Se ha denunciado esta presentación.
Se está descargando tu SlideShare. ×

# Data DistributionM (1).pptx

Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Anuncio
Próximo SlideShare
Basic statistics
Cargando en…3
×

1 de 55 Anuncio

# Data DistributionM (1).pptx

Statistics

Statistics

Anuncio
Anuncio

## Más Contenido Relacionado

Anuncio

### Data DistributionM (1).pptx

1. 1. DATA DISTRIBUTION AND PRESENTATION Nada Mohamed Radwan Elhadidy 1
2. 2. Agenda Data Distribution Identify the concept of probability Recognize Normal distribution curve and its characteristics Calculate the probabilities as areas under the curve by using Standardized Normal Distribution table Deviation from normality
3. 3. Introduction • Every variable to be analyzed in a dataset has both type and distribution. • Distribution are the building blocks of statistics, since the correct identification of a distribution usually allows the statistician to choose which proper statistical test should be used to test statistical significance.
4. 4. Distributions ■ Distributions are statistical constructs that attempt to describe how probability behaves in certain regions. Briefly, probability is the likelihood of specific event happening. Example: What is the probable percentage of students scored less than 49? It is 40.0 % of the students 4 Handbook of clinical research :design, statistics, implementation, 2014, flora et al
5. 5. Normal (Gaussian) Distribution ■ It is the most important probability distribution. ■ It is important tool in analysis of epidemiological data & management science. ■ It is called “Gaussian” The noted statistician professor Gauss developed this. What does a Gaussian distribution tell us? 5
6. 6. Normal (Gaussian) Distribution 6
7. 7. Normal (Gaussian) Distribution 7
8. 8. Normal (Gaussian) Distribution 8 Characteristic of the normal distribution curve: 1. It is bell shaped. 2. The curve rises to its peak at the mean where mean =median = mode. 3. Symmetrically distributed on both sides of mean
9. 9. Normal (Gaussian) Distribution 9 Characteristic of the normal distribution curve: 4. The area starts from -ve to +ve and the two edges of the curve do not meet X line except at infinity 5.The X axis is divided according to standard deviation (SD) into about 3 SD.
10. 10. Normal (Gaussian) Distribution 10 Characteristic of the normal distribution curve: 6. The values lying within the interval (µ ± 1σ) (χ̅± SD) = 68% of all values (µ ± 2σ) (χ̅± 2SD) = 95% of all values. (µ ± 3σ) (χ̅± 3SD) = all values (99.7%).
11. 11. Normal (Gaussian) Distribution 11 Characteristic of the normal distribution curve: 7. The area under normal curve above the X-axis = 100.0%, each half = 50.0%.
12. 12. Normal (Gaussian) Distribution E.g. According to Gaussian distribution, Determine the intervals and calculate the number of observations in each interval for the normally distributed dataset, n= 90, χ̅= 50, SD= 5? Intervals (χ̅± 1 SD) = 50 ± 5 (45 to 55) includes 68.2% of all values equal (61 observations) (χ̅± 2 SD) = 50 ± 2(5) (40 to 60) includes 95.4% of all values equal (86 observations) (χ̅± 3 SD) = 50 ± 3(5) (35 to 65) includes 99.7% of the values equal (90 observations) 12
13. 13. Standardized Normal Distribution: Calculating Probabilities 13
14. 14. Standardized Normal Distribution: Calculating Probabilities 14
15. 15. Standardized Normal Distribution: Calculating Probabilities 15 The test birth weights of 3226 babies in hospital has a mean of 3.4 and with a standard deviation of 0.55. What is the probable percentage of babies scored less than 2.5? ■ Solution: The z score for the given data is, z= (2.5 – 3.4)/0.55= - 1.64
16. 16. Standardized Normal Distribution: Calculating Probabilities 16
17. 17. Standardized Normal Distribution: Calculating Probabilities 17 The test birth weights of 3226 babies in hospital has a mean of 3.4 and with a standard deviation of 0.55. What is the probable percentage of babies scored less than 2.5? ■ Solution: The z score for the given data is, z= (2.5 – 3.4)/0.55= - 1.64 From the z score table, the fraction of the data within this score is 0.050. This means 5.0 % of the babies are within the birthweight less than 2.5.
18. 18. Deviation from normality: Skewed Distribution 18
19. 19. Deviation from normality: Skewed Distribution 19
20. 20. Deviation from normality: Skewed Distribution 20
21. 21. Reasons for non normal data 1. Outliers can cause your data the become skewed. The mean is especially sensitive to outliers. Advise :Try removing any extreme high or low values and testing your data again. 2. Overlap of Two or More Processes Multiple distributions may be combined in your data, giving the appearance of a bimodal or multimodal distribution. Hidden causes Frank causes
