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![References
• Norman GR, Streiner D L. Biostatistics: The Bare Essentials. 2nd Edn. B.C. Decker Inc.
2000; p 43-55
• Dawson B, Trapp RG. Basic & Clinical Biostatistics,4th Edn. LANGE basic science. 2004;
p 61-92
• Field A. Discovering statistics using IBM SPSS statistics, 4th
Edn. SAGE. 2014; p 28-34, 54-
8.
• Sedgwick P. Clinical significance Vs statistical significance; BMJ 2014; 348. doi:
http://dx.doi.org/10.1136/bmj.g2130. Accessed on 20-03-2016
• Fethney J. Statistical and clinical significance, and how to use confidence intervals to
help interpret both. Aust Crit Care [Internet]. 2010;23(2):93–7. Available from:
http://dx.doi.org/10.1016/j.aucc.2010.03.001
• LeFebvre R. P Values, Statistical Significance & Clinical Significance. 2011;(Mcid).
Available from:
https://www.uws.edu/wp-content/uploads/2013/10/P_Values_Statistical_Sig_Clinical_
Sig.pdf
• Van Rijn MHC, Bech A, Bouyer J, Van Den Brand JAJG. Statistical significance versus
clinical relevance. Nephrol Dial Transplant. 2017;32:ii6-ii12.
• Baigent C, Landray MJ, Reith C, Emberson J, Wheeler DC, Tomson C, et al. The effects of
lowering LDL cholesterol with simvastatin plus ezetimibe in patients with chronic
kidney disease (Study of Heart and Renal Protection): A randomised placebo-controlled](https://image.slidesharecdn.com/dataanalysisandinterpretation-250703172019-a2ca144b/75/Data-analysis-and-interpretation-ppt-presentation-59-2048.jpg)
![References
• Norman GR, Streiner D L. Biostatistics: The Bare Essentials. 2nd Edn. B.C. Decker Inc.
2000; p 43-55
• Dawson B, Trapp RG. Basic & Clinical Biostatistics,4th Edn. LANGE basic science. 2004;
p 61-92
• Field A. Discovering statistics using IBM SPSS statistics, 4th
Edn. SAGE. 2014; p 28-34, 54-
8.
• Sedgwick P. Clinical significance Vs statistical significance; BMJ 2014; 348. doi:
http://dx.doi.org/10.1136/bmj.g2130. Accessed on 20-03-2016
• Fethney J. Statistical and clinical significance, and how to use confidence intervals to
help interpret both. Aust Crit Care [Internet]. 2010;23(2):93–7. Available from:
http://dx.doi.org/10.1016/j.aucc.2010.03.001
• LeFebvre R. P Values, Statistical Significance & Clinical Significance. 2011;(Mcid).
Available from:
https://www.uws.edu/wp-content/uploads/2013/10/P_Values_Statistical_Sig_Clinical_
Sig.pdf
• Van Rijn MHC, Bech A, Bouyer J, Van Den Brand JAJG. Statistical significance versus
clinical relevance. Nephrol Dial Transplant. 2017;32:ii6-ii12.
• Baigent C, Landray MJ, Reith C, Emberson J, Wheeler DC, Tomson C, et al. The effects of
lowering LDL cholesterol with simvastatin plus ezetimibe in patients with chronic
kidney disease (Study of Heart and Renal Protection): A randomised placebo-controlled](https://crownmelresort.com/image.slidesharecdn.com/dataanalysisandinterpretation-250703172019-a2ca144b/75/Data-analysis-and-interpretation-ppt-presentation-59-2048.jpg)
Data analysis and interpretation ppt presentation
- 1. Data analysis, Managementand Interpretation Dr. Pradeep T
- 2. Overview •Data •Cleaning and organisingthe data •Descriptive statistics •Presentation of data •Inferential statistics •Summary
- 3. Hypothesis Testing Research Question NullHypothesis (H0) •Assumption of no difference b/w populations Alternative Hypothesis (H1) • A difference exists which can be tested • Difference will be demonstrated after testing Purpose of hypothesis testing • Test the viability of null hypothesis μ1= μ2 μ1 ≠ μ2
- 4. Types of data Ordinaldata Non binary Nominal data Binary Quantitative data / Numerical data Continuous / discrete Interval / ratio scales Categorical data
- 5. Nominal data • Theordering of the categories is completely arbitrary • They do not have units of measurement Eg: - Eye colour: black, brown, blue - Blood group: A, B, AB, O • No information is gained or lost by changing the order
- 6. Ordinal data • Orderedcategories • Each value has unique position with respect to the other • They do not have units of measurement • Differences between categories cannot be considered equal • Example: • Glasgow coma scale for head injury • Stages of cancer I,II,III,IV
