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/ModeMean : AverageMedian : middle value of dataMode : Most Frequent occurring value

Distributions and Ranges

Gaussian distribution normalPositively Skewed

Negatively Skewed

RangeLower quartile Upper quartileInterquartile 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 occurringAdd 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

HypothesisNull hypothesis – NO DIFFERENCE between 2 groups under study

Rejecting Hypothesis when true –Type 1 errorAccepting Hypothesis when false – Type 2 error

Compare test results T-testChi-squared test

Produce p-valueProbability 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 1Risk = 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 meta-analysis.(combine results of several studies to answer a question)

Validity

Study validityInternal and external bias

Internal validityExtent to which conclusions in a study are legitimate.

External validityDegree to which conclusions generated from a study can be generalised to a target population.

Study designs

Experimental RCTCohort

Longitudinal follow-up of 2 or more groups with recorded exposure to risk Provides comparative incidence estimates between groupsCan have surveillance bias

Case controlledUsed when prevalence low

Study designs

ObservationalCross-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

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