STAT1201 Notes Module 1.1: Variability Error variability: natural and measurement variability in data - Natural: dictated by nature, eg. height - Measurement: based on measurement techniques - Having error makes it necessary to replicate experiments Group variability: differences between groups causing variability - Eg. Height differs between genders - Approach: see if group variability is larger than error variability Sampling variability: how much an estimate varies between samples - Eg. One group of males may have different heights than second Variable: characteristic recorded in study Quantitative: measurements · Continuous: any value over range (scale with no limits) · Height, weight, temperature, time, distance · Discrete: small number of possibilities, finite set · Number students in class, cars in carpark, goals scored Categorical: groups of objects with specific characteristic . Nominal: not quantitative · Gender, colour, type of animal · Ordinal: categories without an order " Age group, competition rank, education level Module 1.2: Designing studies Observational: observes sample and measures characteristic, passive - Conclusions made without influencing/changing existing conditions Experimental - Randomly assigned groups (treatment/control) - Blind: either participants or researchers unaware of assigned group - Double-blind: both participant and researchers unaware - Comparative study: 2 groups that are control and treatment group - Randomisation reduces bias Block design: divides subjects into blocks based on factors that may affect outcome - Eg. MT, MC, FT, FC groups if gender could affect results Null hypothesis (Ho): statement of "no effect" Hypothesis (H1): expected relationship/outcome between variables, directional P-value: measure of strength of evidence against null hypothesis - P < 0.05 shows data is statistically significant, reject null - P > 0.05 shows evidence doesn't support hypothesis, accept null
Module 3.1: Visualising Distributions Continuous data can be represented by the following: Dot plot: represents individual data points on number line, shows distribution of variability - Three characteristics shown on plot · Central tendency: median/mode · Spread/variability: shows range of values · Distribution: outliers, data shape, patterns/trends Dot Plot 4 Frequency 2 - N 4 6 8 9 10 10 12 14 16 17 = 19 20 Data Values Histogram: larger samples divided into 'bins', shows density and distribution - Mode: peak of distribution - Unimodal: one mode, bimodal: two modes, multimodal: multiple modes - Two or more modes indicates presence of categorical variable related to quantitative variable being explored - Limited: only discrete choices for number of bins Side by side plot: visualising relationship between quantitative and categorical variable - 2 dot plots alongside each other - Split categorical values to compare, eg. Gender 70 - 60 50 .. Breath Held (s) 40 30 20 Female Male - Skewness: describes asymmetry of distributions (mean, median, mode are not equal) Either positive or negative, concentrated on one side of axis
Module 3.2: Quantiles Quantiles: dividing data into equal-sized intervals with approx. equal number of data points - To calculate: order values in ascending order - First quartile (Q1): 0.25 quantile, lowest 25% of data - Second (Q2) or sample median: value separating data