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 :Average Median :middle value of data Mode:Most Frequent occurring value

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 meta- analysis.(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

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