Chapter 1 Parting CommentsParameters and StatisticsBiasTypes of BiasExamples of BiasAssignmentThe Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentThe Language of SamplingLecture 6Sections 2.1-2.4Robb T. KoetherHampden-Sydney CollegeFri, Jan 23, 2009The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentOutline1Chapter 1 Parting Comments2Parameters and Statistics3Bias4Types of Bias5Examples of Bias6AssignmentThe Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsIt seems ridiculous to sample only one value from thebag and then try to make a decision based on that onevalue.Yet, in a sense, that is what happens in statistics.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsConsider 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 acharacteristic shape (called the bell curve).We will select one of the samples and base ourdecision on that one average.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsThis is the distribution of sample averages from Bag A:20304050600.020.040.060.08The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsThis is the distribution of sample averages from Bag B:20304050600.020.040.060.08The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsBoth bags together.20304050600.020.040.060.08The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParting CommentsHere are the distributions if we sampled 20 values.20304050600.020.040.060.080.100.12The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentThe Language of SamplingDefinition (Population size)The population size is the number of members in thepopulation. It is denoted by the symbol N.Definition (Sample size)The sample size is the number of members in the sample. Itis denoted by the symbol n.Definition (Unit or subject)A unit or subject is a single member of the population.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentThe Language of SamplingDefinition (Parameter)A parameter is a numerical characteristic of the population.Definition (Statistic)A statistic is a numerical characteristic of a sample.Definition (Variable)A variable is a characteristic of individual members of thepopulation.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentThe Language of SamplingDefinition (Sampling Error)The sampling error is the difference between the value of astatistic and the value of the parameter it was meant toestimate.The purpose of a statistic is to estimate thecorresponding parameter.For example, a sample average is used to estimate thepopulation average.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParameters and StatisticsFor numerical data, we usually use the average of thevalues in the sample.For non-numerical data, we usually use the proportionof observations in a specific category.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParameters and StatisticsExample (Averages and Proportions)In the study of the joggers and non-joggers, onevariable was “whether the person was alive 19 yearslater.”This variable is non-numerical.It was summarized as a proportion: 15% of joggers and34% of non-joggers did not survive 19 years.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentParameters and StatisticsExample (Averages and Proportions)Another variable was “number of years until the firstdisability.”This variable is numerical.It was summarized as an average: The averagenumber of years until the first disability was 16 yearslonger for joggers than for non-joggers.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentRandom vs. RepresentativeDefinition (Random sample)A random sample is a sample that is selected using aprocedure at least one step of which is left to chance.Definition (Representative sample)A representative sample is a sample that has all the samecharacteristics (except size) as the population from which itwas taken.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentBiased SamplesDefinition (Biased sampling method)A sampling method is biased if it systematically produces asample whose characteristics differ from those of thepopulation.Definition (Biased sample)A sample is biased if was selected by a biased samplingmethod.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentWhy Sample?The purpose of randomness is to prevent bias.For random samples, the sampling error gets smalleras the sample size gets larger.In other words, if a random sample is large enough,then we can be assured that it is representative.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentTypes of BiasDefinition (Selection bias)A sampling method exhibits selection bias if some units inthe population are more likely to be selected than others.Definition (Nonresponse bias)A sampling method exhibits nonresponse bias if somesubjects that were selected to be in the sample choose notto participate.The Languageof SamplingRobb T.KoetherChapter 1PartingCommentsParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentTypes of BiasDefinition (Response bias)A sampling method exhibits response bias if the subjectsgive what they perceive
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