Statistics introduction
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Statistics is useful in medicine for decision making, acquiring new knowledge, and conducting surveys. It is used in areas like diagnosis, treatment, and research studies. Variables found in the human body include height, weight, and blood pressure. Descriptive statistics are used to describe data through measures of central tendency like mean, mode, and median, and measures of variation like standard deviation and histograms. Inferential statistics are used to make conclusions from data through hypothesis testing.
Statistics introduction
- 2. What is statistics ? ` Statistics involves data or information eg. Information regarding a country Information about weather Information on health status Information about a patient Information on normal subjects WHO Unesco CDC
- 3. What is statistics ? Statistics is the science dealing with analysis, presentationcollection, & interpretation of data
- 4. When is statistics useful in day-to-day life weather report in a shop in an examination in match making in lottery
- 5. Weather report rain will be expected in the central area rest of the country most likely will be dry Likelihood, chance Colombo Weather
- 6. In a shop what will you buy? how to select? which one is good? how much is worth? Previous knowledge Banana
- 7. In an examination what is the pass mark? who has sound knowledge & who has poor knowledge? half knowledge, should you pass? performance, cut off point
- 8. In match making in matching two people previous known details details of the family based on these a prediction is made does it always work ??? prediction
- 9. In lottery choice between number to win and number to lose previous experience guesswork prediction prediction
- 10. Summary Likelihood Chance Previous knowledge Cut off point Guesswork Prediction Probability Statistics
- 11. When is statistics useful in medicine ? decision making on diagnosis eg. a patient with headache • does all signs and symptoms fit into already known diseases • previous knowledge, experience from previous patients • guesswork • does it work ???
- 12. When is statistics useful in medicine ? decision making on treatment eg. a patient with headache • which drug to be given among A,B,C analgesics • previous knowledge, experience of using them • guesswork • does it work ???
- 13. When is statistics useful in medicine ? acquiring new knowledge eg. how does blood flow against gravity • planning a study • doing the study • arriving at conclusions
- 14. When is statistics useful in medicine ? surveys of diseases in a population eg. how far malaria has spread • planning a study • doing the study • arriving at conclusions
- 15. Summary Statistics is useful in medicine in different areas Research studies use statistics in data analysis
- 16. Variables Task: write 3 variables and 1 constant found in the human body eg. Height as a variable almost all biological features show variation it is extremely difficult to find a feature which does not vary???
- 17. Variables What is basis of this ‘variation’ ? fundamentally genetical but environmental factors are always important
- 18. Variables height weight blood pressure pulse rate body temperature size of a swelling social status: income
- 19. Variables response to a question Do you like to treat a patient with AIDS? Y / N / undecided Do you agree with what I say in this lecture? Y/N/? Attitudes - Opinions - What we feel
- 20. Types of variables a) nominal b) ordinal c) interval d) ratio
- 21. Nominal variables Qualitative classification Distinct categories No ranking eg: gender, race, color, city males females
- 22. Ordinal variables Qualitative classification Categories have order or rank eg. Socioeconomic status • Upper • Middle (upper & lower) • Lower
- 23. Interval & ratio variables Quantitative classification Interval variable has no absolute zero eg. T°C Ratio variable has absolute zero eg. Kelvin temp, time, space
- 24. Methods of collecting data questionnaire interview measurement using special instrument BHT studies (Bed Head Ticket) Postal surveys
- 25. Different types of sampling Simple random sample Systematic sampling Stratified sampling Cluster sampling Population Sample
- 26. Simple random sample each subject in the population has an equal chance of getting selected to the sample each subject is given a number subjects selected using random numbers use random tables or computer generated random numbers random table 20 17 42 28 31 17 59 66 38 61 03 51 10 55 92 52 44 25 88 74 49 04 03 08 33 53 70 11 54 48 94 60 49 57 38 65 15 40
