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Chapter 6: Estimation Two methods in inferential statistics: 1. Estimation 2. Hypothesis testing Estimation Two kinds of estimation techniques: 1. Interval Estimation 2. Point Estimation Interval Estimation Concept of sampling error o The difference between the population parameter and the sample statistic o E.g. sample of flipping a coin 20 times, comparing the number of heads obtained to the population parameter (.5), the difference (say, .65-.5=.15) is the sampling error Concept of standard error o A measure of the variability of the sample statistic when multiple samples of the same size are drawn from the same population o There are ways to compute this standard error (SE); does not mean actual collecting of the sample and computing its statistic multiple times o Typically, 2/3 chance that sampling error is smaller than SE o The lower is SE, the closer is the statistic to the parameter o Statistical focus can be on anything (e.g. in flipping coin example, focus is on proportion of heads obtained); e.g. mean, correlation coefficient etc o Common ways of denoting: (mean +/- Standard error) Concept of Confidence Interval o Stated as a percentage (usually 95 or 99) and the range (e.g. 95% CI 0.7 to 0.86) o What it means is there is a 95 out of 100 chance that this interval of 0.7 to 0.86 is one of the many possible intervals that would contain the parameter between the interval limits. o Range of Confidence interval will be greater than add/subtract 1 SE from the mean o Advantage over SE: one reason, there is % of confidence (95 or 99) whereas for SE, there is no % stated (typically about 68 % confidence level) o For a statistic to be close to the parameter, it should have a high confidence interval, small range and based on a large sample size. Point Estimation o Instead of intervals/range, the sample statistic is taken as the estimate for the parameter Warnings about estimation o Number +/- number can mean many things: do not always assume its SE, read the article carefully o SE itself is an estimate, not a for-sure value o For CI, sample statistic not always in the middle of the upper and lower interval o For estimation to work, there must be legitimate connection between sample and population: o For probability sample, sample randomly extracted with no refusals to participate, mortality or response rate problems o For non-prob sample, abstract population match closely with nature of sample