1. Biostatistics
College of Medicine
University of Malawi
2011

2. Definition of Statistics
Statistics is the science that studies the collection and interpretation of numerical data.
Field of statistics is divided into Mathematical and Applied statistics.
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3. Applied statistics concerns the application of the methods of mathematical statistics to specific areas such as public health, economics etc
Biostatistics is the branch of applied statistics that concerns the application of statistical methods to medical and biological problems
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4. Importance of Biostatistics
To better understand reports of research studies in your field
To obtain a foundation in statistical issues for designing and conducting your own research.
To learn a few techniques for analyzing data
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5. Variables, Measurement Scales and Summarizing data
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6. Definition of a Variable
A variable is a characteristic that can have many different values.
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7. Types of Variables
A categorical variable has values with interruptions or gaps between them (categories)
A continuous variable has values that could, theoretically, be measured without gaps
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8. Scales of Measurement Qualitative Quantitative Nominal Ordinal Binary
Discrete
Continuous
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9. Qualitative Consists of a finite set of possible values or categories
Always categorical
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10. Nominal scale Diagnosis Ethnic group
Qualitative categories which have no particular order.
Examples:
Diagnosis
Malaria
AIDS
Accident
Other
Ethnic group
Chewa
Yao
Tumbuka
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11. Binary scale Two qualitative categories Examples: Gender HIV status
Male
Female
HIV status
Uninfected
Infected
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12. Ordinal Scale Qualitative categories that have a natural order.
As a result, we can decide that one outcome is "less-than" or "more-than" another.
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13. Examples:
View of statement that condoms can help prevent spread of AIDS
Agree
No opinion
Disagree
Severity of diarrhea
None
Mild
Moderate
Severe
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14. Quantitative Numerical measurements or counts
May be categorical or continuous
Discrete
Continuous
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15. Discrete scale
There are a limited number of distinct possible values or group of values
Examples:
Number of children in a family
Number of decayed, missing or filled teeth
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16. Continuous
Numeric scale with infinitely many values between any two observed values.
Examples:
Weight in kg
Age
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17. Summary Qualitative Quantitative Categorical Nominal Ordinal Binary
Discrete
Continuous
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18. Understanding the scale of measurement of data is key to knowing the correct methods for
summarizing data
graphical display of data
analysis of data.
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19. Frequency Distributions: summarizing data with counts
Tabular Displays
Graphical Displays
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20. Frequency Distribution of Sex
Sex Frequency Percent
_______________________________ F M
Total
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21. Frequency Distribution
Frequency is the count of occurrence of each value
Relative frequency is:
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22. Relative frequency may be expressed as a
Proportion
Percent
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23. Frequency Distribution of Education of Adults
Education Frequency Percent
None
Jr. Primary
Sr. Primary
Secondary
Total
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24. NB: Re number of significant figures
Don’t use more significant figures for estimates than number of digits in sample size
Example
n=387 report to 3 sig. figures
n=17 report to 2 sig. figures
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25. Data cleaning: Frequency distribution of occupation (partial)
Occupation Frequency Percent
BUSINESS
FARMING
assistant driver
business
cane cutting
carpenter
court messenger
cowboy
domestic work
dulder
employee
employee (forest guard)
f/guard
farmer
farming
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26. Frequency Distribution of Age
Age Frequency Percent
__________________________________
Total
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27. Bar Chart
Method of displaying a frequency distribution or percentage distribution
Length of bars proportional to the frequency of the category
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28. Frequency distribution
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29. 2011

30. Pie Chart Another way of presenting frequencies.
The portion of the pie (in terms of degrees) is determined by computing
360´(relative frequency)
for each category.
Computer graphics packages very useful.
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31. 2011

32. Histogram
Special case of a bar chart where both axes are numerically meaningful
height of bars proportional to frequency of category
width of bars proportional to width of the class interval
bars adjoin
true class limits important in constructing and labeling
The areas of the bars relative to each other give a visual impression of the frequency distribution
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33. Frequency Distribution of Ages of a small sample
Relative
11-20 3
12%
21-30 1 4%
31-40 12
48%
41-50 2 8%
51-60 6
24%
More
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34. Histogram of Age
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35. Histogram of Age of Chikwawa Residents
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36. Stem-and-Leaf Plots
a quick and easy way to organize data to give a visual impression
similar to a histogram while retaining much more detail from the data.
also a great way to sort data.
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37. Each value is retained in the stem-and-leaf:
Figure 16: Stem and Leaf and Box Plot of Age of ICU Patients
Stem Leaf # 4
Each value is retained in the stem-and-leaf:
in the lowest row, represents 3 ages 15, 19, 19,
above, represents ages 31, 34, 39 and so on.
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38. Cumulative Frequency:
Count of the individuals in each category and the ones lower.
Count of individuals with values up to the end of each category.
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39. Cumulative Relative Frequency
Relative frequency or percent of the individuals in each category and the ones lower.
Relative frequency or percent of individuals with values up to the end of each category.
Cumulative relative frequencies are used to find percentiles:
a given percentile, p, is the value of a variable that divides the distribution such that p% are at that value or lower
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40. Frequency Distribution of Ages of Chikwawa Residents
Cumulative Cumulative
Age Frequency Percent Frequency Percent
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41. Cumulative Frequency Polygon of Age
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42. Percentile
The term percentile is the value of a variable, below or equal to which a specific percentage of the values falls.
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43. For example
50th percentile = the value that cuts the distribution of values so that 50% are below or equal to it
25th percentile = lower quartile
75th percentile = upper quartile
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44. Cumulative Relative Frequencies can be used to define percentiles.
In our example, age 20 is the 55th percentile
P55 = 20.
A special use of the cumulative percentage polygon is for estimating percentiles of the sample.
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45. Cumulative Frequency Polygon of Age
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46. Summary: You can do a lot with counts
Be aware of the type of variable
Convert counts to proportions
Proportions can be converted to percentages or other “rates”
Tables and graphs must be carefully constructed and clearly labeled
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