- 7. Discrete data • Assumeonly whole numbers • Example : • How many children admitted to the hospital • Number of cardiovascular deaths reported • Number of pregnancies • Generally, discrete data are counts
- 8. Continuous data • Valuesthat are fractions or decimals • Values between variables depends on the instrument used • Examples : • Cholesterol level (μg/ml) • BP ( mm Hg) • BMI (kg/m2) • Generally, continuous data come from measurements
- 9. Interval data • Distancebetween any two values is fixed and equal • Zero point is arbitrary • Differences between numbers are equal but ratios are not • Eg: - Weight - Height - Degrees Centigrade • Difference between 5kg and 10kg, for example, is same that between 20 kg and 25 kg
- 10. Ratio • Equal intervalsbetween values • Meaningful zero point • Ratios between numbers are meaningful • E.g.: - 20kg is twice as heavy as 10kg, possible to weigh 0 kg - 20°C is not, twice as warm as 10°C, extends below 0°C
- 11. Algorithm – Typeof data
- 12. Data analysis It involvesthree major steps •Cleaning and organizing the data for analysis (Data Preparation) •Describing the data (Descriptive Statistics) •Testing Hypotheses and Models (Inferential Statistics)
- 13. Data analysis It involvesthree major steps •Cleaning and organizing the data for analysis (Data Preparation) •Describing the data (Descriptive Statistics) •Testing Hypotheses and Models (Inferential Statistics)
- 14. Descriptive statistics • Givesnumerical & graphic procedures to summarize a collection of data in a clear and understandable way • Data can come from a sample or from population • Vocabulary of descriptive stats: • Measures of central tendency, measures of dispersion, normal distribution, standard scores
- 15. Common descriptive statistics •Count (frequencies) • Percentage • Mean • Mode • Median • Range • Standard deviation • Variance
- 16. Measures of centraltendency • 3 commonly used measures are : • Mean, Median , Mode • Describe the ‘central point or most characteristic value’ • The choice of which measure to use depends on: • Shape of the distribution (whether normal or skewed) • Type of data - nominal, ordinal or interval
- 17. Mean • Simple arithmeticaverage of all observations • Given by the formula X = ΣX , N = no: of observations N When to Use? • For interval & ratio data • Affected by skewness in data • Not used with ordinal data Disadvantage : Influenced by extreme values X for the mean of a sample μ for the mean of a population
- 18. Example Calculate the meanHbA1c: X = ΣX N 180.6 / 27 = 6.69
- 19. Median • Median isthe middle value, if data are arranged in ↑ order. • Odd no.: middle value • Even no.: mean of 2 middle observations - Presence of outliers - Data are measured in ordinal scale Eg.: SES – low, middle, upper
- 20. Example Calculate the medianHbA1c : HbA1c : 5.8 % , there are 13 values above & below it
- 21. Mode • Category orvalue in the data that has the highest frequency • 2 modes in a group - Bimodal • It is used for categorical data • Not useful for continuous metric data • No two values may be the same
- 22. Example Calculate the modeHbA1c : HbA1c : 5 % , as this value repeats 3 times
- 23. Measure of centraltendency Type of variable Mode Median Mean Nominal Yes No No Ordinal Yes Yes Yes Metric data Yes Yes, if distribution is skewed Yes Metric continuous No Yes, if distribution is skewed yes
- 24. Measures of dispersion •Measures of central tendency not adequate to describe data • 2 data with same mean can be different • Assessment of variability → describe data • Smaller the value for these measures ↑ the consistency • Measures of variability : - Standard Deviation - Interquartile range - Mean Deviation - Variance
- 25. Range • The rangeis the difference between the largest & smallest value • Used for ordinal data when they are numerical • Difference is large for large samples Example : Duration of stay of patients in the hospital: 1,2,2,5,5,6,7,7,8,8,11,12,12,15 days The range here is 15 - 1 = 14 days • Value affected by outliers
- 26. Interquartile range • Indicatesthe spread of middle 50% of distribution • Less sensitive to extreme values • Interquartile range = upper quartile - lower quartile • The 2 ranges form the basis of box & whiskers plot
- 27.
