STATISTICAL METHODS MGMT 2100
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Date Created: 10/19/15
Chapter 3 sections 58 Probability Conditional Probability Conditional Probability the probability that event A occurs given that event B occurs PA B PB Conditional probability works with a reduced sample space the space that contains B and A B PAB PB 0 Text pp 158 Example 316 The investigation of consumer product complaints by the Federal Trade Commission FTC has generated much interest by manufacturers in the quality of their products A manufacturer of an electromechanical kitchen utensil conducted an analysis of a large number of consumer complaints and found that they fell into the six categories shown in the next slide If a consumer complaint is received what is the probability that the cause of the complaint was product appearance given that the complaint originated during the guarantee period Text pp 158 Example 316 Event A cause of complaint is appearance Event B complaint occurred during guarantee period Distribution of Product Complaints Reason for Complaint Complaint Origin Electrical Mechanical Appearance Totals During Guarantee Period 18 13 32 63 After Guarantee Period 12 22 3 37 Totals 30 35 35 100 PA m B 32 PA B32 PAB 51 PB 63 The Multiplicative Rule and Independent Events The Multiplicative Rule PA m B PAPBA or PA m B PBPAB PA B C Example Assignment 2 Q3 The Value Line Survey a service for common stock investors provides its subscribers with uptodate evaluations of the prospects and risks associated with the purchase of a large number of common stocks Each stock is ranked 1 highest to 5 lowest according to Value Line s estimate of the stock s potential for price appreciation during the next 12 months Suppose you plan to purchase stock in three electrical utility companies from among seven that possess rankings of 2 for price appreciation Unknown to you two of the companies will experience serious difficulties with their nuclear facilities during the coming year If you randomly select the three companies from among the seven what is the probability that you select a None of the companies with prospective nuclear difficulties b One of the companies with prospective nuclear difficulties c Both of the companies with prospective nuclear difficulties Solution 1 Example Assignment 2 Q3 S1 S1 S1 S1 S1 32 32 32 32 S3 S3 S3 S4 S4 S4 82 82 82 82 82 83 83 83 83 S4 S4 S4 S5 85 F1 F1 31 F2 F1 82 F2 F1 83 F2 F1 85 F2 F2 83 S1 S4 S1 S5 S1 S4 82 S5 82 85 83 83 S4 S1 S4 S5 S1 85 F1 83 85 S1 84 F1 81 85 F2 83 F1 81 84 F2 83 F2 81 F1 F2 84 85 82 85 F1 82 F1 F2 84 F1 82 85 F2 84 F2 85 F1 83 F1 F2 85 F2 3 Pseectng none F 1035 b Pseecting one F 2035 F1 F2 0 Pseleotng two F 535 Solution 2 Example Assignment 2 Q3 5 5 3 35 3 g a Pselecting none FF 7 35 3 37 3 5 2 5 39gtlt2 2 1 25 2 20 b Pselecting one F 7 7 g 3 37 3 2 5 1 2 1 5 1 IX1 5 c Pselecting two F 39 3939 U 7 7 5 3 37 3 Solution 3 Example Assignment 2 Q3 Use conditional probability and multiplicative rule The Multiplicative Rule and Independent Events Events A and B are independent if the occurrence of one does not alter the probability of the other occurring PAB PA and PBA PB If A and B are independent events PA D B PA PB Text pp 158 Example 316 Event A cause of complaint is appearance Event B complaint occurred durinq quarantee period Distribution of Product Complaints Reason for Complaint Complaint Origin Electrical Mechanical Appearance Totals During Guarantee Period 18 13 32 63 After Guarantee Period 12 22 3 37 Totals 30 35 35 100 Are A and B independent events PAlB 51 PA 32 03 35 A and B are not independent Bayes s Theorem Optional Suppose the events B1 and 82 are mutually exclusive and complementary events such that PB175 and PBZ25 Consider another event A such that PAB13 and PABZ5 a Find PB1nA b Find PanA c Find PA using the results in a and b d Find PB1A e Find PBZA Bayes s Theorem Optional Allows calculation of unknown conditional probability from known conditional probability PBlA PB APA HaVQW 1931 PAB1 1932 PAB2 PBkPABk Read Text pp 174175 Example 323 Random Sampling Assume a desired sample size of n Sample is random if every set of n elements in the population has the same probability