Utts and Heckard. Why Study Statistics? Why Study Statistics? American Heritage College Dictionary, 3rd Ed.

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1 Amerca Hertage College Dctoar, 3rd Ed. 1. (used wth sgular verb) The mathematcs of the collecto, orgazato, ad terpretato of umercal data, esp. the aalss of populato characterstcs b ferece from samplg. Utts ad Heckard Statstcs s a collecto of procedures ad prcples for gatherg data ad aalzg formato order to help people make decsos whe faced wth ucertat.. (used wth plural verb) Numercal data. 1 Wh Stud Statstcs? Several possble aswers to ths questo: I have to because t s a requremet for m major I eed to order to advace at work I wat to because I see more ad more uses of statstcs ad I do t reall uderstad the methods, Wh Stud Statstcs? What ou should recogze s: statstcs s ow a essetal commucatos tool studg statstcs wll gve ou access to powerful problem solvg ad aalss methods the power to make formed decsos about thgs ou hear or read 3 4

2 Tpes of Statstcal Applcatos Descrptve Statstcs uses umercal ad graphcal methods to look for patters a data set, to summarze the formato revealed a data set, ad to preset that formato a coveet form Iferetal Statstcs utlzes sample data to make estmates, decsos, predctos, or other geeralzatos about a larger set of data Basc Terms Raw data --- umbers ad categor labels that are collected, but ot et processed Varable --- a characterstc that dffers from oe dvdual to the ext Populato data --- measuremets take from all dvduals a populato Sample data --- measuremets take from a subset of a populato Statstc --- a summar measure computed from sample data Parameter --- a summar measure computed for a etre populato Descrptve Statstcs --- summar umbers for ether a populato or a sample 5 Relablt---how good s the statstcal ferece? Ifereces based o a complete cesus of the populato s certa Ifereces made from samples cota a elemet of ucertat wat to be able to make statemets about the degree of ucertat estmates based o sample data Tpes of Data Qualtatve varables---caot be measured o a atural umercal scale; data classfed to categores Nomal varables---group or categor ames that have o heret orderg o Tpe of trasportato used to get to school (walk, bus, bke, drve) o Studet lves o/off campus (o, off) Ordal varables---group or categor ames where oe respose s greater tha or less tha aother o Year school (freshma, sophomore, juor, seor) o Exam grades recorded as letter grades (A F) o Clothg szes (XS, S, M, L, XL) 7 8

3 Quattatve varables---recorded umercal values; the data are ether measuremets or couts take o each dvdual Varables are classfed as ether cotuous or dscrete Cotuous varable --- A varable where ever value wth some terval s a possble result; o heght o weght Dscrete varable --- A varable whch ma take o ol oe of a certa umber of possble values o umber of chldre a faml o umber of emergec room admttaces each ght o up-face o the roll of a de Collectg Data Publshed source---data alread collected; publshed a book, joural, ewspaper Desged expermet---sets up strct cotrols over uts the stud; ofte cludes oe or more treatmet ad cotrol groups Surve---coducted va phoe, mal, emal, or -perso Observatoal stud---observato of expermetal uts ther atural settg 9 1 Represetatve Sample---exhbts characterstcs tpcal of those possessed b the target populato; requred to appl feretal statstcal methods, regardless of data collecto method Smple Radom sample---use of a selecto method that esures that ever subset of fxed sze the populato has the same chace of beg cluded the sample Explaator ad Respose Varables Ma questos are about the relatoshp betwee two varables. It s useful to detf oe varable as the depedet varable (explaator varable, predctor, covarate) ad the other varable as the depedet varable (respose varable). Geerall, the value of the depedet varable for a dvdual s thought to partall expla the value of the depedet varable for that dvdual. 11 1

4 Example Age (cotuous) + smokg (es/o) cacer (es/o) Age ad smokg are explaator or depedet varables; ad cacer s the respose NOTE: uless data are from a radomzed expermet, a observed relatoshp betwee explorator ad respose varables does ot mpl a causal relatoshp. Explorator Data Aalss Raw data: (take from case geder school wrte math esteem cof Varable ame case geder school wrte math esteem cof Descrpto ad codg partcpat detfcato umber 1 = female, = male tpe of hgh school: 1 = all female, = all male, 3 = coed wrtg score o the Natoal Assessmet of Educatoal Progress test math score o the Natoal Assessmet of Educatoal Progress test respose to the statemet, "O the whole, I am satsfed wth mself."; 1 = strogl dsagree, = somewhat dsagree, 3 = somewhat agree, 4 = strogl agree respose to the questo "How do ou feel about partcpatg class dscussos." 1-1 Lkert scale: 1= ot at all cofdet, 1 = ver cofdet Data Vsualzato Vertcal bar plot Data Vsualzato Horzotal bar plot Cout 5 school 1 = all female = all male 3 = coed 1 1 geder Cout 15 1

5 Data vsualzato Pe chart Data Vsualzato Hstogram % 1 8 8% 34% 4 3 All female All male Coed wrte Data Vsualzato Box plot 1 M. 1st Qu. Meda Mea 3rd Qu. Max Data Vsualzato Box plot geder: 1 geder: math Mea Meda cotas mddle 5% of the data math

6 Data Vsualzato Scatter plot We wll revst ths topc Summato Notato 34 Let 1,, 3,, be measuremets from the quattatve data set Y. math wrte 1 The defe: o The sum of all the measuremets the data set If Y 8, 81, 3, 3, 77, 9 s a sample of wrtg scores, the , 74 pots 1 o The sum of the squares of the measuremets 1 1 For the wrtg scores, , pots o The sum of the measuremets, quatt squared 1 1 = 1,74 =3, 7, pots Numercal Descrptve Measures Measures of cetral tedec (locato)--- tedec of data to cluster or ceter aroud certa umercal values o Mea---sum of the measuremets dvded b the umber of measuremets the data set Sample mea,, s calculated as 1 3 4

7 For the wrtg scores sample pots Populato mea, (mu), s calculated as N 1 where N s the sze of the populato N o Meda---the mddle umber whe the measuremets are arraged order What s the mddle measuremet for the sample of wrtg scores? 8, 81, 3, 3, 77, 9 77, 81, 8, 9, 3, 3 If the umber of observatos s eve, the meda s the mea of the mddle two umbers M 88 pots If the umber of observatos s odd, the meda s the mddle umber Use ˆM for a sample meda ad use M for a populato meda 5 Shape Numercal Measures of Varablt (Spread) Used cojucto wth measures of cetral tedec to more full summarze a data set

8 Rage---largest measuremet (max) mus the smallest (m) measuremet Note: eas to compute, but beware that two data sets ca have the same rage, but qute dfferet varablt Example: Let X = {1, 5, 5, 5, 5, 5, 5, 9} versus Let Y = {1,, 3, 45, 5, 7, 85, 9} The rages for both sets of data are 9 1 = 8. The secod data set (Y), however, s clearl more varable. 9 3 Sample varace---deoted as s ; equals the sum of the squared dstace from the mea dvded b 1 s 1 1 Sample stadard devato---s the postve square root of the sample varace Populato varace---deoted as (sgma squared); calculated usg populato data; sample mea s replace wth ; 1 s replace wth N Populato stadard devato---deoted as ; calculated as the postve square root of s s For the data the rage examples, the stadard devatos are: Tr to use the gve sx s x data to calculate the stadard devatos ad see f ou get the s s correct aswers. 31 3