- 28. Normal distribution ofdata •Bell curves – Normal distribution – 95% of data within 2 SD
- 29. Non-Normal distribution ofdata •Not bell shaped curves
- 30. Test of Normality •Q-Qplot •Shapiro-wilk test •Kolmogorov-smirnov test
- 31.
- 32. Frequency table Grouped frequencytable is better Unnikrishnan AG, Menon UV. Thyroid disorders in India: An epidemiological perspective. Indian J Endocr Metab 2011;15, Suppl S2:78-81 Thyroid function abnormality Frequency ( n = 971 ) Relative frequency ( % of individual in each category) Normal TFT 777 80 % Hypothyroidism 39 4 % Hyperthyroidism 10 1% Subclinical Hypothyroidism 87 9 % Subclinical Hyperthyroidism 19 2 % Unclassified 39 4 %
- 33. Frequency table –continuous data
- 34. Cummulative frequency • Runningtotal of frequencies • Sum of all previous frequencies to current point • Indicates number of elements below current value • Suitable for metric and ordinal data only. Table : GCS score showing cumulative frequency
- 35. Cross tabulation/ contingencytable • Also known as contingency table • Association between 2 variables in single group of individuals • Provides insight into sub – group structures • Example : Table : Mother smoked during pregnancy ( Y/N) & Apgar score <7 ( Y/N)
- 36. Frequency distribution drawings Pie/sectordiagram Bar diagram Histogram Line chart/graph Cumulative frequency diagram Scatter/ dot diagram Frequency curve
- 37. Pie chart • Usedfor discrete data • Each segment proportional to frequency of category • Disadvantage : • Can represent only one variable • Clarity lost on representation of 5 or ↑ category Thyroid function abnormality Frequency ( n = 971 ) Relative frequency ( % of individual in each category) Normal TFT 777 80 % Hypothyroidism 39 4 % Hyperthyroidism 10 1% Subclinical Hypothyroidism 87 9 % Subclinical Hyperthyroidism 19 2 % Unclassified 39 4 %
- 38. Prevalence of thyroidfunction abnormality Normal TFT Hypothyroidism Hyperthyroidism Subclinical Hypothyroidism Subclinical Hyperthyroidism Unclassified Pie chart
- 39. Bar diagram Thyroid function abnormality Frequency (n = 971 ) Relative frequency ( % of individual in each category) Normal TFT 777 80 % Hypothyroidism 39 4 % Hyperthyroidism 10 1% Subclinical Hypothyroidism 87 9 % Subclinical Hyperthyroidism 19 2 % Unclassified 39 4 % •Represent categorical variable with rectangular bars •Length of bar represents frequency of data •Spacing between the bar is half the width of the bar •One axis of the chart shows specific categories being compared
- 40. N orm al TFT Hypothyroidism Hyperthyroidism Subclinical H ypothyroidism SubclinicalHyperthyroidism Unclassified 0 200 400 600 800 Frequency Bar diagram
- 41. • Used if2 or more groups are present • Useful to compare relative size of group in each category • Example : The following table gives 2 sub- groups Clustered bar chart
- 42. 0 10 20 30 40 50 60 70 Class 1 Class 2 Classs3 Class 4 Rajeev Gupta,KD Gupta :Coronary Heart Disease in Low Socioeconomic Status Subjects in India: " An Evolving Epidemic“, Indian Heart J. 2009; 61:358-367 Clustered bar chart
- 43. Histogram • Graphical representationof distribution of continuous data • X axis : Group size • Y axis : Frequency • No gaps between bars : continuous nature • Example : Table : Histogram of grouped birth weight data
- 44. Frequency polygon • Usefulin comparing 2 frequency distributions • Developed over histogram • By joining mid points of class intervals • At the height of frequency by lines • When done on • Large population - Small intervals • Smooth curve obtained called frequency curve
- 45. Frequency polygon 2700 -29993000 - 3299 3300 - 3599 3600 - 3899 3900 - 4199 4200- 4499 0 1 2 3 4 5 6 7 8 9 Chart Title Series 1 Series 2 Series 3
- 46. Cummulative frequency curve •Also known as ‘ogive’ • Plotted for continuous metric variables • Assumed that a smooth curve will be obtained • Also to estimate frequency for value not belonging to the group • Helps in calculating percentile Table : Cumulative and relative frequency for grouped birth weight
- 47. Cummulative frequency curve 2700-2999 3000 - 3299 3300 - 3599 3600 - 3899 3900 - 4199 4200 - 4499 0 20 40 60 80 100 120 Chart Title Series 3
- 48. Line graph • Displaysdata as series of data points • Used to visualize trend in data over time interval Trends in under 5 mortality in various regions
- 49. Scatter plot Scatter plotshowing relation b/w FEV1 & age in 636 children • Used to examine relationship b/w 2 numerical variables. - Outcome ( dependent variable ) – y - axis - Exposure ( independent variable) – x - axis • Patterns of data described in terms of: • Linearity: pattern maybe linear or curved • Slope : relation between variables X and Y • Strength : degree of scatter in plot
- 50. Scatter plot • Alsoused to display relationship between a categorical & continuous variable • Example : - Relationship b/w FEV1 & reporting of respiratory symptoms over 12 months. - Scatter points randomly over horizontal axis : “Jittering” Interpretation : FEV1 was higher in children who did not report
- 51.
