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Descriptive statistics PG.ppt
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- 2. Manikandan 2 What isintended? Appropriate use of summary statistics When to use which statistic? What is not intended ? To scare you with the mathematical notation and statistical jargon
- 3. Manikandan 3 How toget thro’ statistics with minimal difficulty.... Keep up with the class – the classes will be extremely cumulative. Develop an understanding of the concept – work out the problems yourself Spend quality time in studying – spending five hours on two days before exam is not as effective as spending one hour ten days Look at the assigned material before lecture, review the covered material after lecture
- 4. Manikandan 4 Do nothesitate to ask questions
- 5. Manikandan 5 If youthink you can do a thing or think you can’t do a thing, you’re right. - Henry Ford
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- 7. Manikandan 7 Statistics : Aset of methods for organising, summarising and interpreting information. Population : The set of all individuals of interest in a particular study Sample : Set of individuals selected from a population, usually intended to represent the population
- 8. Manikandan 8 Types ofstatistics DESCRIPTIVE STATISTICS Describing a phenomena Frequencies How many… Basic measurements Meters, seconds, cm3, IQ INFERENTIAL STATISTICS Inferences about phenomena Hypothesis Testing Proving or disproving theories Confidence Intervals If sample relates to the larger population Correlation Associations between phenomena Significance testing e.g diet and health
- 9. Manikandan 9 Parameter : Avalue, usually a numerical value, that describes a population. Variable : Characteristic of an element whose value may differ from element to element Data : Measurements that are collected, recorded & summarised for presentation, analysis & interpretation
- 10. Manikandan 10 Types ofData Data Qualitative Quantitative Discrete Continuous Ordinal Nominal
- 11. Manikandan 11 Scales ofdata measurement Nominal scale : Uses names or tags to distinguish one measurement from another Each measurement is assigned to one of the limited number of categories Does not imply magnitude of individual measurement Cannot be ordered one above the other
- 12. Manikandan 12 Examples ofnominal scale : Gender (male/female) Religion (Hindu, muslim, christian, sikh)
- 13. Manikandan 13 Types ofData Nominal Proportion Expressed as: 10% Christians 18% Muslims 72 % Hindus 18 10 72
- 14. Manikandan 14 Ordinal Scale Data can be placed in a meaningful order No information about the size of the interval No conclusion can be drawn about whether the difference between the first & second category is the same as second & third Examples : Stages of cancer – I, II, IIIa, IIIb and IV
- 15. Manikandan 15 Types ofData Ordinal Scores, ranks How do you rate the pain after the analgesic? Unbearable Very painful Mild pain No pain Painful Data can be arranged in an ORDER and RANKED Expressed as:
- 16. Manikandan 16 Interval Scale A numerical unit of measurement is used Difference between any two measurements can be clearly identified There is no true zero point No meaningful ratio can be got as there is no absolute zero
- 17. Manikandan 17 Example ofinterval scale Measurement of body temperature in celsius The difference bet. 100 & 90oC is the same as between 50 & 40oC.True zero point is absent as temp. can be below zero (-10oC). No meaningful ratio can be got – 100oC is not twice as hot as 50oC.
- 18. Manikandan 18 Ratio Scale Similar to interval scale Also has a absolute zero, and so meaningful ratios do exist. Examples : Most biomedical variables - weight, blood pressure, pulse rate.
- 19. Gitanjali 19 Nominal MaleFemale Ordinal Short Medium Tall Ratio Measure exact height How do you measure?