- 27. Non-random sample this is a biased sample certain subjects have more probability of getting selected to the sample certain situations randomisation is not possible either due to practical difficulties or difficulty in finding subjects
- 28. Statistical concepts In order to arrive at conclusions data are analysed Conclusions are based on concepts just like geometric theorems
- 29. Descriptive statistics Background information Inferential statistics Hypothesis testing
- 30. Central TendencyCentral Tendency A single value representing a datasetA single value representing a dataset eg. pulse rateeg. pulse rate
- 31. Measures of CentralMeasures of Central TendencyTendency MeanMean (x)(x) averageaverage x =x = ΣΣ xx nn ModeMode commonest value or the most frequentcommonest value or the most frequent valuevalue MedianMedian central valuecentral value - -
- 32. exampleexample In a datasetIn a dataset 1 2 2 3 3 3 4 4 51 2 2 3 3 3 4 4 5 mean = 3mean = 3 mode = 3mode = 3 median = 3median = 3
- 33. VariationVariation Central value gives only theCentral value gives only the representative figurerepresentative figure variation of data set is not shownvariation of data set is not shown
- 34. Measures of VariationMeasures of Variation RangeRange from minimum to maximumfrom minimum to maximum Charts or graphsCharts or graphs bar chartbar chart histogramhistogram
- 35. Bar chartBar chart 0 5 10 15 20 25 30 35 frequency males females Patients with headache generally used for categorical variables
- 36. Pie chartPie chart Patients with headache males females
- 37. Multiple bar chartMultiple bar chart 0 50 100 150 200 250 average income 1986 1987 1988 average income in 3 years male female
- 39. Frequency distribution curveFrequency distribution curve
- 40. Standard deviation (SD)Standard deviation (SD) This is an accurate measure ofThis is an accurate measure of variabilityvariability Calculated for continuous dataCalculated for continuous data Based on deviations of data from theBased on deviations of data from the meanmean
- 41. Standard deviation (SD)Standard deviation (SD) If the data set isIf the data set is 1, 2, 2, 3, 3, 3, 4, 4, 51, 2, 2, 3, 3, 3, 4, 4, 5 mean will be 3mean will be 3 deviations are calculateddeviations are calculated (3-1), (3-2), (3-2), (3-3), (3-3), (3-4),(3-1), (3-2), (3-2), (3-3), (3-3), (3-4), (3-4), (3-5)(3-4), (3-5) 2, 1, 1, 0, 0, 0, -1, -1, -22, 1, 1, 0, 0, 0, -1, -1, -2 deviations are squareddeviations are squared 4, 1, 1, 0, 0, 0, 1, 1, 44, 1, 1, 0, 0, 0, 1, 1, 4 mean of squared deviation is calculated= 12/9mean of squared deviation is calculated= 12/9 square root is taken= root of 12/9square root is taken= root of 12/9
- 42. Standard deviation (SD)Standard deviation (SD) datadata deviationsdeviations square of deviationssquare of deviations 11 3-13-1 22 44 22 3-23-2 11 11 22 3-23-2 11 11 33 3-33-3 00 00 33 3-33-3 00 00 33 3-33-3 00 00 44 3-43-4 -1-1 11 44 3-43-4 -1-1 11 55 3-53-5 -2-2 44 12/9 variance = 12/9 SD = √12/9
- 43. Standard deviation (SD)Standard deviation (SD) In the previous example of 292 subjectsIn the previous example of 292 subjects meanmean = 29.41 yrs= 29.41 yrs SDSD = 3.35 yrs= 3.35 yrs minimum = 23.00 yrsminimum = 23.00 yrs maximum= 37.83 yrsmaximum= 37.83 yrs (n = 292)(n = 292)
- 44. Coefficient of variationCoefficient of variation (COV)(COV) SDSD COV = ---------COV = --------- X 100 %X 100 % meanmean COV has no unitsCOV has no units Variations between two variables could beVariations between two variables could be compared using COV (eg. Blood pressure andcompared using COV (eg. Blood pressure and pulse rate)pulse rate)
- 45. Normal distributionNormal distribution generally continuous variables in the humangenerally continuous variables in the human body such as height and weight has a definitebody such as height and weight has a definite patternpattern It is a symmetrical, an inverted bell shapedIt is a symmetrical, an inverted bell shaped curvecurve mean, mode and median are similarmean, mode and median are similar this type of distribution is calledthis type of distribution is called “normal“normal distribution”distribution”
- 46. Normal distributionNormal distribution VAR00001 9.08.07.06.05.04.03.02.01.0 12 10 8 6 4 2 0 Std. Dev = 2.02 Mean = 5.0 N = 50.00
- 47. Normal distributionNormal distribution VAR00001 9.08.07.06.05.04.03.02.01.0 12 10 8 6 4 2 0 Std. Dev = 2.02 Mean = 5.0 N = 50.00 •symmetrical •bell-shaped •mean, mode, median similar •also called a Gaussian curve