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## Statistics 3090

by: Hannah Stephens

59

0

9

# Statistics 3090 Stat 3090-005

Hannah Stephens
Clemson

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These notes cover what we went over during the first and second weeks of class as well as notes from the book.
COURSE
PROF.
Paul J. Cubre
TYPE
Class Notes
PAGES
9
WORDS
CONCEPTS
Statistics, Intro to Business Statistics, Clemson University
KARMA
25 ?

## Popular in Statistics

This 9 page Class Notes was uploaded by Hannah Stephens on Friday January 22, 2016. The Class Notes belongs to Stat 3090-005 at Clemson University taught by Paul J. Cubre in Spring 2016. Since its upload, it has received 59 views. For similar materials see Introductory Business Statistics in Statistics at Clemson University.

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Date Created: 01/22/16
Statistics:  Ch.  1  Important  Definitions     • Statistics—Numerical  description  of  data   • Population—A  set  of  all  subjects  or  elements  about  which  we  are   interested  in  making  inferences   • Frame—A  list  containing  all  members  of  a  population   o Very  expensive  to  make,  would  just  be  names   • Census—Data  that’s  gathered  from  the  entire  population     o Things  like  average  income,  number  of  children  et  cetera   • Parameters—Population  parameters  are  facts  about  the  entire   population   • Sample—A  subset  of  the  population  from  which  data  is  gathered   and  used  to  gain  insight  into  the  population   • Sample  Statistic—A  fact  of  characteristic  of  the  sample     Ex.  1:    We  are  interested  in  avg.  income  of  5000(5000 )  random  US   citizens.     *Can’t  go  find  first  5000  people  in  Clemson  because  that’s   not  geographically  random!   ▯ Population:    US  Citizens   ▯ Sample:    5000  random  US  citizens   ▯ Parameter:    the  mean  or  average  income  (µ)   ▯ Sample  Statistic:    X 5000  the  mean  of  the  sample   o Let  X i be  the  income  of  the  ith  member  of  the   sample   o Avg.  or  mean=  x +x 1…+x 2   N                                                                                                                                                                            N   Ex.  2:    A  survey  of  2041  people  revealed  that  68%  of  the  US   population  attends  college.   ▯ This  is  a  sample  statistic  example!     • Descriptive  Statistic—The  collection,  organization,  analysis  and   presentation  of  information.   • Inferential  Statistic—The  science  of  estimating  population   parameters     Ex.  68%  of  Clemson  students  voted  in  last  election.   • Descriptive  Statistic     Ex.  A  poll  of  2000  Clemson  students  show  the  average  price  of  a   Clemson  student’s  car  is  \$20,000.   • Inferential  Statistic  NOT  descriptive  because  of  wording     Ex.  A  website  consultant  conducted  an  eye-­‐tracking  survey  to  determine   whether  people  ignore  purely  decorative  images  when  viewing  a   webpage.    Comparing  products  on  Pottery  Barns  furniture  website  and   a  page  of  televisions  on  Amazon.com.   • The  study  found  consumers  ignore  televisions  on  Amazon   because  they  were  generic  and  less  interesting.    Pottery  Barns   were  more  inclined  to  view  photos  featuring  the  furnit ure  for  a   larger  period  of  time.   1. Identify  the  population:    Online  Consumers   2. What  are  we  studying:    How  long  consumers  view  product  photos   3. Is  the  purpose  of  the  data  collection  to  perform  descriptive  or   inferential  statistics?   a. They  do  not  have  the  money  to  test  every  member  of   statistic  so  they  have  to  estimate  it.   This  is  an  inferential  statistic!!     • Scientific  Method   1. Formulate  a  hypothesis   2. Design  an  experiment     3. Collect  Data   4. Test  or  Validate  hypothesis   5. Reformulate  the  hypothesis  and  redo.     • Ethics   o Studies  are  approved  by  an  institutional  review  board  (IRB)   for  ethical  consideration.   o Informed  Consent—Disclosing  the  details  of  the  study  and   agreement  to  participate.     More  Definitions!!!     • Bias—A  study  favors  a  certain  result   • Researcher  Bias—Researcher  influences  outcome   • Participation  Bias—Participant  influences  the  outcome   • Sampling  Errors—Errors  from  the  way  the  sample  was  chosen     • Dropout  Errors—The  participant  begins  a  study  then  fails  to   complete  the  study   • Non-­‐Sampling  Errors—Errors  arising  from  other  factors  not   involving  the  sample   o Processing  Error—Error  from  collecting  the  data   o False  Reporting—Participant  inaccurately  reports  the  truth   or  non-­‐adheres  and  doesn’t  follow  directions.     Description  Errors  and  Data   1. Confounding  Variables—Variable  that  was  not  controlled   for  or  accounted  for   2. Response  Variable—The  variable  of  interest   3. Explanatory  or  predictor  variable   4. Anything  that  affects  the  response     Ex.      Does  a  GRE  prep  class  help  your  score?   1. A  group  of  students  take  the  GRE   2. They’re  given  a  prep  course  and  retake  the  test   3. Response  variable—Difference  between  tests   4. Explanatory  Variable—Taking  the  prep  course     • Controlled  Experiments   o Experiment  that  attempts  to  control  the  environment  of  the   experiment  so  that  the  effect  of  one  variable  can  be  isolated   o One  of  the  simplest  is  where  there  is  two  groups  (a  control   and  an  experimental  group)   • Treatment—Applied  to  the  experimental  group  and  changes  the   explanatory  variable   • Placebo—A  false  treatment   • Comparative  Experiment—Randomly  assigning  participants  to   either  a  treatment  group  or  a  control  group   • Before  &  After  Study—Control  group  is  initially  observed.    A   treatment  is  applied  to  control  group.   o Then  group  is  observed  again   • Double  Blind  Study—Subjects  and  evaluators  are  not  told  what   group  they  are  in   • Observational  Studies—Observational  data.    Data  from  observing   an  outcome  of  usually  a  non-­‐reputable  event/experiment.     Ex.    A  study  is  conducted  to  determine  if  chocolate  can  trigger   migraines.   o 12  migraine  prone  subjects  were  given  peppermint  laced   chocolate  candy  and  8  were  given  peppermint  based  placebos   o 5  subjects  from  the  group  given  chocolate  developed  migraines   o No  one  from  other  group  developed  migraines   o Is  a  controlled  experiment!!   o Response  Variable:    Number  of  migraines   o Explanatory/Predictor  Variable:    Amount  of  chocolate     • Levels  of  Measurement     o Nominal  Data—Represents  whether  a  variable  possesses   some  characteristics.  (Encode)   o Ordinal  Data—represents  categories  that  have  an   associated  order   o Both  examples  of  Qualitative  Data!!   • Qualitative  Data—Measures  can  change  in  kind,  but  not  in  degree.   o Consists  of  labels  or  descriptors  that  does  not  have  natural   numerical  values   o Nominal  or  ordinal   • Interval  Data—Data  is  ordered  and  differences  are  meaningful   • Ratio  Data—Meaningful  zero  point  and  the  ratio  of  two  data   points  is  meaningful     • Quantitative  Data—Measurement  that  change  in  magnitude  from   trial  to  trial  such  that  order  or  ranking  can  be  applied.   o Internal  or  ratio   o Quantitative  Variable  can  be  measured  using  a  naturally   occurring  numerical  sale.   Ex.    The  temp  of  patient  in  Celsius,  Fahrenheit,  and  kelvin.   • Degrees  in  Celsius  interval   • Degrees  in  Fahrenheit  interval   • Degrees  in  Kelvin  ratio     Ex.  The  age  an  avg.  person  marries.       -­‐Ratio   Ex.  The  current  time     -­‐On  12  hr.  clock—Interval       -­‐Date  is  common  era—Interval         Types  of  Quantitative  Data:   • Discrete—Observations  are  restricted  to  a  set  of  values  that  have   groups   • Continuous—Data  that  takes  any  value  within  some  interval  are   continuous     Sampling   • Probability  Sampling—Enable  probable  errors  to  be  completed   • Non-­‐Probability  Sampling—Cant  compute  errors   o 2  Types:    Judgment  sampling  and  convenient  sampling     o Convenience—Whatever  is  an  easy  set  of  subjects  to  obtain.   o Judgment—When  an  expert  uses  their  experience  to  select   subjects.   