1. “Victor Babes” UNIVERSITY OF MEDICINE AND PHARMACY TIMISOARA DEPARTMENT OF MEDICAL INFORMATICS AND BIOPHYSICS Medical Informatics Division www.medinfo.umft.ro/dim 2004 / 2005

2. BIOSTATISTICS STATISTICAL PARAMETERS COURSE 3

3. 1. STATISTICAL INFERENCE 1.1. GENERAL CONCEPTS1.1. GENERAL CONCEPTS –a) population, individual –b) definition: Biostatistics = science of estimating population characteristics and comparing populations –c) methods: census - all individuals; the same timecensus - all individuals; the same time screening - large number; selection criteriascreening - large number; selection criteria sampling - subset of populationsampling - subset of population

4. –d) STATISTICAL INFERENCE EXTENDING PROPERTIES COMPUTED FOR A SAMPLE TO A POPULATIONEXTENDING PROPERTIES COMPUTED FOR A SAMPLE TO A POPULATION –e) REPRESENTATIVE SAMPLE CRITERIA:CRITERIA: –EQUIPROPBABILITY –INDEPENDENCE –f) SELECTION METHODS SIMPLE SELECTIONSIMPLE SELECTION –RANDOM NUMBERS ASSOCIATED MULTIPLE LAYER SELECTIONMULTIPLE LAYER SELECTION MIXED SELECTIONMIXED SELECTION –CLUSTERS

5. 1.2. VARIABLES1.2. VARIABLES –a) DEFINITION: a population characteristic which is studied and measured on all sampled individualsa population characteristic which is studied and measured on all sampled individuals –b) STARTING A STUDY variable selectionvariable selection measurement accuracymeasurement accuracy sample sizesample size –c) TYPES OF VARIABLES: NUMERICALNUMERICAL ORDINAL (rank)ORDINAL (rank) NOMINAL (qualitative)NOMINAL (qualitative)

6. Accuracy – Precision Accuracy: how close to real value Precision: reproductibility Ac.~ok, Pr. low Ac. low, Pr. high

7. 1.3. DATA COLLECTION1.3. DATA COLLECTION –tables –graphs: histogramshistograms piespies lineslines scattergramsscattergrams mapsmaps

9. 2. STATISTICAL PARAMETERS 2.1. EXAMPLE:2.1. EXAMPLE: –study of children development population: 10 years old children, from Timisoara, in 1996population: 10 years old children, from Timisoara, in 1996 size: 400 childrensize: 400 children collected data: height, in cmcollected data: height, in cm accuracy : 1 cmaccuracy : 1 cm –data table and histogram

10. 2.2. TABLE & HISTOGRAM

11. Conclusions:Conclusions: –extreme values - rarely –central values - more often CENTRAL TENDENCY INDICATORSCENTRAL TENDENCY INDICATORS –variability DISPERSION INDICATORSDISPERSION INDICATORS

12. 2.3. CENTRAL TENDENCY INDICATORS a) ARITHMETIC MEAN: a) ARITHMETIC MEAN:

13. b) MEDIANb) MEDIAN –THE VALUE DIVIDING THE SAMPLE INTO TWO EEQUAL PARTS Ex: for odd or even number of elementsEx: for odd or even number of elements Recommended for ordinal variablesRecommended for ordinal variables c) MODEc) MODE –THE MOST FREQUENT –MODAL CLASS –UNI~, BI~ AND MULTIMODAL DISTRIBUTIONS recommended for nominal variablesrecommended for nominal variables

14. d) RELATIVE POSITIONd) RELATIVE POSITION –SYMMETRICAL DISTRIBUTIONS: –X = Me = Mo –ASSYMMETRICAL DISTRIBUTIONS (skewed distributions): –X = the most sensitive –Mo = least sensitive

15. DISPERSION INDICATORS. A.Numerical variables B.Ordinal (rank) variables C.Qualitative variables (proportions)

16. 2.4. DISPERSION PARAMETERS A For NUMERICAL VARIABLES A For NUMERICAL VARIABLES a) Standard deviation sa) Standard deviation s b) Variation coefficientb) Variation coefficient

17. c) NORMAL DISTRIBUTION (GAUSS BELL)

18. d) Intervals with “s”

19. EXAMPLE A STUDY ON CHILDREN SOMATIC DEVELOPMENTA STUDY ON CHILDREN SOMATIC DEVELOPMENT N = 25 children, age 10, Timisoara, 1997N = 25 children, age 10, Timisoara, 1997 mean X = 137 cmmean X = 137 cm standard deviation s = 5 cmstandard deviation s = 5 cm

20. C. NOMINAL VARIABLES Class Proportion (percent)Class Proportion (percent) p i = N i / N (. 100) Proportion standard deviation:Proportion standard deviation:

21. 2.4. SKEWNESS2.4. SKEWNESS –PEARSON’S –  = (Mo - x) / s –assimetry 2.5. KURTOSIS2.5. KURTOSIS –flatness

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