Descriptive statistics PG.pptx in statistics
- 2. Manikandan 2 What is intended? 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 to get 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 not hesitate to ask questions
- 5. Manikandan 5 If you think you can do a thing or think you can’t do a thing, you’re right. - Henry Ford
- 7. Manikandan 7 Statistics : A set 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 of statistics 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 : A value, 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 of Data Data Qualitative Quantitative Discrete Continuous Ordinal Nominal
- 11. Manikandan 11 Scales of data 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 of nominal scale : Gender (male/female) Religion (Hindu, muslim, christian, sikh)
- 13. Manikandan 13 Types of Data 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 of Data 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 of interval scale Measurement of body temperature in celsius The difference bet. 100 & 90o C is the same as between 50 & 40o C.True zero point is absent as temp. can be below zero (-10o C). No meaningful ratio can be got – 100o C is not twice as hot as 50o C.
- 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. tanjali 19 Nominal Male Female Ordinal Short Medium Tall Ratio Measure exact height How do you measure?
- 20. Manikandan 20 What is frequency 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 of distributions 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
- 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 of Central 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 nth root 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 of Central 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 of Central 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 measure of central tendency is best with a particular set of observations? This depends on Scale of measurement Distribution of observations
- 30. Manikandan 30 Guidelines for using 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 is not 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) The extent to which data are tightly clustered around the central tendency e.g. range, variation, standard deviation Measure of uncertainty
- 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 a distribution 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 between 25th 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. tanjali 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. tanjali 38 Normal (Gaussian) Distribution Frequency Parameter
- 39. tanjali 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. tanjali 40 Non Normal Distribution 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. tanjali 41 Can we know 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.