03 26 2013 Probability Mutually Exclusive two events happen at some point Addition Rule P A P B Probability of A Probability of B General Addition Rule P A P B P A B Independence One event does not affect the outcome of the next General Multiplication Rule P A x P BlA Probability of B given A P BlA P A B P A How to check for independence P A x P B P A B If equal than A B are independent Compliment Rule P A c 1 P A Statistics and Variation 03 26 2013 Intro to Book Statistics a way of reasoning along with a collection of tools and methods designed to help us understand the world quantities calculated from data Data values along with their context singular form Datum Data Data 03 26 2013 Answering Who What When Where Why and How can provide a context for data values o If you cant answer who and what then you don t have data o Add the context of Who and What and organize the values into a data table The rows of a data table correspond to individual cases about whom or about which if they re not people we record some characteristics Case Respondents Subjects or Participants Experimental Units subjects that are tested on an individual about whom or which we have data individuals who answer a survey people on whom we experiment animals plants websites and other inanimate Records Variables in a database rows are called records ex Purchase records the characteristics about each individual case What has been measured Relational Database two or more separate data tables linked together so that information can be merged across them Categorical Variable variable names that categorize and answer questions about how cases fall into those categories Quantitative Variable when a variable measured numerical values with units and the variable tells us about the quantity of what is measured tell us how each value has been measured Units There are exactly as many categories as individuals and only one individual in each category This is called the Identifier variable Nominal Variables Categorical variables used only to name categories Ordinal Values Time Series the numeric location of an item within an order when you have the same variable measured at regular intervals over time popular in business Ratio Level Similar to interval except there is a true zero or starting point and the ratios of data values have meaning Cross Sectional Data same time point where several variables are measures at the when you actively manipulate variables to see what Observational Studies Observations and measurements are made in a way that does not change the response or the variable being the analysis of large transactional data sets for purposes other than those for which the data were originally Experiment happens measured Data Mining collected Surveys and Sampling 03 26 2013 Three ideas of Sampling 1 Examine a Part of the Whole o Sample Survey survey designed to ask questions of a small group of people in the hope of learning something about the entire population o When a sample is biased the summary characteristics of a sample differ from the corresponding characteristics of the population it is trying to represent 2 Randomize o Randomization a defense against bias in the sample selection process in which each individual is given a fair random chance of selection o The variability from sample to sample is often referred to as sampling error even though no error has occurred 3 The Sample Size is What Matters o The size of the sample determines what we can conclude from the data regardless of the size of the population o Many people think that we need a large percentage or fraction of the population but in fact all that matters is the size of the sample A Census Does It Make Sense Census An attempt to collect data on the entire population of interest It can be difficult to complete a census It could be bad information because the population may change It can be cumbersome many errors Populations and Parameters Parameter A numerically valued attribute of a model for a population We rarely expect to know the value of a parameter but we do hope to estimate it from sampled data Population Parameter A numerically valued attribute of a model for a population Sample Statistic parameter a value calculated for sampled data particularly one that corresponds to and thus estimates a population Representative Sample A sample from which the statistics computed accurately reflect the corresponding population parameters Simple Random Sample SRS SRS A sample in which each set of n elements in the population has an equal chance of selection Sampling frame a list of individuals from which the sample will be Sampling Variability or sampling error isn t a problem drawn Other Sampling Designs Stratified Sampling o Strata subsets of a population that are internally homogeneous but may differ one from another A sampling design in which the o Stratified Sampling population is divided into several homogeneous subpopulations or strata and random samples are drawn from each stratum Cluster and Multistage Sampling o Cluster A representative subset of a population chosen for reasons of convenience cost or practicality o Cluster Sampling A sampling design in which groups or clusters representative of the population are chosen at random and a census is taken of each o What s the difference between cluster and stratified sampling Strata are homogeneous but differ from one another Clusters are more or less alike each heterogeneous and resembling the overall population o Sampling schemes that combine several methods are called multistage samples Systematic Samples o Systematic Sampling A sample drawn by selecting individuals systematically from a sampling frame Defining the population The sampling frame limits what your survey can find out Target sample are the individuals whom you intend to measure responses You re not likely to get responses from all of them The Valid Survey Use the right sampling frame Know what you want to know Ask specific rather than general questions Watch for biases Be Careful with question phrasing Be careful with answer phrasing o Measurement Errors inaccurate responses intentional or unintentional o Pilot Test administered a small sample that is drawn from the sampling frame and a draft form of the survey instrument is Convenience sampling when you include the individuals who are convenient Undercoverage in which some portion of the population is not sampled at all or has a smaller representation in the sample than it has
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