The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics The Language of Sampling Lecture 6 Sections 2 1 2 4 Bias Types of Bias Examples of Bias Assignment Robb T Koether Hampden Sydney College Fri Jan 23 2009 Outline The Language of Sampling Robb T Koether 1 Chapter 1 Parting Comments Chapter 1 Parting Comments 2 Parameters and Statistics 3 Bias 4 Types of Bias 5 Examples of Bias 6 Assignment Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias It seems ridiculous to sample only one value from the bag and then try to make a decision based on that one value Types of Bias Examples of Bias Assignment Yet in a sense that is what happens in statistics Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Consider Bag A and Bag B again Suppose we sample say 10 values and average them There are 92378 possible samples The averages of these 92378 samples take on a characteristic shape called the bell curve We will select one of the samples and base our decision on that one average Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics This is the distribution of sample averages from Bag A 0 08 0 06 Bias Types of Bias Examples of Bias 0 04 Assignment 0 02 20 30 40 50 60 Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics This is the distribution of sample averages from Bag B 0 08 0 06 Bias Types of Bias Examples of Bias 0 04 Assignment 0 02 20 30 40 50 60 Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Both bags together 0 08 0 06 Bias Types of Bias Examples of Bias 0 04 Assignment 0 02 20 30 40 50 60 Parting Comments The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Here are the distributions if we sampled 20 values 0 12 0 10 0 08 Bias Types of Bias Examples of Bias 0 06 0 04 Assignment 0 02 20 30 40 50 60 The Language of Sampling The Language of Sampling Robb T Koether Chapter 1 Parting Comments Definition Population size The population size is the number of members in the population It is denoted by the symbol N Parameters and Statistics Bias Types of Bias Examples of Bias Definition Sample size The sample size is the number of members in the sample It is denoted by the symbol n Assignment Definition Unit or subject A unit or subject is a single member of the population The Language of Sampling The Language of Sampling Robb T Koether Definition Parameter Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias A parameter is a numerical characteristic of the population Definition Statistic A statistic is a numerical characteristic of a sample Definition Variable Assignment A variable is a characteristic of individual members of the population The Language of Sampling The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Definition Sampling Error The sampling error is the difference between the value of a statistic and the value of the parameter it was meant to estimate The purpose of a statistic is to estimate the corresponding parameter For example a sample average is used to estimate the population average Parameters and Statistics The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias Assignment For numerical data we usually use the average of the values in the sample For non numerical data we usually use the proportion of observations in a specific category Parameters and Statistics The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Example Averages and Proportions In the study of the joggers and non joggers one variable was whether the person was alive 19 years later This variable is non numerical It was summarized as a proportion 15 of joggers and 34 of non joggers did not survive 19 years Parameters and Statistics The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Example Averages and Proportions Another variable was number of years until the first disability This variable is numerical Types of Bias Examples of Bias Assignment It was summarized as an average The average number of years until the first disability was 16 years longer for joggers than for non joggers Random vs Representative The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Definition Random sample A random sample is a sample that is selected using a procedure at least one step of which is left to chance Bias Types of Bias Definition Representative sample Examples of Bias A representative sample is a sample that has all the same characteristics except size as the population from which it was taken Assignment Biased Samples The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Definition Biased sampling method A sampling method is biased if it systematically produces a sample whose characteristics differ from those of the population Types of Bias Examples of Bias Assignment Definition Biased sample A sample is biased if was selected by a biased sampling method Why Sample The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Bias Types of Bias Examples of Bias Assignment The purpose of randomness is to prevent bias For random samples the sampling error gets smaller as the sample size gets larger In other words if a random sample is large enough then we can be assured that it is representative Types of Bias The Language of Sampling Robb T Koether Chapter 1 Parting Comments Parameters and Statistics Definition Selection bias A sampling method exhibits selection bias if some units in the population are more likely to be selected than others Bias Types of Bias Examples of Bias Assignment Definition Nonresponse bias A sampling method exhibits nonresponse bias if some subjects that were selected to be in the sample choose not to participate Types of Bias The Language of Sampling Robb T Koether
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