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Soc202 Chapter 7 & Chapter 8.docx

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Scott Schieman

Soc202 Readings notes 2 Chapter 7 - Using Probability Theory to Produce Sampling Distributions (Focus on pages 206 - 215 (up to "Nominal Variables"); pages 219 – 222 ) Point Estimates  Sampling error – the difference between the calculated value of a sample statistic and the true value of a population parameter (unknown)  Point estimate – a statistic provided without indicating a range of error. (mean of a population) o There’s a variability in statistical outcomes from sample to sample Predicting Sampling Error  Repeated sampling – drawing a sample and computing its statistics and then drawing a second sample, a third, a fourth, and so on. (learned that sampling is only a estimate)  Symbols to represent population parameter for interval/ratio variables o UX = the mean of a population o OX = the standard deviation of a population  Sampling error = Xbar – UX  Sampling error is patterned and systematic and therefore is predictable o 1) The resulting sample means were similar in value and tended to cluster around a particular value. o 2) sampling variability was mathematically predictable form probability curves Sampling distribution  From repeated sampling, a mathematical description of all possible sampling outcomes and the probability of each one  A raw score distribution is scores of each person in your sample Sampling distribution for interval/ratio variables  Example: Physicians o 48 years = mean of sample means o UX = mean of a sampling distribution of means, will always equal to population mean o As with any normal curve, standard deviation is the distance to the point of inflection of the curve o Sampling distribution of means (X bar) describes all possible sampling outcomes and the probability of each outcome. Standard Error  Standard error – the standard deviation of a sampling distribution. The standard error measures the spread of sampling error that occurs when a population is sampled repeatedly o Measures the spread o Equation – the standard error of a sampling distribution of means is the samples standard deviation divided by the square root of the sample size (S(xbar) = sx/square root of N) Law of large numbers  The larger the samples size, the smaller the standard error  Replacing n with higher number, sample error decreases The central limit Theorem  Regardless of the shape of a raw score distribution of an interval/ratio variable, its sampling distribution will be normal when the sample size, n, is greater than 121 cases and will center on the true population mans.  Sampling distribution has a small range than the raw score distribution (not a normal curve)  Distributions are rectangular in shape when the raw scores have equal chances of getting picked Bean Counting as a Way of Grasping the Statistical Imagination  Sampling distribution is a probability distribution, it tells us how frequently to expect any and all sampling out comes when we draw random samples  The central limit theorem essentially states that random sampling results in normal curves: symmetrical distributions that bunch in the middle and tail out to the sides  As long as sample size is sufficiently large, the sample distribution of proportions takes the bell shape of a normal curve Distinguishing Among Populations, Samples, and Sampling Distributions  Sample = Statistics, Population = Parameter, Sampling distribution = Hypothetical distribution of an infinite number of samples of size N. Statistical Follies and Fallacies: Treating a point estimate as though it were absolutely true  No single statistics is the last word on estimating a parameter of the population Chapter 8: Parameter Estimation Using Confidence Intervals Focus on pages 237 - 256 (up to "choosing sample size"); also, skip "confidence intervals of the mean for small samples" paragraph on page 251  The statistics of a sample are estimates.  In this chapter we learn to say confidently just how close this single point estimate is to the true parameter within a range of error.  Confidence Interval – a range of possible values of a parameter expressed with a specific degree of confidence ( draw only one sample and compute point estimate) o With this, we take a point estimate and couple it with a knowledge about sampling distribution o The objective is to estimate a population parameter within a specific span or “interval” of values o Frequently used in exploratory studies o The level of confidence – a calculated degree of confidence that a statistical procedure conducted with sample data will produce a correct result for the sampled population (success rate) Confidence Interval if a Population Mean  Sample statistics are the tools to answer what is the value of UX?  The level of expected error – the difference between the stated level of confidence and “perfect confidence” of 100 percent.  Calculation: the level of confidence and the level of significance o a symbolize the level of expected error/ level of significance o Level of confidence = 100% - a o a = 100% - level of confidence  Calculation: the standard error for a confidence interval of population mean o Because the
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