•
FWACP
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REVISION
Medical Statistics
1 Numerical
facts on individuals or a group of people:
- Biochemical
measurements of 100 students.
- Age of
patients at PCC.
- Genotype
of medical students in KSU.
- Collecting
- Organising
- Analysing
- Interpreting
- Presenting
3. Need
for in Medicine.
Because of ever present variation in measurements.
4. Source of variation in Medical Data.
- Inherent
biological differences.
- Instruments
used.
- Observers.
- Subjects.
- Environment
5. Note
there are variations in the:
- Physiological.
- Anatomical.
- Biochemical
and Physical characteristics of individuals.
- Statistics
help to sort out and explain these variations.
6. Types of
variations.
- Random
(inherent) cannot be controlled.
- Systematic
(measurements) can be controlled.
7. Measurements
in Medicine.
Expression of any medical phenomenon in numbers or
categories - to give
- Size or
extent, or magnitude.
- Impressions.
8. How to
Measure? (Physical or Non-physical)
Use of Instrument.
- Questionnaire.
- Laboratory
equipment.
- Senses.
- Clinical
equipments (Sphyg.)
9. Level of
Measurements.
Four levels:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Nominal.
- Merely
classifies or categorise.
- No
notion of numerical magnitude
Example:
Blood Group: A, B, AB, O
Sex - male, female
Ordinal
- Has
nominal property.
- Values
defined by related categories.
- Rank or
order property.
- Differences
between any two levels cannot be quantified meaningfully. e.g. level of pain:
Mild, Moderate, Severe.
Interval.
- Has
nominal and ordinal properties.
- Measurements
expressed in numbers.
- Starting
point arbitrary.
- Differences
between any two value on this scale is meaningful.
But ratio of any two values dependent on the unit of
measurement e.g. temperature - centigrade or Farehen heights.
. Ratio.
- Has
nominal, ordinal and interval properties.
- Has true
zero point.
- Ratio of
any two numbers is meaningful and does not depend on unit of measurement. e.g.
height, age, hb.
14. Quality of
Measurements.
Must have good
- Validity
and
- Reliability
15. Validity.
Extent to which instrument measures what it is supposed to
measure. Physicians concerned with diagnostic value of instruments.
16. Reliability.
- Closeness
of measurements to each other.
- How
reproducible or repeatable.
17. Measurement
of Validity.
- Sensitivity.
- Specificity.
18. Sensitivity.
- Ability
of a measuring device to identity correctly those who truly have a condition
i.e. positive.
19. Specificity.
- Ability
of a test to classify has negative those who are truly negative i.e. do not
have the condition.
Data Set.
-
Information collected on all items or
characteristics of an individual or group of individuals.
-
Usually we deal with groups of individuals.
Example of Data Set.
|
Serial
No.
|
Age
|
Sex
|
Ht.
|
Blood
Group
|
|
1.
|
37
|
M
|
1.73
|
0
|
|
2.
|
31
|
F
|
1.64
|
0
|
|
3.
|
34
|
M
|
1.68
|
0
|
Types of
Data
·
Qualitative
·
Quantitative
Qualitative
Data
-
Measured
on nominal or ordinal scale.
-
Categories
are attributes.
-
No
notion of numerical magnitude.
-
Binary
if only 2 categories possible.
Example Outcome of Exam - Pass or Fail.
Educational level Primary, Secondary,
University.
Quantitative Data.
- Measurements
are in numbers.
- Discrete
if integer values only (e.g. Apgar Score).
- Continuous
it can assume any values (e.g. weight, height, skinfold thickness).
Sources of Health Data
(1st) Routine
- Census
- Vital
Registration systems
- Institutions
(school health, hospitals, health centers).
- Notification
centers (infections diseases, cancer).
(2nd) Surveys or
Experiments.
- Planned
studies (research).
- Well
designed with measurable objectives.
Descriptive
Statistics
Statistical Methods that deal with description of
characteristics(s) of a finite population
•
Frequency Tables
·
Diagrams (Graphs/charts)
•
Summary Indices
Frequency Tables
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Arrangement of data by rows & columns
•
Qualities
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Simple Information (not more than 3 variables)
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Clear title to indicate what? when? where?