of being selected Random number generators often used to produce a random sample Read Text pp 171172 Example 322 Assignment 3 1 10th edition pp166 ex 47 2 10th edition pp 168 ex 62 3 suggested exercise for Bayes s Theorem optional 10th edition pp 176 ex 80 Due Date Sept 29 2011 Thursday Chapter 2 sections 69 Methods for Describing Sets of Data Interpreting the Standard Deviation How many measurements fit within 1 n standard deviations of the mean Chebyshev s Empirical Rule Rule i 1S i 10 No useful info Approximately or 68 i 23 iZG At least 75 Approximately 0F 95 i 3S0r i 3039 At least 89 Approximately 997 Text pp 86 ex84 The National Education Longitudinal Survey NELS tracks a nationally representative sample of US students from eighth grade through high school and college Research published in Chance Winter 2001 examined the Standardized Admission Test SAT scores of 265 NELS students who paid a private tutor to help them improve their scores The next table summarizes the changes in both the SATMath and SATVerbal scores for these students Text pp 86 ex84 score changes SATMath SATVerbal Mean change in score 19 7 Standard deviation of 65 49 Suppose one of the 265 students who paid a private tutor is selected at random Give an interval that is likely to contain this student s change in the SATMath score Repeat part a for the SATVerbal score Suppose the selected student increased their score on one of the SAT tests by 140 points Which test the SAT Math or SATVerbal is the one most likely to have the 140point increase Explain Numerical Measures of Relative Standing Descriptive measures of relationship of a measurement to the rest of the data Common measures percentile score zscore Numerical Measures of Relative Standing Percentile scores make use of the pth percentile The median is an example of percentiles Median is the 50th percentile 50 of measurements lie above it and 50 lie below it For any p the pth percentile has p of the measurements lying below it and 100p above it Numerical Measures of Relative Standing zscore the distance between a measurement x and the mean expressed in standard units Use of standard units allows comparison across data sets x x x U z 039 s Numerical Measures of Relative Standing More on zscores Zscores follow the empirical rule for mound shaped distributions y 393 cl Q 3 a 2 as Q 3 5 E m ue3lt5 ueZG uec u u6 u20 u36 Measurement scale 3 2 1 O 1 2 3 z scale 2005 Pearsnn Prentice Hall I L Methods for Detecting Outliers Outlier a measurement that is unusually large or small relative to the data values being described Causes Invalid measurement Misclassified measurement A rare chance event Two detection methods Box Plots zscores Methods for Detecting Outliers Box Plots based on quartiles values that divide the dataset into 4 groups Lower Quartile QL 25th percentile Middle Quartile median Upper Quartile QU 75th percentile lnterquartile Range IQR QU QL Methods for Detecting Outliers Box Plots Boxplot of RDPct Potential Outlier 9 RDPct 39 Whiskers 9 3 7 6 5 l Qu k hinge ltlledian hinge Not on plot inner and outer fences which determine potential outliers Methods for Detecting Outliers Rules of thumb Box Plots measurements between inner and outer fences are suspect outliers measurements beyond outer fences are highly suspect outliers Zscores Scores of i3 in moundshaped distributions i2 in highly skewed distributions are considered outliers Graphing Bivariate Relationships Bivariate relationship the relationship between two quantitative variables Graphically represented with the scatterplot Variable 1 Variable 2 a Positive relationship O o 00 0 oo o 09 v lt V l 4 0 8 00 00 lt90 0 o a 00 a c o 5 oo 3 oo 0 0 00 S 000 3 00 0 o o 3 1 0 H w 000 3 000063000 0 gt o gt o o o o 0 o o o o o o 000 0 00 0 O o Variable2 b Negative relationship Copyright 2005 Pearson Prentice Hall Inc Variable 2 c No relationship Summary Distribution Rules Chebyshev s Rule Empirical Rule Measures of relative standing Percentile scores zscores Methods for detecting Outliers Box plots zscores Summary Method for graphing the relationship between two quantitative variables Scatterplot Statistical Thinking GolfCEO Example THCDQOO39QJ Describe the target population