Final Project Posters

Research Goals-Basic naturs of the research question/objective Descriptive-Characterize attributes of the population Causative Understanding new change in explanatory variable influences value of Categorical vs Quantitative Spipchart plots data as a point and shows variation in samples and density of distribution Boxplot-5-number summary in a graph with every horizontal line representing o value in the summary Maans Plot-avisual representation of the mean, often with measure of spread as error bars response variabile Predictive predicting the sutzoima for a specific unit in a papulation Sampling Processes selecting a subset of units collect, data bom (sbould use probability sampling in order to avoid bins Quantitative vs Quantitative Scatterplot about direction and strength (strong vs weak), in the Bias-Misleading data caused by systematic favouritiam in the selection process Undercoverage-some group(s) in the population are left out Bampling-systematic favouritiem during samping misteading data Non-Response-some individuals from intended sample don't respund Self-Selection-individuals self-select to participate in response to open call Sampling Frame ast of units that we take our sample from, identified by the researcher Sampling Strategies Simple Random Sampling-alt cumbinations equally katy Random Sampling-every unit has same chance of being selected Stratified Sampling-some units drawn from each stratum Systematic Sampling-unit selected as starting point, then more units selected at an interval, an Cluster Sampling (sampling frame is subdivided into 2 clusters based on selected variable(s) then all units are selected from some clusters) Multistage Sampling-at least 2 iterations of sampling strategies Confounding Presence of additional variables whose effects on the response cannot be separated from that of the factor(s) of interest (hard to identify what is actually responsible for the observed group differences) Methods to Prevent Confounding unding Control Accounting for variation in potential explanatory variables ta isolate impact of factor(s) of interest Limit (or remove) Variation Distribute Variation Across Treatments Use Comparison Groops Collect Data on Variables of Concern Randomization-Only in experimentation (using chance to assign individuals from sample. to treatments or the treatment order) Replication Inclusion of more than one individual thom the sample in each treatment or comparison group Study Design Observational Measure explanatory and response variables as they naturally occur Survey-collecte info on variables of interest and other variables as well Cohort Studies-emergence of condition observed over time Case-Control Skutty sampa cases selected and compared against sample of controls Experimental-Impose a condition related to the saplanatory variabte(s) to effect change on the response variable Completely Randomized Design each unit randomly assigned to treatments Randomized Block Design units subdivided into blocks then randomly assigned to treatments Matched Pairs Desigs pairs of units matched and randomly assigned to Treatments Repeated Moses Designach unit assigned to all treatwilts Types interval (distance between consecutive values is constant), quantitalive ( means none) of Variables nominal (values con bo narmed), erdinal (values can be ordered), Types of Samples" Independent (no 1-1-1 matching across comparison groups Matched/Paired Samples (1-11-1] matching ocross comparison groups, is comparing initial vs tinat weight) Measures of Spread Range-infated by outliers and skews 5-number summary-breaks into min, first quartile, hatt, second quartile, and max Interquartile range-determines how spread out the middle of the data are Variance takes every value of X minus mean, squares it, divides by total number of samples (typical squared difference) Standard deviation-square root of variance Describing Shape Symmetric Right for Left-) Skewed-tail on side of peak that graphis named after is more spread out Modality number of prominent peaks quantitative distibution. More prominent feature than symmetry Measure of Centre Describe the typical or expected value of a quantitative distribution Mean and median are mest ceremon, with mean being influenced by skew and outliers and mediant being resistant. Representing Relationships Categorical vs Categorical Two-Way Table-all variables suns to 1 veth columns and rows both having variables Conditional Distribution Table-rows sum to 1, alloves us to relationships between distributions of variables Bar Goph at least one categoncal variable on the horizontal avis and some kind of frequency on vutical axis. Can bo stacked or side by side (conditional dist, for stacked so same height across all hars) shape of a function, can add colour to represent categorical variables Parameters (theta) numbers that characterize the probability distribution of a variable for the poputation Probability Distribution-how likely values are for some vanables Examples of distribution-Normal, Poisson (discrete variables), uniform (all Random Variables-have numerical outcomes from a procedure governed by one value), binomial chance and are described by the expected value (E[X]an average value of X weighted by the likelihood of the possible X values) and the variance (Var(X)-measures the spread of X) Estimators (theta hat) an equation/function for estimating a parameter form a sample Sampling distribution-probability distribution of an estimator, based on many samples of the same size from the population Choosing an estimator favour unbiased estimators with the lowest MSE, mean is unbiased, median and some 5Ds are biased Sampling emer-random difference between an estimate and the parameter due to taking a random sample Parameter is the unknown constant, estimator is a function of the random variable (X), estimate is a constant (observed value of the estimator) Statistical Models. generalized description of the DOP (function and associated assumptions) Normal Distributions-X-Nip,aj continuous probability distributions, defined by mean and variance, values are Real nuntiers, bell-shaped unimodal and symmetric around the mean Probability Density Function (PDF)-parameters are constanta for a particular distribution, total area is 1, density is always greater than 0. Basic modet structure- Data Model Extor Empty model-Y Y (value) and (emor) are random variables, often assumed that e-, στ Categorical exp, var You and Y Quantitative exp. var... Confidence Intervals-estimates value of a parameter, use intervals of the form -q 10+GO Chose aq such that PYYqaYo) cicis success rato of the method for capturing the parametar) Of the form 000 O is point estimate (observed value) qis critical value (constant cliosen from PDF based on desired confidence lovel) CD (accounts for potential vanability of estimator) P-Values and Null Hypothesin Testing Analyze the design in terms of number, identity, and type of comparison groups and types of variables Statistical Hypothesis-statements about the unknown parameter, based on research claim/prediction Null Hypothesis (4) assumed to be true, provides one value for the parameter, assumes no difference, relationship, or effect Alternative Hypothesis (M.j-what we conclude if evidence against Ha, can be two-tailed or one-tailed Extreme & values are evidence against H Patue-probability of observing sample data as extreme or more extreme if the mall model is correct t confidence interval and test for the san Sampling distribution of the means-unbiased for random samples, approximately Normal if the observations are from a Normal distribution and/or n is tange (30-50) Standard error of sample mean-sarmate variance (s) estimates the population variance (0) so se estimates (0) -distributions, Yot, class of continuous POFs, only parameter i dugress of freedont, possible values are Real numbers, have heavier taits than Normal distributions Normal QQ Plot-assesses the fit of the Normal model (line) to data (points) with Sample Quantiles on y-axis and Theoretical Quantibes on x-Conditions of t precedures for p-observations must be from a SRS with replacement from a population with a Nurmat distribution (robust to some deviations from Nommality if n is large enough and from an approximatoly symmetric distribution wittiout extreme outliers) Cifers//nimargin of enar is t s/n) 1-test for mean-2 paired comparison groups 1-test for difference b/w means independent samples from 2 populations Simple Linear Regression (SLR)-1-tust for stope, different samptes may suggest different relationships (used for 2 quantitative variables). Used for relationship b/w 2 quant, variables Residuals y difference between observed value of response (y) and that predictet ty) by the sample regression They should appear normalty distributed on a QQ pilot and show ne apparent pattern in vertical spread on a residual plot Must be independent, linear (Y vs X), Normal, and have constant 50 to fil SU