Hemodynamics and Core Statistical Concepts: A Combined Review

2 Measures of Central Tendency The Average is broadly classified into the following categories: 1) Mathematical Average 2) Positional Average Following chart reveals that their further categories Average -> Mathematical Averages -> Arithmetic Mean Geometric Mean Harmonic Mean Positional Averages -> Position Value Mode Positional Averages -> Median -> Partition Value -> Mode Quartile Percentile Median - M (Mid Value) Is that value of which is located at the middle of the series Rules :- 1. Parts of tables: Number of tables: 9, 8, 23 Each Table Should be given a number for readily reference 2. Title: Each Table Should be given a clear & precise title. The purpose of the title is to precisely describe the content of the table. 3. The material of the table 4. The time of Collection 5. The area Covered 6. Head Note: The purpose of Head Note is to state units and to qualify the title. 7. Caption: Caption refers to Heading of the Columns. If there are many Columns Sub-heading should be given 8. Stub: Stub refers to the heading of the rows. They are given at the extreme left. 9. Body: This is the main part of the Table where in data given below. Parametric Test T Test Z Test F Test T Test: * T Test is a small sample test * It was developed by William Gosset in 1908. * It is also called student t test [pen name] t = (x̄ - μ) / (s/√n) Uses of T-Test / Application - Size of Sample is small [n<30] - Degree of freedom is [v=n-1] - T test is used for test of significance of regression coefficient in regression model.   - We used t-statistics when parameter of population are normal. - population variable are unknown. - It is also called Welch T-Test - Correlation of coefficient in population is ρ Z Test * Z Test was given by Fisher. * t-test Variance: σ² = ∑(x - x̄)² / N = ∑u²/n SD: σ = √(∑u²/n) Combined Variance: σ² = (n₁σ₁² + n₂σ₂²) / (n₁ + n₂) Combined Mean: X̄ = (n₁x₁ + n₂x₂) / (n₁ + n₂) Coefficient of Variation: CV = (SD / Mean) × 100 = (σ / X̄) × 100 Quartiles 1) In data: Q₁ = 1 + h(N/4 - cf) Q₃ = 1 + h(3N/4 - cf) 2) Raw data: Q₁ = (N+1)/4 th value OR Q₁ = (N/4)th value Q₃ = 3(N+1)/4 th value OR Q₃ = 3(N/4)th value QD = (Q₃ - Q₁) / 2 Measures of Dispersion Absolute Measure Relative Measure of in independent of unit of measurement Formulated in same unit of measurement in which data is given The size of the actual scatter of the data Range, MD, SD, σ² Range = L-S Coefficient of Variation = (SD / Mean) × 100 Mean Deviation (MD) - about mean = ∑|x - Mean|/N (Raw data) - about median = ∑|x - Median|/N (Raw data) - MD about mode = ∑|x - Mode|/N (Raw data) - MD about mode = ∑f|x - Mode|/N (Discrete & Continuous) Standard Deviation (SD) SD = √(∑(x - x̄)² / N) = √(∑u²/n) Variance (σ²) σ² = ∑(x - x̄)² / N = ∑u²/n P(A|B) exp(t) exponential Conditional probability distribution E(X) expectation Value std (X) Cov (X,Y) standard deviation Correlation Algebra Symbol. ()