- 52. Data analysis It involvesthree major steps •Cleaning and organizing the data for analysis (Data Preparation) •Describing the data (Descriptive Statistics) •Testing Hypotheses and Models (Inferential Statistics)
- 53.
- 54. Inferential statistics • Useto determine the probability ( or likelihood) that a conclusion based on analysis of data from a sample is true • Inferential statistics: • Tells how confidant we can be that the ‘sample statistic’ is real • Vocabulary of inferential statistics: • Hypothesis testing, level of significance, Type I/II errors, t- test, chi- square test
- 55. PARAMETRIC NON PARAMETRIC Variable of interest is a measured quantity Not a measured quantity Assumption about distribution of data Normal distribution No such assumption Assumption about variance Equal variance among sample population No such assumption Type of data Ratio or Interval Nominal or Ordinal Makes hypothesis about Numerical values like mean & variance Medians, Ranks or Frequencies of data Parametric vs Non Parametric
- 56. Non parametric tests •Nonparametric tests • When data are not normally distributed • Data is ranked, i.e. data that can be put in order • Sample size is small (<10)
- 57. Tests Parametric Non-parametric Correlationtest Pearson Spearman Independent measures, 2 groups Independent- measures t-test Mann-Whitney U test Independent measures, >2 groups One-way, independent- measures ANOVA Kruskal-Wallis test Repeated measures, 2 conditions Matched-pair t-test Wilcoxon Signed Rank test Repeated measures, >2 conditions One-way, repeated measures ANOVA Friedman's test Non parametric tests
- 58. Summary Types of data• Discrete, continuous • Nominal, ordinal, Interval and Ratio data Representation of data Histograms, bar charts, pie chart, frequency curve Measures of central tendency Mean, Median, mode Measures of dispersion Standard deviation, variance, interquartile range Inferential statistics Parametric test – independent t test, paired t test, ANOVA Nonparametric test – Mann whitney U test, wilcoxan signed rank test, Kruskal wallis test, Chi square test
- 59. References • Norman GR,Streiner D L. Biostatistics: The Bare Essentials. 2nd Edn. B.C. Decker Inc. 2000; p 43-55 • Dawson B, Trapp RG. Basic & Clinical Biostatistics,4th Edn. LANGE basic science. 2004; p 61-92 • Field A. Discovering statistics using IBM SPSS statistics, 4th Edn. SAGE. 2014; p 28-34, 54- 8. • Sedgwick P. Clinical significance Vs statistical significance; BMJ 2014; 348. doi: http://dx.doi.org/10.1136/bmj.g2130. Accessed on 20-03-2016 • Fethney J. Statistical and clinical significance, and how to use confidence intervals to help interpret both. Aust Crit Care [Internet]. 2010;23(2):93–7. Available from: http://dx.doi.org/10.1016/j.aucc.2010.03.001 • LeFebvre R. P Values, Statistical Significance & Clinical Significance. 2011;(Mcid). Available from: https://www.uws.edu/wp-content/uploads/2013/10/P_Values_Statistical_Sig_Clinical_ Sig.pdf • Van Rijn MHC, Bech A, Bouyer J, Van Den Brand JAJG. Statistical significance versus clinical relevance. Nephrol Dial Transplant. 2017;32:ii6-ii12. • Baigent C, Landray MJ, Reith C, Emberson J, Wheeler DC, Tomson C, et al. The effects of lowering LDL cholesterol with simvastatin plus ezetimibe in patients with chronic kidney disease (Study of Heart and Renal Protection): A randomised placebo-controlled