- 20. Manikandan 20 What isfrequency distribution? The organization of raw data into several classes using frequency tally. e.g. Height (cm) No. of students 121-125 5 126-130 17 131-135 25 136-140 30 141-145 20 146-150 3 Total 100 0 5 10 15 20 25 30 Frequency Height (cms)
- 21. Manikandan 21 Features ofdistributions When you assess the overall pattern of any distribution (which is the pattern formed by all values of a particular variable) look for: number of peaks general shape (skewed or symmetric) centre spread
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- 24. Manikandan 24 Central tendency The point in the distribution around which the data are centered e.g. mean, mode, median
- 25. Manikandan 25 Measures ofCentral Tendency Arithmetic mean: Sum of all values divided by number of observations 1 2 5 3 4 5 8 Mean = 28/7 = 4
- 26. Manikandan 26 Geometric Mean nthroot of the product of the observations When to use geometric mean? When data is measured on logarithmic scale (eg) Dilution of small pox vaccine
- 27. Manikandan 27 Measures ofCentral Tendency Mode Most common value observed 1 2 5 3 4 5 8 1 2 3 4 5 5 8 Mode = 5 For nominal data MODE is the most appropriate measure
- 28. Manikandan 28 Measures ofCentral Tendency Median Value that comes half-way when the data are ranked in order 1 2 5 3 4 5 8 1 2 3 4 5 5 8 Median = 4 For ordinal data only MODE and MEDIAN can be used
- 29. Manikandan 29 Which measureof central tendency is best with a particular set of observations? This depends on Scale of measurement Distribution of observations
- 30. Manikandan 30 Guidelines forusing measures of central tendency The mean is used for numerical data and for symmetric distribution. The median is used for ordinal data or for numerical data if the distribution is skewed. The mode is used for bimodal distribution. The geometrical mean is used for observations measured on a logarithmic scale.
- 31. Manikandan 31 Mean isnot enough Take 2 populations A & B A consists of scores 10,10,10,10,10 B consists of 5,15,5,15,10 Mean in both cases is 10, but the distributions are different Hence a measure of variation is required in addition to measure of central tendency
- 32. Manikandan 32 Dispersion (Spread) Theextent to which data are tightly clustered around the central tendency e.g. range, variation, standard deviation Measure of uncertainty
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- 34. Measures of Dispersion Range:Difference between lowest and highest scores in a set of data SD: describes the variability of observations about the mean SEM: describes the variability of means 80, 70, 80, 5, 2, 3,1 Range=80-1=79 80, 6, 7, 30,12, 2,1 Range=80-1=79 80, 70, 80, 5, 2, 3,1 S.D.= 34.4 ± 39.7 80, 6, 7, 30,12, 2,1 S.D.= 19.7 ± 28.3 80, 70, 80, 5, 2, 3,1 SEM= 34.4 ± 15.0 80, 6, 7, 30,12, 2,1 SEM= 19.7 ± 10.7
- 35. Percentiles Percentage of adistribution that is equal to or below a particular number When to use percentiles? Compare an individual value with a norm (eg) Interpret physical growth charts
- 36. Interquartile range Difference between25th and 75th percentiles, also called the first and third quartile Contains the central 50% observations When to use interquartile range? Describe central 50% of distribution (regardeless of shape) For skewed distribution, better than S.D for describing the dispersion
- 37. Gitanjali 37 Normal(Gaussian) Data are symmetrically distributed on both sides of the mean Forms a bell shaped curve in a frequency distribution plot Non-normal (Non-Gaussian) Data are skewed to one side Bimodal, Poisson, Rectangular Types of Distribution
- 38. Gitanjali 38 Normal (Gaussian)Distribution Frequency Parameter
- 39. Gitanjali 39 Normal (Gaussian)Distribution Characteristics: Symmetric Unimodal Extends +/- infinity Area under the curve=1 Described by mean and SD 95% of observations lie within 1.96 SD on either side of the mean
- 40. Gitanjali 40 Non NormalDistribution Some distributions fail to be symmetrical If the tail on the left is longer than the right, the distribution is negatively skewed (to the left) e.g. No. of times a child with diarrhoea passes stool If the tail on the right is longer than the left, the distribution is positively skewed (to the right) e.g. No of alleles responsible for a polymorphism
- 41. Gitanjali 41 Can weknow the shape of the distribution without actually seeing it ? The mean is smaller than 2 S.D the observations are probably skewed. If the mean and median are equal, the distribution is symmetric. If the mean is larger than median, the distribution is skewed to right. If the mean is smaller than median, the distribution is skewed to left.