Describe variable of interest Describe data collection method Describe types of data collected Describe the sample Think about the reliability of the statistical inference of the study InClass Assignment Text pp91 ex 98 Due on Thursday Sept 22 2011 Chapter 2 sections 15 Methods for Describing Sets of Data Objectives Describe Data using Charts Graphs A Graph is worth a thousand words Describing Qualitative Data Qualitative data are nonnumeric in nature Best described by using Classes Use 2 descriptive measures class frequency number of data points in a class class relative class frequency frequency total number of data points in data set class percentage class relative frequency x 100 Describing Qualitative Data Displaying Descriptive Measures Summary Table DEGREE Cumulative FTEQLIEDCV PM XWM Valid Bachelors 6 240 240 240 Law 3 120 120 360 Masters 9 360 360 720 None 4 160 160 880 PhD 3 120 120 1000 Total 25 1000 1000 Copyright 2005 Pea3K1 Prentice Hall Inc Class Frequency Class percentage class relative frequency x 100 Describing Qualitative Data Qualitative Data Displays Chart of DEGREE 9 8 7r 4 3 2 1 r u l l l l l Bachelors Law Masters None PhD DEGIEE Pearson Prenth Describing Qualitative Data Qualitative Data Displays Pie chart Pie Chart of DEGREE Describing Qualitative Data Qualitative Data Displays Pareto Diagram Palate Diagram 40 Graphical Methods for Describing Quantitative Data The RampD Data Percentage of Revenues Spent on Research and Development Company Percentage Company Percentage Company Percentage Company Percentage 1 135 14 95 27 82 39 65 2 84 15 81 28 69 40 75 3 105 16 135 29 72 41 71 4 90 17 99 30 82 42 132 5 92 18 69 31 96 43 77 6 97 19 75 32 72 44 59 7 66 20 111 33 88 45 52 8 106 21 82 34 113 46 56 9 101 22 80 35 85 47 117 10 71 23 77 36 94 48 60 11 80 24 74 37 105 49 78 12 79 25 65 38 69 50 65 13 68 26 95 Graphical Methods for Describing Quantitative Data Dot Plot O O O I O I I I C I O I I I I O O O I O I O C O O O O O O O I I O O O l l l l l T l l 52 54 75 88 100 112 124 136 Copyright 2005 Pearson Prentice Hall Inc Graphical Methods for Describing Quantitative Data Stem andLeaf Display 0 D l E F l G StemandLeaf Display for RDPct Stem unit 1 6055568999 711224557789 8001222458 902455379 Stem I Leaf Stem I Leaf 101556 I 11137 1 Cuuyugm a 2005 Peanut Renate Hall n u 13255 Graphical Methods for Describing Quantitative Data Histogram Histogram of RDPct Frequency Copyright 2005 Pearson Prentice Halt Inc Graphical Methods for Describing Quantitative Data More on Histograms gt gt gtx l D U G l l 0 CD CL 5 s 5 cr 0quot 0quot U Q Q at d J O D d 2 2 2 H d l H 3 E 3 lt1 0 O of 5 tr D 0 Measurement classes Measurement classes Measurement classes a Small data set b Larger data set 0 Very large data set Copyright 2005 Pearson Prentice Hall Inc Number of Observations in Data Set Number of Classes Less than 25 56 2550 714 More than 50 1520 Summation Notation Used to simplify summation instructions Each observation in a data set is identified by a subscript x1 x2 x3 x4 x5 xn Notation used to sum the above numbers together is n ZXiZX1X2X3X4m Xn i1 Summation Notation Data set OH 2 3 4 4 2 Are these the same Zx and i1 4 Zx I 4 9 16 30 i1 4 2 3 42 102 mo i1 Numerical Measures of Central Tendency Central Tendency tendency of data to center about certain numerical values Three commonly used measures of Central Tendency Mean Median Mode Numerical Measures of Central Tendency The Mean Arithmetic average of the elements of the data set Sample mean denoted by 3c Population mean denoted by u Calculated as EZEM 236139 n N Numerical Measures of Central Tendency The Median Middle number when observations are arranged in ascending or descending order Median denoted by m dentified as the g05 observation if n is odd and the mean of the g and g1 observations if n is even Numerical Measures of Central Tendency The Mode The most frequently occurring value in the data set Data set can be multimodal have more than one mode Data displayed in a histogram will have a modal class the class with the largest frequency Numerical Measures of Central Tendency TheDataset 13 5 6 8 8 91112 Meanle quot13 5 6 8 8 91112 Q n 9 9 7 Median is the g05 or 5th observation 8 Mode