Statistics
By Z S Chaudry
Why do I need to know about
statistics ?
Tested in AKT
To understand Journal articles and
research papers
Data
Qualitative (Descriptive)
Quantitative(Numeric)
Discrete
Continuous (range)
Mean/Median/Mode
Mean
:
Median
:
Mode
:
occurring value
Average
middle value of data
Most Frequent
Distributions and Ranges
Gaussian distribution normal
Positively Skewed
Negatively Skewed
Range
Lower quartile
Upper quartile
Interquartile range – around median
Standard deviation – spread around
mean
Square root of the variance
Variance = sum of the square
deviations from the mean / n
65% of values lie within 1 SD
95% of values lie within 2 SD
99% of values lie within 3 SD
Key Terms
Probability - likelihood or uncertainty
of an event occurring
Add probabilities if EITHER/OR events
Multiply probabilities if AND events
Power
Related to size of study if study too small may
not be able to detect a significant significance
Errors
Random Error
Systematic Error (bias)
Key Terms
-
contd
Hypothesis
Null hypothesis – NO DIFFERENCE between 2
groups under study
Rejecting Hypothesis when true –Type 1 error
Accepting Hypothesis when false – Type 2 error
Compare test results
T-test
Chi-squared test
Produce p-value
Probability of result occurring by chance alone
– p<0.05 significant
– p<0.01 highly significant
Key Terms -
contd
Confidence interval
Level of uncertainty in following :
Odds ratios, relative risk,risk
difference,sensitivity,specificity
The wider the range the less
certain/significant the results
CI usually 95 % i.e. 2 SD from mean in
either direction.
Provided study not biased true value can
be expected to lie in the CI.
Key Terms -
contd
The more people in a study the smaller the
CI.
CI range including zero not statistically
significant or if results expressed as ratios
a CI including 1 is not statistically
significant.
Measures of Risk
INCIDENCE – New cases
(New cases/population at risk over specific
time) X 100
PREVALENCE-Existing cases
(No of individuals with disease/population
size during specific time) X 100
Measures of Association
Risk varies from 0 to 1
Risk = probability of disease/death (R)
Risk = No with disease/no at risk of disease
Risk Difference = R1 – R2
Relative Risk = R1/R2
<1 intervention reduces risk of outcome
=1 no effect on outcome
>1 intervention increases risk of outcome
Absolute Risk = R1 – R2 / R2
ODDs and ODDs Ratios
Odds – ratio of probability of an event
happening to that of it not happening
Odds Ratio – measure of effectiveness of
treatment compared to control
OR = ODDs in treated grp/ODDs in control
grp
<1 effects of treatment less than control group
=1 effect of treatment same as control group
>1 effect of treatment greater than control
group
Diagnostic Testing
SENSITIVITY – Positive test /total
number of positives
SPECIFICITY- Negative test when
disease free
Positive Predictive Value – likelihood
that positive test will be a true positive
Negative Predictive Value – likelihood
that a negative test is a true negative
NNT= Number needed to treat
= 1/ ARR
So the smaller the ARR the greater the
NNT
Bias
Publication –positive results more likely to
be published
Selection – systematic differences between
sample and target population.
Information – systematic errors in
measures of outcome or exposure
? Language – may be bias in inclusion of
studies to be selected in metaanalysis.(combine results of several
studies to answer a question)
Validity
Study validity
Internal and external bias
Internal validity
Extent to which conclusions in a study
are legitimate.
External validity
Degree to which conclusions generated
from a study can be generalised to a
target population.
Study designs
Experimental
RCT
Cohort
Longitudinal follow-up of 2 or more groups
with recorded exposure to risk
Provides comparative incidence estimates
between groups
Can have surveillance bias
Case controlled
Used when prevalence low
Study designs
Observational
Cross-sectional
Gives prevalence estimates
Forest plots
Pictorial representation of ODDs
ratios in form of a horizontal line
If horizontal line crosses vertical line
results are not significant!
Horizontal line represents the 95% CI
of each trial being plotted
Further Reading
High-Yield Biostatistics by Lippincott
Williams and Wilkins
The Complete nMRCGP Study Guide
by Sarah Gear
CASP tools – Critical Analysis to
review papers – available on the web
THE END
THANK YOU