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Basic Course in Statistics for Medical Doctors

Basic Course in Statistics for Medical Doctors. Dr. Sanjib Bandyopadhyay Assistant Director Medical Education Assistant Professor, Community Medicine, Calcutta National Medical College. About Statistical Class. Some one said “If I had only one day to live,

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Basic Course in Statistics for Medical Doctors

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  1. Basic Course in Statistics for Medical Doctors Dr. SanjibBandyopadhyay Assistant Director Medical Education Assistant Professor, Community Medicine, Calcutta National Medical College

  2. About Statistical Class Some one said “If I had only one day to live, I would live it in my statistics class”

  3. “it would seem so much longer”

  4. Descriptive Statistics Measures of Central Tendency Measures of Dispersion Range Variance Standard Deviation • Mean • Median • Mode

  5. Measures of Central Tendency • We will study three measures of central tendency: • The mean, the preferred measure for interval data • The median, the preferred measure for ordinal data • The mode, the preferred measure for nominal and dichotomous data

  6. Standard Error • Sample mean is an estimate of the population mean • Mean Blood Loss of 100 patients was 1240 ml (sd=553ml) • Can we say that the population mean is also 1240ml? • Uncertainty associated with our estimate 1240 ml • How do we measure the uncertainty?

  7. Variance or Standard Deviation • On an average, how far each and every observation deviates from the mean. • About the study itself.

  8. Standard Error • Take many samples of same size from the population  asses the variability of such means • These means follow Normal Distribution • Mean of these means is the population mean • This variability can be estimated from a single study. • SE = σ̸√n or √ (pq/n)

  9. SD vs SE • The contrast between these two terms reflects the important distinction between data description and precision/inference • SD : is a measure of variability and explains how widely scattered some measurements are in a group • SE : applicable for large samples & indicates the uncertainty around the estimate of the mean measurement

  10. Standard Deviation • Description of data : • Example : • If the mean weight of a sample of 100 men is 72 kg and the SD is 8 kg. • Assuming normal distribution 68% of the men are expected to weigh between 64 and 80 kg.

  11. Standard Error • 72 kg is also the best estimate of the mean weight of all men in the population. • How precise is the estimate 72 kg? • While testing hypothesis, Difference in mean or proportions between groups.

  12. TABULATION

  13. SAMPLE DATA SET Pt. No. Hb. Pt. No. Hb. Pt. No. Hb. 1 12.0 11 11.2 21 14.9 2 11.9 12 13.6 22 12.2 3 11.5 13 10.8 23 12.2 4 14.2 14 12.3 24 11.4 5 12.3 15 12.3 25 10.7 6 13.0 16 15.7 26 12.7 7 10.5 17 12.6 27 11.8 8 12.8 18 9.1 28 15.1 9 13.5 19 12.9 29 13.4 10 11.2 20 14.6 30 13.1

  14. TABLE I FREQUENCY DISTRIBUTION OF • 30 ADULT MALE PATIENTS BY Hb • Hb (g/dl) No. of patients • 9.0 – 9.9 1 • 10.0 – 10.9 3 • 11.0 – 11.9 6 • 12.0 – 12.9 10 • 13.0 – 13.9 5 • 14.0 – 14.9 3 • 15.0 – 15.9 2 • Total 30

  15. DIMENSION OF A TABLE • Dimension = No. of variables according to which • the data are classified • One-way Table - Freq. distn. of 30 adult male pts. by Hb • Two-way Table - Freq. distn. of 30 adult pts. by Hb & Sex • Three-way Table - Freq. distn. of 30 pts. by Hb, Sex & Age

  16. ELEMENTS OF A TABLE • 1. Number (To refer ) • 2. Title (What, How classified, Where & When) • 3. Column headings (concise & clear) • 4. Foot-note (Headings, Special cell, Source)

  17. A TYPICAL EXAMPLE OF A ONE-WAY TABLE • Table II • Distribution of 120 (Madras) Corporation Divisions according to annual death rate based on registered deaths in 1975 &1976 • Figures in parentheses indicate percentages SOURCE: Radhakrishna, S. et al (1983). Study of variation in area mortality rates in Madras city & its correlates. IJMR, 78, 732 – 739.