is 8 Numerical Measures of Central Tendency C B n For the distribution drawn here identify the mean median and mode A A mean B mode C median B mode B mean C median A mode B median C mean D A median B mode C mean Numerical Measures of Variability Variability the spread of the data across possible values Three commonly used measures of Variability Range Variance Standard Deviation Numerical Measures of Variability The Range Largest measurement minus the smallest measurement Loses sensitivity when data sets are large These 2 distributions 6 have the same range How much does the range tell you about 10 0 Sgt1132 30 40 all 0 IO 20 30 40 Profit We bl Cost estimator B on Prentice Hall Inc Number ufjobs 4 21 C051 estimator A Copyright 2005 Pears Numerical Measures of Variability The Sample Variance 2 The sum of the squared deviations from the mean divided by n1 Expressed as units squared 2 xi 2 S n l Numerical Measures of Variability The Sample Standard Deviation s The positive square root of the sample vanance Expressed in the original units of measurement Numerical Measures of Variability Samples and Populations Notation Sample Population Variance 2 02 Standard Deviation S a AfterClass Assignment not required for grading Read Ch2 sections 69 and think about the CEO GolfPerformance study Do ex84 on Text pp 86 Bring your solutions to the class on Thursday 9152011 Chapter 3 sections 14 Probability Thinking Challenge FLORIDA 73 L D T T E R V Exlllrlll ck s Thursday January 25 2007 mom Hays AH3 use am 37571771 973539 101 53043 471172572133 9727170 ltL Janna 24 21107 January232007 Janua 2 2007 Janus 24 20TH Januz fznm answer three questions immune If you get the correct vou comma Hm ML L V 9 solution to one of these a Winner 1 anglnefsplnrerrracksquot lsed ford lsplfymg questions raise your 0 luse itm ll nut piawllps O l hand and demonstrate play lunery games luse Mo nd out if I have won 0 your solution to the class You will be PMquot rewarded with 1 bonus point Events Sample Spaces and Probability Experiment process of observation that leads to a single outcome with no predictive certainty Sample point most basic outcome of an experiment Sample Space a listing of all sample points for an experiment Experiment tossing a die Six Sample Points Sample Space S 1 2 3 4 5 6 n Sample point probability relative frequencyis f 1 quotA quot of the occurrence of the sample point 39 Events Sample Spaces and Probability Venn Diagram Events Sample Spaces and Probability How to assign Sample Point Probabilities Multiple repetitions of an experiment Prior knowledgeassumption Estimation based on survey Probability Rules for Sample Points Sample Point Probabilities must lie between 0 and 1 The sum of all sample point probabilities must be 1 Events Sample Spaces and Probability Event a specific collection of sample points Probability of an event the sum of the probabilities of all sample points in the collection Events Sample Spaces and Probability How to assign Event Probabilities Define experiment List sample points Assign probabilities to sample points ldentify collection of sample points in Event Sum sample point probabilities Events Sample Spaces and Probability What is the probability of rolling an eight in a single toss of a pair of dice Experiment is toss of pair of dice 0 11 136 0 12 136 13136 14136 15136 0 16 136 21 136 22 136 0 23136 24136 25 136 0 26 136 31 136 32 136 33136 34136 35 136 35 136 0 41 136 0 42 136 0 43136 O 44136 0 45 136 0 46 136 0 51 136 0 52 136 0 53136 O 54136 0 55 136 0 56 136 0 61 136 0 62 136 0 63 136 0 64136 0 65 136 0 66 136 Probability of rolling an 8 136136136136136 536 14 Events Sample Spaces and Probability What is the probability of rolling at least a 9 with a single toss of two dice Pat least 9 P9 P10 P11 P12 436 336 236 136 1036 518 28 Events Sample Spaces and Probability What do you do when the number of sample points is too large to enumerate Use the Combinations Rule to count number of sample points when selecting sample of size n from N elements N N n nN n where n nn 1n 2321 Assumption without replacement of each element before the next is selected Events Sample Spaces and Probability If you had 30 people interested in being in a