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Corso di STATISTICA Prof. Giovanni LATORRE e-mail: g.latorre@unical.it

Corso di STATISTICA Prof. Giovanni LATORRE e-mail: g.latorre@unical.it sito web: www.ecostat.unical.it / latorre /. Statistics in Medicine Robert H. Riffenburgh Ed. Academic Press Price: 53,95€ su Amazon. Steps in a scientific process to increase knowdlege : observe ;

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Corso di STATISTICA Prof. Giovanni LATORRE e-mail: g.latorre@unical.it

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  1. Corso di STATISTICA Prof. Giovanni LATORRE e-mail: g.latorre@unical.it sito web: www.ecostat.unical.it/latorre/

  2. Statistics in Medicine Robert H. Riffenburgh Ed. Academic Press Price: 53,95€ su Amazon

  3. Steps in a scientificprocess to increaseknowdlege: observe; gather data; describe; explain; predict. Scienceis a set of facts and theoriesbaseduponinformation obtainedwith Scientific Method Characteristics of the Scientific Method: a) the Method has to beobjectiveor unbiased ; b) the Methodshould involve the control of variables; c ) the Method should be repeatable; d) the Method shouldallow the accumulation of results.

  4. ElementaryConcepts Statistical Unit or Unit Population Sample Sample Survey Experimental Design Variable: Discrete, Continuous (quantitative), Categorical (qualitative) Data: Discrete, Continuous, Categorical

  5. Example In the GynecologicalDepartmenteach woman wasaskedabout the number of live birthstheyhaddelivered so far. Answers: Raw Data 3 1 3 2 2 0 2 1 5 4 2 2 3 1 1 2 2 0 2 1 4 2 1 2 1 4 3 2 1 3 0 4 3 2 0 3 2 2 1 2 3 1 0 2 2 1 2 2 1 3 Thisis an example of discrete variable and discrete data.

  6. Frequency Distribution Tabulated Data

  7. FrequencyHistogram

  8. Volume of Prostate in 300 patients (VOL in ml) – Raw Data Thisis an example of continuousvariable and continuousdata.

  9. Frequency Distribution Tabulated Data

  10. Frequency Distribution DRE = digital rectal examination Thisis an example of categoricalvariable and categoricaldata.

  11. Frequency Distribution of the Volume of Prostate in 300 Patients

  12. 55

  13. 55

  14. 0,50

  15. 0,50

  16. Symbols X = Quantitative Variable (i.e.: N° of births per woman, Volume of Prostate per patient) xi = Value of X in the i-th out of nunit x1, x2, …. , xi, …. ,xn= Data (they can either be: Population or Sample Data)

  17. Location Measures SummationSign: Properties: Ifk=1/a :

  18. ArithmeticMean: WeightedMean:

  19. Also: Examples: N° of Live Births per Woman: M = (3 + 1 + 3 + 2 +…… + 2 + 2 + 1 + 3) / 50 = 1,96; alternatively: M = (0*5 + 1*12 + 2*19 + 3*9 + 4*4 + 5*1) / 50 = 1,96; alternatively: M =(0*0,10+1*0,24+2*0,38+3*0,18+ 4*0,08+5*0,02)=1,96 2) Volume of Prostate per Patient: M = (32,26+25,59+….+34,40+25,00+15,80)/300 = 36,30427; alternatively: M=(10*42+30*166+50*56+70*28+90*7+110*1)/300=36,33333; alternatively: M=(10*0,14+30*0,55+50*0,19+70*0,09+90*0,02+110*0,00)=35,5.

  20. Median • Letx1, x2, …. , xi, …. ,xn, nobservations on the variableX and y1, y2, …. , yi, …. , yn the same data arranged in increasingorder, then: • ifnis an oddnumber: Median = Me = y(n+1)/2 • ifnis an evennumber: Median = Me = [ yn/2 + y (n/2)+1 ]/2 • Examples: • N° of Live Births per Woman: 3 1 3 2 2 ….. 1 2 2 1 3 • arranged in increasingorder: • 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 • 3 3 3 3 3 3 3 3 3 4 4 4 4 4; • Median = Me = (2 + 2)/2 = 2. • 2) Volume of Prostate per Patient: 32.26, 25.59, 62.06,….., 15.80 arrangedin increasingorder: 3.30, 6.50, 6.90, 7.17,….,98.09, 114.03; • Median = Me = (y50 – y51)/2 = (21,38 + 21,50) / 2 = 21.44

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