial distribution? The usual recommendation is that the approximation is good if np
More information1 Hypothesis Testing. H 0 : population parameter = hypothesized value:
1 Hypothesis Testing In Statistics, a hypothesis proposes a model for the world. Then we look at the data. If the data are consistent with that model, we have no reason to disbelieve the hypothesis. Data
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationSampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Proportion From earlier material remember that if X is the count of successes in a sample of n trials of a binomial random variable then the proportion of success is given
More informationNonparametric Statistics
1 14.1 Using the Binomial Table Nonparametric Statistics In this chapter, we will survey several methods of inference from Nonparametric Statistics. These methods will introduce us to several new tables
More informationPigeonhole Principle Solutions
Pigeonhole Principle Solutions 1. Show that if we take n + 1 numbers from the set {1, 2,..., 2n}, then some pair of numbers will have no factors in common. Solution: Note that consecutive numbers (such
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationStats for Strategy Fall 2012 FirstDiscussion Handout: Stats Using Calculators and MINITAB
Stats for Strategy Fall 2012 FirstDiscussion Handout: Stats Using Calculators and MINITAB DIRECTIONS: Welcome! Your TA will help you apply your Calculator and MINITAB to review Business Stats, and will
More informationLAB : PAPER PET GENETICS. male (hat) female (hair bow) Skin color green or orange Eyes round or square Nose triangle or oval Teeth pointed or square
Period Date LAB : PAPER PET GENETICS 1. Given the list of characteristics below, you will create an imaginary pet and then breed it to review the concepts of genetics. Your pet will have the following
More informationHypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test...
Hypothesis Testing COMP 45 STATISTICS Dr N A Heard Contents 1 Hypothesis Testing 1.1 Introduction........................................ 1. Error Rates and Power of a Test.............................
More informationTesting Group Differences using Ttests, ANOVA, and Nonparametric Measures
Testing Group Differences using Ttests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Phone:
More informationTABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2
About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (Oneway χ 2 )... 1 Test of Independence (Twoway χ 2 )... 2 Hypothesis Testing
More informationSupplement on the KruskalWallis test. So what do you do if you don t meet the assumptions of an ANOVA?
Supplement on the KruskalWallis test So what do you do if you don t meet the assumptions of an ANOVA? {There are other ways of dealing with things like unequal variances and nonnormal data, but we won
More informationLecture 13  χ 2 Tests
Lecture 13  χ 2 Tests Statistics 102 Colin Rundel March 6, 2013 Weldon s dice Weldon s dice Walter Frank Raphael Weldon (18601906), was an English evolutionary biologist and a founder of biometry. He
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More information1. Comparing Two Means: Dependent Samples
1. Comparing Two Means: ependent Samples In the preceding lectures we've considered how to test a difference of two means for independent samples. Now we look at how to do the same thing with dependent
More informationRandom Uniform Clumped. 0 1 2 3 4 5 6 7 8 9 Number of Individuals per SubQuadrat. Number of Individuals per SubQuadrat
41 Population ecology Lab 4: Population dispersion patterns I. Introduction to population dispersion patterns The dispersion of individuals in a population describes their spacing relative to each other.
More informationAP Statistics 2002 Scoring Guidelines
AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought
More informationContingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables
Contingency Tables and the Chi Square Statistic Interpreting Computer Printouts and Constructing Tables Contingency Tables/Chi Square Statistics What are they? A contingency table is a table that shows
More informationChapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other ChiSquare Tests
11/4/015 Chapter 11 Overview Chapter 11 Introduction 111 Test for Goodness of Fit 11 Tests Using Contingency Tables Other ChiSquare Tests McGrawHill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11
More informationCrosstabulation & Chi Square
Crosstabulation & Chi Square Robert S Michael Chisquare as an Index of Association After examining the distribution of each of the variables, the researcher s next task is to look for relationships among
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationMINITAB ASSISTANT WHITE PAPER
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. OneWay
More informationMendelian and NonMendelian Heredity Grade Ten
Ohio Standards Connection: Life Sciences Benchmark C Explain the genetic mechanisms and molecular basis of inheritance. Indicator 6 Explain that a unit of hereditary information is called a gene, and genes
More informationMendelian Genetics in Drosophila
Mendelian Genetics in Drosophila Lab objectives: 1) To familiarize you with an important research model organism,! Drosophila melanogaster. 2) Introduce you to normal "wild type" and various mutant phenotypes.
More informationZtable pvalues: use choice 2: normalcdf(
Pvalues with the Ti83/Ti84 Note: The majority of the commands used in this handout can be found under the DISTR menu which you can access by pressing [ nd ] [VARS]. You should see the following: NOTE:
More informationInvestigating the Investigative Task: Testing for Skewness An Investigation of Different Test Statistics and their Power to Detect Skewness
Investigating the Investigative Task: Testing for Skewness An Investigation of Different Test Statistics and their Power to Detect Skewness Josh Tabor Canyon del Oro High School Journal of Statistics Education
More informationOneWay Analysis of Variance
OneWay Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We
More informationChi Squared and Fisher's Exact Tests. Observed vs Expected Distributions
BMS 617 Statistical Techniques for the Biomedical Sciences Lecture 11: ChiSquared and Fisher's Exact Tests Chi Squared and Fisher's Exact Tests This lecture presents two similarly structured tests, Chisquared
More informationABSORBENCY OF PAPER TOWELS
ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?
More information