study and you needed 5 how many different combinations of 5 are there 30 30 30 3029o28o27o26o253o2o1 5 530 5l Sl25l 543o2o125o243o2o1 Unions and Intersections Compound Event a composition of two or more events Can be the result of a union or intersection EDtiIe shaded area is Shaded area is A U B A W B a Union b Intersection Cup lrigili 2005 Pearson Pieniiue Haii luu Text pp 147 Example 310 Suppose a distributor of mailorder tools is analyzing the results of a recent mailing The probability of response is believed to be related to income and age The percentages of the total number of respondents to the mailing are given by income and age classification The table in next slide is called a twoway table because responses are classified according to two variables income and age in columns and rows Text pp 147 Example 310 Event A being over 50 years old Event B earning between 25K and 50K Twoway Table with Percentage of Respondents in AgeIncome Classes Income Age lt25K 25K 50K gt50K lt30 yrs 5 12 10 3050 yrs 14 22 16 gt50 yrs 8 10 3 PA21 PB44 PA B10 PAUB081003122255 Complementary Events Complementary Event The complement of Event A AC is all sample points that do not belong to Event A o 0 0 o 0 A O O o o Complementary Events IfA is having at least 1 head appear in the toss of2 coins AC is having no heads appear The Additive Rule and Mutually Exclusive Events The Additive Rule PAUB PAPB PA B 081003122210 1055 Twoway Table with Percentage of Respondents in AgeIncome Classes Income Age lt25K 25K 50K gt50K lt30 yrs 5 12 10 3050 yrs 14 22 16 gt50 yrs 8 10 3 The Additive Rule and Mutually Exclusive Events Mutually Exclusive Events Events are mutually exclusive if they share no sample points G The Additive Rule and Mutually Exclusive Events The Additive Rule for Mutually Exclusive Events PA U B PA PB Assignment 2 1 10th edition pp 91 ex 98 2 10th edition pp154 ex 36 3 See next slide Due on Sept 26 2011 Monday Assignment 2 3 The Value Line Survey a service for common stock investors provides its subscribers with uptodate evaluations of the prospects and risks associated with the purchase of a large number of common stocks Each stock is ranked 1 highest to 5 lowest according to Value Line s estimate of the stock s potential for price appreciation during the next 12 months Suppose you plan to purchase stock in three electrical utility companies from among seven that possess rankings of 2 for price appreciation Unknown to you two of the companies will experience serious difficulties with their nuclear facilities during the coming year If you randomly select the three companies from among the seven what is the probability that you select a None of the companies with prospective nuclear difficulties b One of the companies with prospective nuclear difficulties c Both of the companies with prospective nuclear difficulties Chapter 1 Statistics Data and Statistical Thinking The Science of Statistics Statistics the science of data Collection Evaluation classification summary organization and analysis Interpretation Types of Statistical Applications in Business Descriptive Statistics describe collected data 514 of all credit card purchases in the lst quarter of 2003 were made 102003 with a Visa Card Types of Statistical Applications in Business Inferential Statistics make generalizations about a larger set of data population based on a subset Sample of that population Industry Returnto Pay Ratios of CEOs Financial 2463 Telecommunications 287 Financial Industry CEOs are underpaid relative to CEOs in Telecommunications L73 7 x1 projem of die L l ewResem c I391 Im II vr 65 of online adults use social networking sites Women maintain their foothold on SNS use and older Americans are still coming aboard Mary Madden Senior Research Specialist Kathryn Zickuhr Research Specialist Methodology This report is based on the findings of a survey on Americans39 use of the internet The results in this report are based on data from telephone intewiews conducted by Princeton Survey Research Associates International from April 26 to May 22 2011 among a sample of 2277 adults age 18 and older Telephone interviews were conducted in English anmll and cell phone 755 including 346 without a