**Statistics**

**Diagnostic tests:** Sensitivity : Probability that a diseased individual will have a positive test result – TPR Sensitivity : diseased with +ve test all diseased

**Specificity : Probability that a disease –fore individual** will have a negative test result – TNR Specificity:disease for with –ve test all disease free FNR: Probability that a diseased individual will have a –ve test result FNR = diseased with –ve test all diseased

**FPR : Probability that a disease – free individual will** have a +ve test result FPR =disease – free with +ve test all disease free Prevalence : prop of individuals in a population who have the disease . Prior probability or pretest probability = No .with disease total no.of individuals I study

**Continuous variable** • One in which research participants differ in degree or amount. • “susceptible to infinite gradations” Examples: height, weight, age

**Categorical variable** • Participants belong to, or are assigned to, mutual exclusive groups • Nominal • Used to group subjects • Numbers are arbitrary • Examples: sex, race, dead/alive, marital status • Ordinal (rank) • Given a numerical value in accordance to their rank on the variable • Numerical values assigned to participants tells nothing of the distance between them • Examples: class rank, finishers in a race

**Independent** “predictor variable” Usually on the “x” axis Dependent “outcome” variable Usually on the “y” axis The independent variable (a treatment) leads to the dependent variable (outcome) Ultimately, we are interested in differences between dependent variables Independent vs Dependent Variable Dependent Independent

**Descriptive Statistics** • These are measures or variables that summarize a data set • 2 main questions • Index of central tendency (ie. mean) • Index of dispersion (ie. std deviation)

**Data set for ICD complications in 2005** 14 patients Sex: F, F, M, M, F, F, F, M, F, M, M, F, F, F Make: G, S, G, G, G, M, S,S, G,G, M, S Central tendency is summarized by proportion or frequency Sex: M 5/14 = .36 or 36% F 9/14 = .64 or 64% Make: G 6/12 = .5 or 50% S 4/12 = .33 or 33% M 2/12 = .17 or 17% Dispersion not really used in categorical data Descriptive Statistics • Categorical data

**Data set SBP among a group of CHF pts in VA clinic** 13 patients 100, 95, 98, 172, 74, 103, 97, 106, 100, 110, 118, 91, 108 Central Tendency Mean mathematical average of all the values Σ (xi+xii…xn)/n Median value that occupies middle rank, when values are ordered from least to greatest Mode Most commonly observed value(s) Descriptive Statistics • Continuous variable

**Data set SBP among a group of CHF pts in VA clinic** 13 patients 100, 95, 98, 172, 74, 103, 97, 106, 100, 110, 118, 91, 108 Central Tendency Mean mathematical average of all the values Σ (xi+xii…xn)/n = (100+95+98+172+74+103+ 97+106+100+110+118+ 91+108)/13 = 105.5 Descriptive Statistics • Continuous variable

**Data set SBP among a group of CHF pts in VA clinic** 13 patients 100, 95, 98, 172, 74, 103, 97, 106, 100, 110, 118, 91, 108 Central Tendency Median value that occupies middle rank, when values are ordered from least to greatest 74, 91, 95, 97, 98, 100, 100, 103, 106, 108, 110, 118, 172 Useful if data is skewed or there are outliers Descriptive Statistics • Continuous variable

**Range:** SS=ΣXi2 - ΣXi2 n Sample variance s2 = Σ ((Xi-X’)2 n-1 SD s=√ s2 SEM = SD √n

**Data set SBP among a group of CHF pts in VA clinic** 100, 95, 98, 172, 74, 103, 97, 106, 100, 110, 118, 91, 108 Index of dispersion Standard deviation measure of spread around the mean Calculated by measuring the distance of each value from the mean, squaring these results (to account for negative values), add them up and take the sq root Descriptive Statistics • Continuous variable

**95% CI: mean+ or – 2sem.**

**Descriptive Statistics: “Normal”**

**Descriptive Statistics: Confidence Intervals** • “Range of values which we can be confident includes the true value” • Defines the “inner zone” about the central index (mean, proportion or ration) • Describes variability in the sample from the mean or center • Will find CI used in describing the difference between means or proportions when doing comparisons between groups Altman DG. Practical Statistics for Medical Research ;1999

**Descriptive Statistics:Confidence Intervals** • For example, a “95% CI” indicates that we are 95% confident that the population mean will fall within the range described • Can be used similar to a p-value to determine significant differences • CI is similar to a measure of spread, like SD • As sample size increase or variability in the measurement decrease, the CI will become more narrow

**Descriptive Statistics: Confidence Intervals** • Prospective, randomized, multicenter trial of different management strategies for ACS • 2500 pts enrolled in Europe with 6 month follow-up • Primary endpoints: Composite endpoint of death and myocardial infarction after 6 months L a n c e t 1999; 3 5 4 : 7 0 8 – 1 5

**Descriptive Statistics: Confidence Intervals** L a n c e t 1999; 3 5 4 : 7 0 8 – 1 5

**Descriptive Statistics: Confidence Intervals** L a n c e t 1999; 3 5 4 : 7 0 8 – 1 5 *Risk ratio= Riskinvasive / Risknoninvasive When CI cross 1 or whatever designates equivalency, the p-value not be significant.

**Review** Calculate: RRR, ARR, NNT RRR = (12.1-9.4) / 12.1 = 22% Descriptive Statistics: Confidence Intervals L a n c e t 1999; 3 5 4 : 7 0 8 – 1 5 ARR = 12.1 - 9.4 = 2.7% NNT = 100 / ARR = 100 / 2.7 = 37