SP INTRO CRSE INTRO INTERNATNAL STUDIES
SP INTRO CRSE INTRO INTERNATNAL STUDIES A&S 100
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Date Created: 10/23/15
A858 100 007 Statistics for Teachers Dr Gri ith Department of Statistics University of Kentucky 2005 1 Lecture 1 11 Collecting Data Individuals objects desscribed by a data set Variable characteristic of an individual Example 11 Individuals students7 variables age7 gender7 GPA7 etc Observational Studies observes individuals and measures variables of inter est7 but does not attempt to in uence responses Sample Surveys a type of observational study population sample Example 12 Public opinion polls7 TV ratings7 Experiment deliberately imposes some treatment on individuals to observe their response 12 Sampling Bad ways Biaised systematically favor certain outcomes 0 Convenience sampling easiest to reach 0 Voluntary response sampling call in or write in polls Good ways Simple random samples SRS of size n is one chosen in a way such that every set of 71 individuals has the same chance of being chosen Choosing a SRS 1 Assign a numerical label to numbers of the population so that all num bers have the same number of labels 2 Use a table of random digits or computer software to select sample population sample parameter statistic 13 How Sample Surveys Can Go Wrong Sampling Errors 0 Random sampling error variability from sample to sample Margin of error statements include this only 0 Bad sampling methods such as convenience sampling 0 Sampling frame Population issue Undercoverage Method personal interview7 phone7 mail Nonsampling Errors 0 Mistakes in data entry 0 Response errors o Wording of questions Questions to ask when reading a poll 0 Who carried out the survey What was the population How was the sample selected 0 How large was teh sample Margin of error What was the response rate 0 How were subjects contacted When was the survey conducted What were the exact questions 14 Exercises lnserted copy of book material 2 Lecture 2 21 Strati ed Random Samples STEP 1 Divide the sampling frame into distinct groups of individuals7 called strata Choose the strata because you have a special interest in these groups within the population or because the individuals within strata are like one another in some ways STEP 2 Choose a simple random sample from each stratum Example 21 Strata based on either of the following gender7 age group7 education level This strategy can reduce the margin of error 22 Systematic Random Sample Example 22 Pick a random starting point and sample that and each fth person for example STA 291 may have 130 in a lecture Pick a number from 1 to 6 at random Say you pick 3 Now 3813 form your sample 23 Exercises lnserted book material 24 ExperimentsComparative Experimentation Response variable measures outcome of a study Explanatory variable we think it explains or causes changes in the response variable Treatment speci c condition applied to subjects Example 23 Online versus classroom course new drug versus old drug or placebo How do we assign individuals to treatments 0 Self select 0 Selected by experiments but not necessarily at random 0 Confounding Randomized Comparative Experiment Group 1 Treatment 1 Random compare ASSIgnment outcomes Group 2 Treatment Randomization produces groups that should be similar In uences other that the treatments operate equally on all groups Therefore7 observed dif ferences in the response variable should be due to the treatments So we choose groups like we choose simple random samples 25 Exercises lnserted book material 3 Lecture 3 31 Placebo Effect Double blind experiments neither the subjects nor the observers know which treatment the subject is recieving Generalizability Another empem39mental design Randomized Complete Block Design Nonrandom assignment to homogeneous blocks Block 1 Block 2 Random allocation Treatment 1 to treatments This is a more elaborate way of controlling for extraneous factors as well as a way which allows one to study effects within blocks Analogoue of strati ed random sampling Example 31 A clinical trial is investigating a new drug for high blood pressure7 Examples of blocks menwomen7 over 65under 657 Caucaisan African American Nonrandom Assignment Block 1 Women Block 2 Men Treatment 1 Treatment 2 Treatment 1 Treatment 2 4 Lecture 4 41 Measurement Scales Nominal puts things in categories Example 41 male or female employed7 unemployed7 or not in labor force Ordinal puts things in order Example 42 small7 medium7 or large strongly disagree7 disagree7 neutral7 agree7 strongly agree IntervalRatio measures amount of something present Example 43 width of room7 or temperature 42 Organizing and Displaying Data 0 Frequency 0 Relative frequency 0 Histograms o Stemplots 43 Examples Inserted book material 5 Lecture 5 51 Numerical Summaries Graphical Techniques Challenger data 844961408367456670698058 686067727370576370785267 5367756l708176 79 757635831 0 Stemplot 0 Measures of Location 0 Quartiles 0 Five Number Summary 0 Boxplot Box and whisker display 52 Measures of location Mean Median Mode Median 77half above half below Notation i For n 36 there are two 77middle observations 67 and 68 We take the midpoint of these 675 as the median If n is odd then there is only one 77middle observation and we take that to be the median m arithmetic average 7 zz x 6586 Mode most frequently occuring value not necessarily unique 67 and 70 are modes 53 Quartiles and Five number summary First Quartile median of observations to the left ofthe median when ordered from smallesto largest Third Quartile median of the observations to the right of the median when ordered from smallest to largest Five number summary Minimum First Quartile Median Third Quartile Maximum Boxplot Min Max 1Q Median 3Q For the Challenger data Minimum 317 rst quartile 597 median 6757 third quartile 757 maximum 84 31 84 59 675 75 6 Lecture 6 61 Measures of Spread or Variability Range max min lnterquartile range third quartile rst quartile Five Number Summary minimum rst quartile median third quartile maximum Interquartile Range Range 62 Variance and Standard Deviation 22196139 7 nil A2 Variance is measured in square of original unit 5 52 Standard deviation is measured in original unit 7 Lecture 7 71 Bivariate Data Examples height7 weight or weight of car7 mpg Positive Association increases in one associated with increases in the other Negative Association increases in one associated with decreases in the other 10 17y17 27y27 39 39 39 7 rmyn 77Five number surnrnary77 Mean and Standard Deviation of 1727 J E SE Mean and Standard Deviation of y hyg7 7y y7 5y Correlation Coe cient 229 WM 7 7 7 smsy Properties of r 1 rneaseure of association7 unitless D 7lgrgl if r E 71717 then points in scatterplot lie on a straight line 00 measures how tightly points Cluster about straight line 7 rneasures straight line association in sense r2 is the proportion of the variance of one variable that can be explained by straight line relation ship Cf 72 Examples Inserted book material scatterplots with various r 73 Sample linear Regression Regression Prediction Find the line which best ts Question what do we mean by tting 77best What criteria should be used Least squares line least squares line enlarged VleW Given the data 17y1727y27 7 muyn7 the least squares line rnini mizes n i 7302 1 Example 71 173727474757578 Concider L1y z 2 Then 1 37ny 47ny 67714 7 4 2111i i20057628772 2 Consider L2y 2x 1 Then 1 37ny 57ny 97lf4 11 4 2yiiy7i20116926 i1 4 Consider L3 y 2x 71 Then 1 17ny 3793 77714 9 4 2yiizji24141 10 i1 Which of the lines L17L27L3 ts best How do we nd the line which best ts The line which best ts passes through 5 and has slope rj Z Homework Find the regression line for the data set of the preceeding example