22. 22. Reasons for non normal data 3.Insufficient Data  For example, classroom test results are usually normally distributed., if you choose three random students and plot the results on a graph, you won’t get a normal distribution.  You might get a uniform distribution (i.e. 62/ 62/ 63) or a skewed distribution (80 /92/ 99).  Advise : Increase your sample size. 4.Data may be inappropriately graphed.  E.g: graphing people’s weights on a scale of 0 to 1000 lbs, you would have a skewed to the left 5. Values close to zero or natural limit 6. Data Follows a Different Distribution by nature as follow
23. 23. Normality test This can be done by many statistical methods including Kolmogorov-Smirnov test (for large data sets) and Shapiro-Wilk test (for small data sets <50) where data will be considered normally distributed if the test result is non significant (p value > 0.050) and data will be considered non-normally distributed (skewed) if the test result is significant (p value ≤ 0.050) 23
24. 24. Normality test 24
25. 25. The mean age±2 standard deviation of a sample of 100 sample equals 55± 10. Considering that age is normally distributed you are expected that nearly 95 patients will have their age: A.Between 45 and 65 years. B.Between 25 and 85 years. C.Between 35 and 75 years. D.Between 55 and 65 years.
26. 26. Serum cholesterol levels in a group of young adults found to be approximately normally distributed with mean level 170 mg/dl and standard deviation 8 mg/dl. which of the following intervals include approximately 68% of serum cholesterol in this group? A)160-180 mg/dl B)162-178 mg/dl C)150-190 mg/dl D)154-186 mg/dl E)140-200 mg/dl
27. 27. Agenda Tabular presentation Requirements for tabulation Frequency distribution tables Cross tabulations
28. 28. Tabular presentation: Requirements ■ Each table is a separate entity to be easily read and interpret. ■ Title at the top of the table to precisely define the content. ■ The heading gives a brief description of the variable. ■ The body contains the values. ■ Total (row, column, grand). 28
29. 29. Frequency distribution tables: ■ It is a tabular summary of the data showing the frequency of observations in each category together with the percentage (proportion *100). 29
30. 30. Frequency Distribution table: Describing qualitive nominal variable Marital status N(%) Single 6 (37.5) Married 7 (43.8) Divorced 2 (12.5) Widow 1 (6.3) Total 16 Table: Marital status of the study participants Marital status Study paricipants (n=16) N(%) Single 6 (37.5) Married 7 (43.8) Divorced 2 (12.5) Widow 1 (6.3)
31. 31. Frequency Distribution table: Describing qualitive ordinal variable Satisfaction Frequency Cumulative frequency Cumulative percentage Very dissatisfied 2 2 12.5 dissatisfied 3 5 31.3 Satisfied 7 12 75.0 Very satisfied 4 16 100.0 Total 16 Table:: Satisfaction grades of the study participants The cumulative percentage is quite useful to show the percentage below a certain cutoff. Here can highlight percentages of dissatification among study participants is 31.3%
32. 32. Frequency distribution tables: Describing quantative variable ■ 1- Find out the smallest and the largest values of the given data ■ 2- Subsrtact smallest from the largest value (largest – smallest) ■ 3- Choose the proper class interval (e.g. 10) ■ 4- Divide the range by the decided class interval to get the number of classes. ■ 5- Count the frequency in each class interval. 32
33. 33. Frequency Distribution table: Describing quantative variable Table:: Reference table illustrates data from a health center survey Age 18 20 19 19 23 21 18 18 26 22 20 19 20 18 21 19 Table:: Age of the study participants Age Frequency Cumulative frequency Cumulative percentage 18- 8 8 50.0 20- 5 13 81.3 22- 2 15 93.8 24-26 1 16 100.0 Total 16
34. 34. Cross tabulation: Satisfaction level Study participants Total Gender Male Female Very dissatisfied 41 22 63 dissatisfied 24 18 42 Unsure 22 31 53 Satisfied 40 24 64 Very satisfied 15 12 27 Total 142 107 249 Table: Satisfaction level of the provided healthcare services within gender of study participants It is often useful to show the percentage of the categories of one variable by the another variable.
35. 35. Cross tabulation: Khashaba et al. (2017): Risk factors for non-fatal occupational injuries among construction workers: A case – Control study.
36. 36. Graphical presentation: 36
37. 37. Graphical presentation of data nominal ordinal Continous Discrete
38. 38. Agenda
39. 39. Pie chart: For describing qualitative or discrete variables 39 If you have one variable and its data arranged in categories and summarized on a percentage basis (100%), it is suitable to choose a pie chart. A pie chart is a circular statistical graphic, which is divided into slices to illustrate the numerical proportion of each category. Figure: pie chart showing the percentage of type of occupational injury fatalities