Probability  Sampling   o Cluster  Sampling—Divide  population  into  groups.  Then   select  random  groups.   o Stratified  Sampling—Divide  population  into  groups.    Then   select  a  portion  from  each  group.     th • Systematic  Sampling—K  member  of  population  is  selected   • Sampling  with  Replacement—After  each  selection  the  subject  is   returned  to  the  population   • Sampling  without  Replacement—Subject  from  population  is  not   returned                   Process'of'Statistical'Study' ' Procedure:))Conducting)a)Statistical)Study) 1. Determine)the)design)of)the)study.) a. State)the)question)to)be)studied.) b. Determine)the)population)and)variables) c. Determine)the)sampling)method.) 2. Collect)the)data) 3. Organize)the)data) 4. Analyze)the)data)to)answer)the)question) ) Observational)Study—Observes)data)that)already)exist) ) Experiment—generates)data)to)help)identify)causeHandHeffect)relationships)) ) Representative)Sample—Has)the)same)relevant)characteristics)as)the)population) and)does)not)favor)one)group)from)the)population)over)another.) ) Random)Sampling—One)of)the)most)basic)sampling)techniques.))Occurs)when)every) member)of)the)population)has)an)equal)chance)of)being)selected.) ) Stratified)Sampling—A!few)members)of)each)group.)***Members)of)the)population) are)divided)into)2+)subgroups)(strata))that)share)similar)characteristics)(i.e.)age,) gender,)ethnicity).))A)random)sample)from)each)stratum)is)then)drawn.) ) i.e.)divide)the)population)of)college)students)into)strata)based)on)number)of) courses)completed,)then)our)strata)would)be)freshmen,)sophomores,)juniors,)and) seniors.))Then)select)sample)by)choosing)a)random)sample)of)freshmen,)sophomores) and)so)on.) ) Quota)Sampling:))Each!member)of)a)few)groups.))For)example,)if)freshmen)make)up) 40%)of)our)population,)then)we)can)choose)40%)of)our)sample)from)the)freshmen) stratum.) ) Cluster)Sample:))One)chosen)by)dividing)the)population)into)groups)(clusters))that) are)each)similar)to)the)entire)population.))Researcher)then)selects)some)of)the) clusters)randomly.))Consists)of)the)data)collected)from)every)member)of)only)those) clusters)that)are)selected.) ) Systematic)Sampling:))One)chosen)by)selecting)every)nth)member)of)the)population) ) Convenience)Sampling:)Sample)is)“convenient”)for)the)researcher)to)select.)) Members)of)sample)often)have)a)similar)characteristic)and)prone)to)create) nonrepresentative)samples.) ) Types)of)Observational)Studies:) 1.)))CrossHSectional)Study—Data)that)is)collected)at)a)single)point)in)time.) ) 2.))Longitudinal)Study—Data)that)is)gathered)by)following)a)group)over)a)period)of) time) ) ) MetaHanalysis:))Study)that)compiles)info)from)previous)studies.) ) Case)Study—Looks)at)multiple)variables)that)affect)a)single)event.) ) Treatment—Some)condition)that)is)applied)to)a)group)of)subjects)in)an)experiment.) ) Subjects—People)or)things)being)studied)in)an)experiment.) ) Participants—People)being)studied)in)an)experiment) ) Response)Variable—Variable)in)an)experiment)that)responds)to)the)treatment.) ) Explanatory)Variable—Variable)in)an)experiment)that)causes)the)change)in)the) response)variable.) ) Procedure:)Principles)of)Experimental)Design) 1. Randomize)the)control)and)treatment)groups.) 2. Control)for)outside)effects)on)the)response)variable.) 3. Replicate)the)experiment)a)significant)number)of)times)to)see)meaningful) patters.) ) Control)group—A)group)of)subjects)to)which)no)treatment)is)applied)in)an) experiment.) ) Treatment)group—A)group)of)subjects)to)which)researchers)apply)a)treatment)in)an) experiment.) ' Confounding)variables—Factors)other)than)the)treatment)that)cause)an)effect)on)the) subjects)of)an)experiment.) ) Placebo)effect—A)response)to)the)power)of)suggestion,)rather)than)the)treatment) itself,)by)participants)of)an)experiment.) ) Placebo—Substance)that)appears)identical)to)the)actual)treatment)but)contains)no) intrinsic)beneficial)elements.) ) SingleHblind)experiment—Subjects)do)not)know)if)they)are)in)the)control)group)or) the)treatment)group,)but)the)people)interacting)with)the)subjects)in)the)experiment) know)in)which)group)each)subject)has)been)placed.) ) DoubleHblind)experiment—Neither)the)subjects)nor)the)people)interacting)with)the) subjects)know)to)which)grouSp)each)subject)belongs.)

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