landline phone For results basecl on the total sample one can say with 95 confidence that the error attributable to sampling is plus or minus 24 percentage points Social networking site use by unline admits 2905 2011 The percentage of a adult intemer users who use sucial networking sites since 2135 n x39 43 19 35 Yesterday 27 15 59 IDES ENE 2m 2m 200939 21110 l ii Sauna Pew Research Center39s Internet ii American Life iject surveys februanj ems August 21105 May IBM Aprih 2009 May 2am and May 2D11 Sncial networking site use by gender EDIE2311 The percentage 13f adult internet users clf39 each gentler whnx use suciaIJ networking sites 51 59515 6 213115 ENE ZED7 ENE EDIE 201D 2311 Snurce Pew Research center s Internet i39i American Life iject surveys February ems August 2am May 20cm Ap rill am May 2mm and May 201 1 Social netwmiking Site use by age gmup 2005 2 11 The perpenta ge nf admit inmemset users in each age gmup who use sandal n ewmrkmg sites 1003 35 33 15 h 2035 200 2003 3009 I 3011 Note Tmal in far dntemet users age 65 in 211115 was 1m and 543 mull for that gm up are mt nduda Source Pew 3231de Gemten Internet 1 American Life Praject surveys February EDGE August 20136 May was April 2019 May mm and May 2011 39 1 project of die L l ewResean I391 Im II vr 65 of online adults use social networking sites Women maintain their foothold on SNS use and older Americans are still coming aboard Mary Madden Senior Research Specialist Kathryn Zickuhr Research Specialist Methodology This report is based on the findings of a survey on Americans39 use of the lnternet The results in this report are based on data from telephone intewiews conducted by Princeton Survey Research Associates International from April 26 to May 22 2011 among a sample of 2277 adults age 18 and older Telephone interviews were conducted in English and Spanish by landline 1522 and cell phone 755 including 346 without a landline phone For results based on the total sample one can say with 95 confidence that the error attributable to sampling is plus or minus 24 percentage points Fundamental Elements of Statistics Experimental Unit an object of interest example a graduating senior in 2010 at RPI Population the entire set of units we are interested in learning about example all 1167 graduating seniors in 2010 at RPI Variable a characteristic of an individual experimental unit example age or gender at graduation Fundamental Elements of Statistics Sample subset of population example 100 graduating seniors in 2010 at RPI Statistical Inference generalization about a population based on sample data example The average age at graduation is 219 based on sample of 100 Measure of reliability statement about the uncertainty associated with an inference Fundamental Elements of Statistics Text Example 12 pp10 Cola Wars is the popular term for the intense competition between CocaCola and Pepsi displayed in their marketing campaigns Their campaigns have featured movie and television stars rock videos athletic endorsements and claims of consumer preference based on taste tests Suppose as part of a Pepsi marketing campaign 1000 cola consumers are given a blind taste test Le a taste test in which the two brand names are disguised Each consumer is asked to state a preference for brand A or brand B a Describe the population b Describe the variable of interest c Describe the sample d Describe the inference Fundamental Elements of Statistics Text Example 13 pp 11 Refer to Example 12 in which the cola preferences of 1000 consumers were indicated in a taste test Describe how the reliability of an inference concerning the preferences of all cola consumers in the Pepsi bottler s marketing region could be measured Fundamental Elements of Statistics Elements of Descriptive Statistical Problems population or sample of interest 2 variables of interest 3 numerical summary tools charts graphs tables 4 Identification of patterns in data A Fundamental Elements of Statistics Elements of lnferential Statistical Problems 1 999 population of interest variables of interest sample taken from population inference about population based on sample data a measure of reliability for the inference Types of Data Quantitative Data