ARA0103 A�fer�afr��i - PowerPoint by HC12030702736

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									                   TFG0152 Tölfræði
                           Fyrirlestur 2
                   Kafli 1 “Statistics”/Tölfræði

 individuals/einstaklingar
 objects/hlutir
 events/atburðir

06/03/2012                   Dr Andy Brooks        1
               5 kr. peningur: hvað viltu?



Eyða        32%
Halda áfram 65%
Veit ekki             3%



     skífurit/pie chart

  06/03/2012               Dr Andy Brooks    2
lýsandi tölfræði                               ályktunartölfræði
               Two kinds of statistics
• Descriptive statistics: collecting, describing and presenting
  sample data. (tíðni, meðaltal, staðalfrávik,...)
• Inferential statistics: drawing conclusions about populations.
  (álykta um þýði á grunni úrtaks, tölfræðipróf,...)
• A population/þýði is a collection of individuals or objects or
  events whose properties are to be analyzed.
• A sample/úrtak is a subset/hlutmengi of the population.

  Iceland has a population of 300,000 but how many
  Icelanders responded to the question about the 5 kr. coin?
  10 eða 100 eða 10.000?
                     Alltaf, þu verður að vita af úrtaksstærð.
  06/03/2012               Dr Andy Brooks                      3
              Definitions/Skilgreiningar
Variable/breyta: A characteristic about each individual element of a
population or sample. (aldur, hæð, þyngd,…)
Data (singular): The value of the variable associated with one
element of a population or sample (this value may be a number, a
word, or a symbol).                                              gögn
Data (plural): The set of values collected for the variable from each
of the elements belonging to the sample.
Experiment (tilraun): A planned activity whose results yield a set of
data.
Parameter (þýðiseinkenni): A numerical value summarizing all the
data of an entire population.
Statistic (úrtakseinkenni): A numerical value summarizing the
sample data.
 06/03/2012                  Dr Andy Brooks                        4
 The university rektor is interested in knowing
 the average height of students at HA.
1. The population is the height of every student at the university.
2. A sample is any subset of that population (t.d. heights are determined
   for only 10 students).
3. The variable is the height of each student.
4. One piece of data would be the height of an individual student.
5. The data would be the set of values of the variable in the sample.
6. The experiment would be the method used to select the students
   forming the sample and determining the height of each student in the
   sample.
7. The parameter of interest is the average height of the students at the
   university.
8. The statistic is the average height for students in the sample.
 06/03/2012                      Dr Andy Brooks                             5
 Tegundir breyta/Types of variables
                                        Discrete
                                           rofin      age, number of modules
                                                       aldur, hve mörg námskeiðar


                                        Continuous
               Quantitative                samfelld      weight, height
Variable          megindleg
                                                          þyngd, hæð
 breyta
                                        Nominal
                                        nafnbreyta     red, blonde,brown,black
                 Qualitative                             rautt, ljóshærð, brúnt, svart
                   eigindleg

                                        Ordinal        hot, warm, cold
 ekki hægt að reikna út meðaltal         raðbreyta       hot>warm>cold          í röð
06/03/2012                         Dr Andy Brooks
                                                         heitur>hlýr>kaldur        6
             Gengur ekki...

 rautt  ljóshær ðbrúnt  svart
                4

     heitur  hlýr  kaldur
                3
                                  Interactivity 1-B
06/03/2012       Dr Andy Brooks                       7
     Collecting data/Að safna gögn
1.    Define the objectives of the survey or experiment.
      Skilgreina markmið könnunar/tilraunar.
         •    Estimate average household income.
         •    Compare the effectiveness of a new drug.
2.    Define the variable and the population.
      Skilgreina breytu og þýði.
         •    Total income for each household in the country
         •    Recovery time for HA students with a headache.
3.    Define the data-collection and data-measuring
      devices/mælitæknar.
         •    sample size/úrtaksstærð, sampling procedures/úrtaksgerð
         •    questionnaire/spurningalisti, interview/viðtal, telephone/sími,...
4.    Define the appropriate descriptive (súlurit?) or inferential
      data-analysis techniques (t-próf?).

                                                     “household income”
 06/03/2012                         Dr Andy Brooks       www.google.com            8
Experiment or observational study?
   Tilraun eða áhorsfathugun?
• In an experiment the investigator controls the
  environment and then measures the effect on
  the variable under study.
     – Subjects U1-U10 take the usual drug.
     – Subjects N1-N10 take the new drug.
     – Measure the recovery time from headaches.
• Surveys/kannanir are observational studies
  where the investigator samples the population of
  interest.
     – A census/manntal involves getting data for the entire
       population.
     – Oft er ekki raunhæft að athuga allt þýðið, bara afla
       upplýsinga um úrtak úr því.
06/03/2012                 Dr Andy Brooks                      9
                     Random sampling
                     Tilviljunarval í úrtak                   forðast skekkju
• It is important that samples are taken randomly to avoid bias.
    – People answering questionnaires may represent a self-
      selecting/sjáfval group rather than a random sample.
         • A questionnaire about satisfaction with hospital doctors may only
           attract responses from people who are dissatisfied/óánægð.
    – Selecting people because they are more accessible will result in
      a biased sample/skekkt úrtak.
         • Interviewing HA students will not be representative/ekki dæmigert of
           the population of all university students á Íslandi.
• Simple random sampling is the most common method.
   – Every element in the population has an equal probability of
     being chosen.
   – Investigators can use a random-number generator on a
     computer (over the internet) or a table of random numbers.
                        http://www.graphpad.com/quickcalcs/randomSelect1.cfm
06/03/2012                        Dr Andy Brooks                               10
                Probability and statistics
                   Líkindi og tölfræði
• Probability/líkindi
     – Questions are answered about a sample based on
       knowing the properties of the population/þýði.
             • Suppose 15 students have brown hair and the other 85 have
               black hair and that we randomly select 10 students. What is
               the probability that 3 of the 10 students have brown hair?
• Statistics/tölfræði       að álykta
     – A sample/úrtak is drawn to infer conclusions about
       the population.
             • Suppose ten students are randomly selected from 100
               students. Three of the students from the sample of 10 have
               brown hair. What percentage of the 100 students have brown
               hair?
                                                   estimate/spágildi
06/03/2012                        Dr Andy Brooks                         11
              Variability in data
             Breytileiki í gögnum
• There is always variability in data that is
  measured./Breytileiki er til alltaf.
• A 0.5L can of Coke may contain a little under
  (0,49L), a little over(0,51L), or exactly 0,5L.
• In manufacturing processes, it is important to
  control and reduce unwanted variability.
• Measuring/að mæla and describing/að skýra frá
  variability is one of the primary objectives of
  statistics.
                  meðaltal og staðalfrávik
06/03/2012           Dr Andy Brooks             12

								
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