Unit 1 Intro to Statistics

Unit 1 Intro to StatisticsTerminologySampling and BiasExperimental versus Observational StudiesExperimental Design

StatisticsSet of methods used to describe and make inference on dataNumbers that describe a set of data that is drawn from a population

PopulationSet of all measurements of interest to an experimenterSampleSubset of the populationNeed to be careful to ensure that it is representative of the populationA sample is biased if in some important way it does not represent the populationWe can avoid bias by incorporating randomness into the selection process (more on this later)Numerical MeasurementsPopulationParameterPopulation Mean Population Standard Deviation SampleStatisticSample Mean x-barSample Standard Deviation sTriola page 10

Types of DataQuantitative Data (numeric)Discrete finite number of values or infinitely countableContinuous infinitely uncountable, covers an interval of values w/o gapsQualitative Data (categorical)Can be classified and separated into different categories that are distinguished by some nonnumeric characteristicTriola Page 10

Uses of StatisticsEducationPsychologySociologySportsScienceMedicalPoliticalAnd Many MoreDescriptiveInferentialMisuse of StatisticsSample BiasGraphs designed to be misleadingUse of methods for inappropriate situations (required conditions not met)Incorrect conclusions (correlation vs causality, confounding/lurking variables and more)Levels of MeasurementNominal categorical data that cannot be ordered (eg. Gender)Ordinal data can be ordered but differences are meaningless (eg. Letter grades)Interval similar to ordinal data but differences are meaningful. Zero does not mean absence of quantity. Ratios are not meaningful (eg. Temperature)Ratio zeros and ratios are meaningfulTriola page 10

Sampling BiasSimple random sample (SRS) where every element in the population has an equal chance of being selected.This can be done with random number generators found in texts, calculators, computer programsTypes of bias: non random, non response, self selected, loaded questions, small sample sizeTriola page 15

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Designing Our StudyExperimental researcher uses randomization to assign subjects to appropriate groups (treatment vs control) eg Salk vaccine in the 1950sObservational study no choice as to which subjects are assigned into tratment/control groups (smoking studies)Triola page 23

Experimental vs ObservationalExperimenter can control conditions so that an effect can be observed on the responseCompletely randomized design (blind, double blind)Completely randomized block design (paired data)Use only if it is unethical or impossible to impose treatment or if it unnecessary to impose treatmentCan be confounded with other variablesCannot say that a treatment causes a certain responseConfoundingConfounding occurs when the researcher is not able to determine which factor (often one planned and one unplanned) produced an observed effect.For example, if a restaurant tries adding an evening buffet for one week and it is the same week a nearby theatre happens to show a real blockbuster that attracts unusual crowds to the area, the restaurant can not know whether its increased business is due to the new buffet or the extra traffic created by the theatre.SamplesEnsure that the sample is large enoughEnsure that the sample is representative of the populationRandomizationRandom sample means that every element in the population has an equal chance of being selectedSimple random sample (SRS) means that every sample of size n has an equal chance of being selected

RandomizationRandom number generators found on computers, calculators, tables of random numbers

RandomizationHow would we select a random sample of size 200 from our school?Write each students name on a slip of paper, place slips in a box, mix thoroughly then select 200 of them.Assign each student to a number (ID number, last 4 digits), use a random number generator to generate 200 random numbers to identify the students selected

Types of SamplesSystematic sample choose every kth element in the populationConvenienceStratified population is divided into strata and a sample is selected from each strataCluster - population is divided into clusters, clusters are randonly selected and all elements from those clusters are sampledTriola page 23

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Question 25a. Stratified samples result in random samples only if the sample size for each stratum is proportional to the size of the stratum. If the strata are all the same size, then use the same sample size for each. If one strata is half the size then its sample size should be half of the other samples. It will never result in a SRS

b. If there each element in the population is in only one cluster, then yes, a random sample occurs. The chance that an element is selected is the chance its cluster is selected. But it will never result in a SRS