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Good labeling of rows & columns
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Indicate units of measurements
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Row, column & grand total to add up
Method
•
Determine the range
•
Determine number of classes
•
Divide the range by number of classes
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Class interval must not overlap
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Tally the observations
Diagrams
•
Quantitative or numerical Data
•
Histogram, Frequency Polygon
•
Qualitative
or categorical data
•
Bar , Pie chart
Measures of
Dispersion
•
Range
•
Variance
•
Standard Deviation
Usefulness of mean and standard deviations
.Useful to summarise data measured on at least interval
scales.
- For
mathematical description of the distribution of biological, biochemical,
heamological and physiological variables.
- Most of
the values of these variables appear in the middle of the distributions and
have symmetric distributions.
- Sometimes
tail at one end more prominent than tail on the other - skewed.
- Skewed
distributions are asymmetric but unimodal e.g. hemoglobin.
Distributions change with characteristics of subjects like
age, sex or nutrition.
Normal and Sampling Distributions.
Frequency distribution of continuous variables.
- Usual or
typical feature is for observations on most biological variables to concentrate
or cluster around the central value.
- Fewer
observations are observed as one moves away from the central value to the
tails.
- Norman
Gauss wrote a model of that completely describe the shape of this distribution.
- Today it
is called a Gaussian distribution or Normal distribution.
- It
occupies a central role in statistical inference.
1. Properties
of Normal Distribution.
- Bell
shaped and symmetric about central value.
- Completely
determined by its mean and standard deviation.
- Mean,
median and mode have same value.
- Total
area under the curve is 1 (100%).
- 68% of
all observations lie within one standard deviations of the mean value.
- 95% of
observations lie within 1.96 standard deviations of the mean value.
- 99% of
all observations lie within 2.58 standard deviations.
Presentation of
Normal Distribution.
- As a
mathematical equation
- Graph
- Table
Data Analysis and
Presentation.
1. Scope of
Data Analysis.
1. Preparation
for data collection and designing of appropriate data collection instruments.
2. Designing
coding rules for data collection instruments.
3. Evaluation
of data collected for completeness and accuracy .
4. Choosing
appropriate mode of data management- viz Manual vs Computer.
5. Choosing
the appropriate statistical program for data entry and analysis
6. Carrying
out the statistical analysis of the data
Choosing mode of data
management
(i) Manual.
: For small data, manual check may
discover – transposition, coding and routine errors.
(ii) Computers.: Validate data entry by picking,
copying errors.
- Use double-entry method to validate.
- Compare data to ensure no difference.
- Customize data entry for range and
consistency checks.
6. Carrying
out the statistical analysis of the data
Purpose: Processing
of data collected manipulation and provision of useful results.
- Examination
of the dataset i.e. the set of observations collected on each values of the
variables on all the study units.
- Sort out
relevant variables to the study objectives.
- Organization
of data to focus attention on salient features.
- Identify
independent and dependent variables in the data.
- Apply appropriate descriptive statistical
tools.
- Making
necessary cross-classification of variables.
- Application of appropriate statistical
theories to test specified hypothesis.
Data Analysis.
- Construct
frequency distribution tables for all variables.
- Check
for further errors (range check!)
- Check
kind of data and design method.
- Use
appropriate summary statistics, tables and graphs.
- Examine
each objective in relation to data.
- Use
appropriate test statistics to test significance of hypothesis.
Statistical
Analysis (Standard)
- Description
of characteristics of study population.
- Test
of specific hypothesis using appropriate statistical methods.
- Presentation
using tables, graphs and summary statistics.
1Common Statistical Analysis
A. Descriptive
Statistics.
- Tables
- Diagrams
- Summary statistics
B. Comparative
Statistical Analysis.
- Testing association between
variables.
- Comparing mean values.
- Multivariate analysis
C. Data
Presentation.
- To convey information obtained to
targeted audience.
- Use appropriate statistical tools
mentioned in earlier sections.
USE CHI-SQUARE-
TEST
USE T-TEST
PAIRED-T FOR DEPENDENT SAMPLES
T-TEST INDEPENDENT
SAMPLES