  18. GUIDELINES TO PREPARE A TABLE • 1. Decide No. of classes (5 - 15) • 2. Decide Width of classes (Equal / Unequal) • 3. Decide class limits (Closed / Open ) • 4. Precise & Non-overlapping ( 9.0 - 9.9, 10.0 - 10.9 )

  19. DIAGRAMS

  20. TYPES OF DIAGRAMS • Type of VariableDiagram • Qualitative or discrete Bar diagram • (religion, gender, Pie chart • place of residence) • Continuous • (height, weight, blood sugar ) Histograms • Line diagrams

  21. Table 1 Distribution of blood group of patients of essential hypertension

  22. Fig.-1 : Distribution of blood groups of patients with essential hypertension

  23. Age group Male Female Total 1 to 10 12 11 23 11 to 20 25 22 47 21 to 30 18 18 36 31 to 40 20 22 42 41 to 50 17 15 32 Table 2: Sex-wise Distribution of studied population

  24. Component Bar Diagram

  25. Percentage Bar Diagram

  26. PIE DIAGRAM • Considered for qualitative or discrete data • A circle is divided into different sectors • Areas of sectors are proportional to frequencies

  27. Table - 2 Distribution of newly detected leprosy patients by Type, Govt. Leprosy Treatment & Study Centre, Arakandanallur, 1955-57

  28. Fig 2 Distribution of newly detected leprosy patients by Type, Govt. Leprosy Treatment & Study Centre, Arakandanallur, 1955-57 nie

  29. HISTOGRAM • Essentially a bar diagram • Bars are drawn continuously • Width - usually equal • Area - proportional to frequencies

  30. Table 3 Frequency distribution of Haemoglobin levels of adult male patients (n=30)

  31. Fig. 3 Frequency distribution of Haemoglobin levels of adult male patients (n=30)

  32. LINE DIAGRAM • Diagram is drawn by taking • X – axis - time (e.g., Years) • Y – axis - value of any index or quantity • (e.g., couple protection rate) • Displays how a variable has changed over time

  33. Table 4 Number of smear- positive new leprosy cases registered at the Acworth Municipal Leprosy Hospital, Mumbai, 1985-1995 Source: Juwatkar PS, Chulawala RC, Naik SS.Correspondence Indian J Lepr 1997;62 (2):197

  34. Fig 4 Number of smear- positive new leprosy cases registered at the Acworth Municipal Leprosy Hospital, Mumbai, 1985-1995 No. of cases nie

  35. Scatter graph Total Cholesterol vs LDL Cholesterol

  36. Scatter graph Total Cholesterol vs HDL Cholesterol

  37. NORMAL DISTRIBUTION

  38. NORMAL DISTRIBUTION

  39. The Distribution of Data(Rule of Thumb) • The statistical & clinical applications of the term “normal” are often confused and vague • SD> ½ mean --------> Skewed / Non-normal data • Note : Applicable only for variable where negative values are impossible • Ref : Altman BMJ 1991

  40. Same distribution on Normal “Q-Q” Plot Assessing Departures from Normality Approximately Normal histogram Normal distributions adhere to diagonal line on Q-Q plot

  41. Negative Skew Negative skew shows upward curve on Q-Q plot

  42. Positive Skew Positive skew shows downward curve on Q-Q plot

  43. Same data as prior slide with logarithmic transformation The log transform Normalize the skew

  44. Normal Distribution Graph-Box Plot

  45. Data may have a positive skew (long tail to the right, or a negative skew (long tail to the left). Skewed Data

  46. Positive Skew

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