1. Introduction to Bio-Medical statistics
Vikas Dhikav,
Department of Neurology, Dr. RML Hospital & PGIMER, New Delhi

2. Statistics
Collection, Interpretation & Analysis (CIA) of data

3. “Facts are many, but truth is one” - Rabindranath Tagore

4. “There are no fundamental differences between Eastern and Western minds”
JC Bose, 1917, “father of radio science”

5. Data type

6. Discrete verses continuous data
Whole number
Continuous
Any value

8. Types Nominal Ordinal Interval Ratio Yes/no good, better, best
What’s there in name?
Ordinal
good, better, best
Interval
Differences between two variable is meaningful
Ratio
Relation between data like 10 is 2 times of 5

10. Ordinal scale

11. Interval scale
Difference between data is meaningful
Time
Temperature

12. Ratio scale
Perfect type of data
Measures ratio between two quantities

13. Measure it!
“if you can not describe a phenomena in quantitative terms, your knowledge is unsatisfactory and meager”
-Lord Kelvin

14. Population & sample
Also called study universea small group is called sample

15. Data Numbers of measurements to be donedata
Variablescharacters or attributes

16. Describe data Done before analysis Tabulation or plotting
Stem and leaf plot
Histogram
Bar chart
Dot plot
Scatter plot

17. Stem and leaf plot Useful in knowing shape of distribution
Retains original data
Also describes outliers
Tells about mode

18. Histogram (histo=upright)
Graphical distribution of tabulated frequencies
Continuous data
Numbers get converted into ranges

19. Bar chart >200 years old Used for caregorical data
One axis shows categories, another shows values
Could be horizontal or vertical
Spaces between valuesbar, no spacehistogram

21. Dot plot Dots plotted on a simple scale Used for moderate size data
Described 100 years back as a handrawn graph
Used for moderate size data
Mostly for continuous data
Clusters, gaps and outliers can be highlighted

22. Dot plot example

23. Box and wisker plot Depicts numerical data via quartiles
Tells about range, Median, skewness and outliers
Data distribution can be known

24. Example
The oldest person in Neurology OPD of Dr. RML hospital is 90 years. The youngest person is 15.
The median age is 44, while the lower quartile is 25, and the upper quartile is 67.

25. Tests of normalty
Its important to know data distribution right from beginning
In descriptive data
Goodness of fit
Inferential statstics
Null hypothesis

26. What is normalcy?

27. Tests… Descriptive statistics Inferential Histogram Box & Whisker plot
Kurtosis
Inferential
Kolmogrov-Smnirov test

28. Rules of thumb for normality
When n is greater than 30, this is a good approximation to results from more sensitive tests.
If the standard deviation is more than 3 points from mean, question normality of data

29. Methods of dispersion Range Standard deviation (S.D.)
Coefficient of variation (C.V.)

30. Methods..
Range
High-low values

31. Calculate standard deviations from the range
Standard deviation is 1/4th of range.
(Maximum – Minimum)/4

32. Example Number of hours resident doctors duties in RMLH (n=10) Mean=17
12, 12, 14, 15, 16, 18, 18, 20, 20, 25.
Mean=17
Standard deviation =4.1.
Range=25 – 12 = 13
13/4 = 3.25.

33. Variance Squared value of standard deviation (s2) Limited value
Standard deviation used more commonly

34. Standard deviation Most widely used measure of dispersion
Square root of mean
Depicts average deviation from mean
Expressed in same units as data

35. Standard deviation…
A low standard indicates data is close to its mean, while high SD indicates data is far from mean

36. Chebyshev rule
3/4 of data with in 2 Standard deviations

37. Standard error (SE)
Standard deviation tells about variability of data and hence spread
95% of observations lie with in 2 standard deviations
Standard error tells about how different is our sample from population.

38. SE… Standard error accuracy with which data represents population.
Measures the accuracy with which sample mean deviates from actual mean
Smaller the SE; better estimates
Larger sample size-smaller SE

39. Pearson index of skewness
Subtract mean from median
Multiply by 3
And divide by standard deviation
Value ranges from -1 to +1
<-1 means left skewness
>+1 means right skewness

40. Coefficient of variation
CV=SD/mean x 100
Tells about percentage of deviation from mean
Can help in comparing different datasets

41. Thank you!