1Class 14 Statistical InferenceSurvey ResearchClass Outline• Statistical Inference– Sampling Error– Sampling Distribution– Point Estimate and Confidence Interval• Survey Research– Asking Questions– Advantages and Disadvantages of Various Survey Methods– Secondary Data AnalysisSampling Error• We are interested in certain characteristics of a population. These characteristics are called population parameters. • We do not observe the whole population. Instead, we draw a sample and calculate sample statistics. • We use sample statistics to estimate population parameters. • Differences between population parameters and sample statistics that are due only to chance factors are called sampling error.• The magnitude of sampling error can be estimated statistically.2Point Estimate and Interval Estimate• When a population parameter is estimated by a single number, that number is called a point estimate. (Point estimate is unlikely to be the true population parameter.)• An interval estimate of the population parameter µ consists of two bounds within which µ is estimated to lie. That is, L ≤ µ ≤U, where L is the lower bound, and U is the upper bound.Confidence Levels and Confidence Interval• Statistical inference: Suppose that we draw a sample of 100 families and measure their income. The mean income comes to $40000, and the standard deviation is $5000. Then the true population parameter for mean family income lies between (39020, 40980) with a probability of 95%.• A confidence interval is the interval within which you believe that the true parameter lies with a fixed probability. That probability is called the confidence level.• The 95% confidence interval is calculated as )*96.1,*96.1(nsdXnsdX +−Confidence interval Confidence levelSampling Distributions• Sampling distribution is a hypothetical distribution of a statistic (such as the mean) across all the random samples that could be drawn from a population.• Intuition: larger samples result in a sampling distribution more tightly clustered around the population mean. That is, the larger the sample size, the less the sampling error. • A larger sample size means a smaller confidence interval for the population parameter.• Stata demo: sample mean distribution (smddemo))*96.1,*96.1(nsdXnsdX +−3Determining Sample Size• Less sampling error is desired Æ larger sample is needed• Homogeneous population Æ smaller sample may be adequate.)*96.1,*96.1(nsdXnsdX +−Errors in Survey Research • Two common sources of survey errors– Errors of observation (poor measurement) – Errors of non-observation (omission of cases that should have been included in the sample)Basic Modes of Survey• Self-administered mail survey• Face-to-face interview survey • Telephone interview survey• Web survey• Multi-mode survey4Guidelines for Asking Questions• Use the right question forms– Closed- vs. open-ended questions.– Contingency questions with clear instructions on skip pattern.– Matrix questions.• Use mutually exclusive and exhaustive categories.Guidelines for Asking Questions• Avoid ambiguity.– native American; residential location• Avoid double-barreled questions.– Do you think the President should be impeached and compelled to leave the presidency?• Avoid negative items.– Do you agree that there should not be a tax increase?(Does “no” mean tax increase or no tax increase?)• Avoid double-negatives. – Does it seem possible to impossible to you that the Nazi extermination of the Jews never happened?• Avoid biased items and terms.– Assistance to the poor vs. welfare– Halting rising crime rate vs. law enforcementGuidelines for Questionnaire Construction• Respondents must be competent to answer.• Respondents must be willing to answer.• Short items are best.• Decide whether to add an explicit neutral response category.– Eliminating the “neutral” category reduces fence-sitting.– Adding the “neutral” category reduces floating.5Questionnaire Design• Include instructions for the questionnaire. • Be aware of issues with ordering items. • Use existing question sets if available (e.g. CES-D scale of depression)• Pretest the questionnaire.Improving the Response Rate• Give an incentive (gift, cash).• Send a notification letter.• Follow up on non-response.– Mail survey: send a reminder.– Face-to-face or telephone survey: Vary the days and times to visit/call. • ProbeSelf-Administered Mail Survey • Advantages– Low cost– Can offer anonymity• Disadvantages– Requires literacy– Low response rates (non-response biases)– Can only ask simple questions– Interviewer cannot observe6Face-to-face Interview Survey• Advantages – Fewer incomplete questionnaires– Higher response rate– Interviewer can take observation notes– Appropriate for complex questionnaires– Allows for relatively long questionnaires• Disadvantages –Higher cost – Slow field work– Interviewer effectsTelephone Interview Survey• CATI (computer-assisted telephone interview)• Advantages– Lower cost than interview surveys– Quick implementation– Easier to supervise field work • Disadvantages – Questions must be short and simple– Answering machinesWeb Survey• Advantages– Low cost– Quick implementation– Data entry errors are eliminated– Quick results– Can program contingency questions• Disadvantage– Selective sample– Not good at ensuring completion7Comparison of Various Survey ModesGoodPoorGoodPoorTime-savingGoodPoorAverageGoodLower costGoodPoorAverageGoodAvoid distortion of answersAverageGoodAverageAverageAllowable length of questionnaireGoodGoodPoorAverageHandling complex questionsPoorGoodAverageAverageQuestionnaire completionPoorGoodGoodAverageResponse ratePoorGoodGoodAverageReaching a representative sampleWebInterviewPhoneMailSecondary Data Analysis• Secondary data analysis has become the primary means of conducting empirical research. • Reasons:– Concern with generalizability.– Increased cost of conducting independent surveys.– Wide availability of existing data, such as
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