40. 40. Simple bar chart: For describing qualitative or discrete variables 40 If you have one variable and its data arranged in categories and summarized on a percentage basis, it is suitable to choose a simple bar chart. Figure: simple bar chart showing the frequency distribution of type of burns in hospital
41. 41. Simple bar chart: For describing qualitative or discrete variables 41 This is a chart with frequency on the vertical axis and category on the horizontal axis. A bar is drawn for each category, its length being proportional to the frequency in that category. The bars are separated by small gaps to indicate that the data are categorical or discrete Figure: simple bar chart showing the frequency distribution of type of burns in hospital
42. 42. Multiple (clustered) bar chart: For describing qualitative or discrete variables 42 If you divide the sample into different (two or more) groups, and you want to compare category proportion within each group (e.g. frequency of girls vs frequency of boys in group A) and you can use the multiple bar chart. Figure: multiple bar chart showing the frequency distribution of girls and boys within groups
43. 43. Multiple (clustered) bar chart: For describing qualitative or discrete variables 43 If you divide the sample into different (two or more) groups, and you want to comparealso the relative sizes of the groups within each category (e.g. frequency of girls in group A vs Group B vs Group C vs group D), you can use the multiple bar chart. Figure: multiple bar chart showing the frequency distribution of girls and boys within groups
44. 44. Component (stacked) bar chart: For describing qualitative or discrete variables 44 If you divide the sample into different (two or more) groups, and you want to compare the relative sizes of the groups within each category(e.g. frequency of blood group A in city X vs city Y vs city Z), you can use the component bar chart
45. 45. Component (stacked) bar chart: For describing qualitative or discrete variables 45 If you divide the sample into different (two or more) groups, and you want to compare category proportion within each group (e.g. frequency of blood group A vs B vs AB vs O in city X), you can use the component bar chart Figure: component bar chart showing the frequency distribution of blood groups across some Egyptian citie
46. 46. Histogram: For describing continuous variables 46 A histogram is a graph of the frequency distribution of a continuous variable. A histogram looks like a bar chart but without any gaps between adjacent bars to emphasize the continuous nature of the variable and to represent the number of observations for each class interval in the distribution. Figure: Histogram showing the frequency distribution of weights of patients
47. 47. Frequency polygon: For describing continuous variables 47 Mid points of upper bases of rectangles are connected by a series of straight lines. Figure: frequency polygon showing the frequency distribution of heights of patients
48. 48. Smooth curve: For describing continuous variables 48 Figure: Histogram with normal distribution curve taking bell-shaped curve Figure: histogram with skewed curve
49. 49. Box and whisker plot: For describing continuous variables 49 Figure: box and whisker plot showing median (interquartile range) of birth weights across different types of d
50. 50. Scatter diagram: For describing continuous variables 50 It is useful for analyzing the relations between two variables. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis.
51. 51. Graphical presentation: The most common types of graphical presentation: ■ For describing qualitative or discrete variables are bar and pie charts. ■ For describing continuous variables are histogram, frequency polygon, smooth curves, box and whisker plot. ■ For relation between variables are scatter diagram 51
52. 52. Which of the following data is best described by Histogram? a. Height of infants in cm of b. Gender of a group of patients c. Type of treatment d. Severity of pain e. Height of patients (short-average-tall) Questions
53. 53. Graph showing the relation between serum calcium and bone mineral density variables is called: (a) Scatter diagram (b) Frequency polygon (c) Picture chart (d) Histogram (e) pie chart Questions
54. 54. You are preparing a report to present mortality & morbidity from covid 19 according to age groups(<20 years,20- 40,>40) during the last 12 months. Which graph best describes these data? A)Simple bar chart B)Multiple bar chart C)Frequency polygon D)Histogram E)Pie chart Questions
55. 55. 55