measured on a natural numerical scale equal intervals along scale allows for meaningful mathematical calculations data with absolute zero zero has value is ratio data eg grade number of pizzas I can eat before fainting Data with relative zero zero means no value is interval data eg my level of happiness rated from 1 to 10 temperature in Fahrenheit degrees Types of Data Qualitative Data measured by classification only Nonnumerical in nature Meaningfully ordered categories identify ordinal data best to worst ranking age categories Categories without a meaningful order identify nominal data political affiliation industry classification ethniccultural groups Types of Data Example Text ex 16 pp26 Colleges and universities are requiring an increasing amount of information about applicants before making acceptance and financial aid decisions Classify each of the following types of data required on a college application as quantitative or qualitative a High school GPA Quantitative ratio b Honors awards Qualitative nominal c Applicant s score on the SAT or ACT Quantitative ratio d Gender of applicant Qualitative nominal e Parents income Quantitative ratio f Age of applicant Quantitative ratio Types of Data Different statistical techniques used for quantitative and qualitative data Qualitative and Quantitative data can be used together in some techniques Quantitative data can be transformed into Qualitative data through category creation Qualitative data cannot be meaningfully transformed into Quantitative data Collecting Data Data Sources Published source databases books journals abstracts Eg unemployment rate data can be collected from the US Bureau of Labor Statistics Survey Data gathered through questions from a sample of people Designed Experiment Often used for gathering information about an intervention Observational Study Data gathered through observation no interaction with units Collecting Data Sampling Sampling is necessary if inferential statistics are to be used Samples need to be representative Reflect population of interest Random Sampling Most common sampling method to ensure sample is representative Ensures that each subset of fixed size in the population is equally likely to be selected Common Sources of Error in Survey Data Selection bias exclusion of a subset of the population of interest prior to sampling Nonresponse bias introduced when responses are not gotten from all sampled members Measurement error inaccuracy in recorded data Can be due to survey design interviewer impact or a transcription error Collecting Data Example What percentage of Web users are addicted to the Internet To find out a psychologist designed a series of 10 questions based on a widely used set of criteria for gambling addiction and distributed them through the Web site ABCNewscom A sample question Do you use the Internet to escape problems A total of 17251 Web users responded to the questionnaire If participants answered yes to at least half of the questions they were viewed as addicted The findings released at the 1999 annual meeting of the American Psychological Association revealed that 990 respondents or 57 are addicted to the Internet Tampa Tribune Aug 23 1999 a Identify the data collection method b Identify the target population c Are the sample data representative of the population Summary Two types of statistical applications Descriptive and Inferential Six fundamental elements of statistics population experimental units variable sample inference measure of reliability Summary Two types of data Quantitative and Qualitative Four Data collection methods published source designed experiment survey observation Summary Sources of Error in Survey Data selection bias nonresponse bias measurement error Statistical Thinking Statistical thinking involves applying rational thought and the science of statistics to critically assess data and inferences Statistical Thinking GolfCEO Example THCDQOO39QJ Describe the target population Describe variable of interest Describe data collection method Describe types of data collected Describe the sample Think about the reliability of the statistical inference of the study
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