STAT1008 SEMESTER NOTES
STAT1008 SEMESTER NOTES SECTION 1 What is statistics? − − −
A way to get information from data Framework for dealing with variability A way to make decisions under uncertainty
Statistical inference: The problem of determining the behaviour of a large population by studying a small sample of that population Population: All elements sharing some set of characteristics − − − −
A collection of the whole of something Comprises the universe for the purpose of marketing research problems Gives parameters – True values for spread, centre, etc. Census: A study of all elements of a population
Sample: A subgroup of the population selected for participation in a study − −
A set of individuals drawn from the a population Gives statistics – Estimate the parameters o Use inference for the estimation o Examples: Sample mean, sample standard deviation
Statistical inference: The process of making an estimate, prediction or decision about a population, based on a sample
TYPES&OF&ERRORS& Sampling error: The differences that exist between a population and a sample as a result of sample selection − − − −
Reduced by taking a larger sample The variation or chance differences from sample to sample Referred to as the ‘margin of error’ in pools Will always occur to some extent – Try to minimise nonsampling to compensate
Nonsampling+Errors+ Nonsampling error: Larger samples won’t reduce nonsampling error – More serious −
Includes coverage error, nonresponse error and measurement error
Coverage error: −
Results from selection bias
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− −
o Group skewed a certain way Doesn’t cover the entire spectrum Eg. Girls in our class as a sample of ANU would only be 1st year, only CBE students, etc.
Nonresponse error: − −
−
People in upper and lower economic classes respond less frequently to surveys than those in the middle class – Leads to nonresponse bias Cant assume that those who do respond to surveys are the same as those who don’t o Know more about middle than upper and lower Need to follow up in order to reduce error
Measurement error: −
3 sources: o Ambiguous working of questions o Hawthorne effect ! Respondent feels obligated to please the interviewer ! Must train interviewers ! Questions must be neutral and not leading o Respondent error ! People answering questions incorrectly ! Minimised by: • Screening responses and re-contacting respondents with unusual answers • Establishing a program of recontacting a small number of randomly chosen individuals to determine the reliability of responses
Ethical+Issues+ − − − −
Coverage error becomes an ethical issue if particular groups/individuals are purposely excluded Nonresponse error if survey is designed so that some groups are less likely to respond Sampling error if findings are purposely presented without reference to survey size and margin of error Measurement error if: o Leading questions o Interviewer intentionally creates a Hawthorne effect or guides respondent o Respondent willingly provides false information
SAMPLE&VS.&CENSUS&
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SAMPLING&PROCESS& Want sample to be representative of the full population – Want every characteristic present Issue with self-selected samples: People choosing to do the survey are more interested in the topic than the general population – Sample is biased Steps: 1. Define sample frame − List of ALL items that make up the population − Eg. population list, directory − Choice of frame is important − Sample is then chosen from sample frame 2. Nonprobability vs. Probability Sampling? − Nonprobability sampling: Choose the items to be included without knowing their probabilities of selection o No statistical inference o Cheaper and faster but cannot apply many tests − Probability sampling: Selecting items based on known probabilities o Statistical inferences may be made based on result
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A way to get information from data Framework for dealing with variability A way to make decisions under uncertainty
Statistical inference: The problem of determining the behaviour of a large population by studying a small sample of that population Population: All elements sharing some set of characteristics − − − −
A collection of the whole of something Comprises the universe for the purpose of marketing research problems Gives parameters – True values for spread, centre, etc. Census: A study of all elements of a population
Sample: A subgroup of the population selected for participation in a study − −
A set of individuals drawn from the a population Gives statistics – Estimate the parameters o Use inference for the estimation o Examples: Sample mean, sample standard deviation
Statistical inference: The process of making an estimate, prediction or decision about a population, based on a sample
TYPES&OF&ERRORS& Sampling error: The differences that exist between a population and a sample as a result of sample selection − − − −
Reduced by taking a larger sample The variation or chance differences from sample to sample Referred to as the ‘margin of error’ in pools Will always occur to some extent – Try to minimise nonsampling to compensate
Nonsampling+Errors+ Nonsampling error: Larger samples won’t reduce nonsampling error – More serious −
Includes coverage error, nonresponse error and measurement error
Coverage error: −
Results from selection bias
Page 1 of 41
− −
o Group skewed a certain way Doesn’t cover the entire spectrum Eg. Girls in our class as a sample of ANU would only be 1st year, only CBE students, etc.
Nonresponse error: − −
−
People in upper and lower economic classes respond less frequently to surveys than those in the middle class – Leads to nonresponse bias Cant assume that those who do respond to surveys are the same as those who don’t o Know more about middle than upper and lower Need to follow up in order to reduce error
Measurement error: −
3 sources: o Ambiguous working of questions o Hawthorne effect ! Respondent feels obligated to please the interviewer ! Must train interviewers ! Questions must be neutral and not leading o Respondent error ! People answering questions incorrectly ! Minimised by: • Screening responses and re-contacting respondents with unusual answers • Establishing a program of recontacting a small number of randomly chosen individuals to determine the reliability of responses
Ethical+Issues+ − − − −
Coverage error becomes an ethical issue if particular groups/individuals are purposely excluded Nonresponse error if survey is designed so that some groups are less likely to respond Sampling error if findings are purposely presented without reference to survey size and margin of error Measurement error if: o Leading questions o Interviewer intentionally creates a Hawthorne effect or guides respondent o Respondent willingly provides false information
SAMPLE&VS.&CENSUS&
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SAMPLING&PROCESS& Want sample to be representative of the full population – Want every characteristic present Issue with self-selected samples: People choosing to do the survey are more interested in the topic than the general population – Sample is biased Steps: 1. Define sample frame − List of ALL items that make up the population − Eg. population list, directory − Choice of frame is important − Sample is then chosen from sample frame 2. Nonprobability vs. Probability Sampling? − Nonprobability sampling: Choose the items to be included without knowing their probabilities of selection o No statistical inference o Cheaper and faster but cannot apply many tests − Probability sampling: Selecting items based on known probabilities o Statistical inferences may be made based on result
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