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Estimation

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the process of determining a likely value for a population parameter.

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Point estimate

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for a population parameter is a single-valued estimate of that parameter; the population mean or proportion.

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Confidence interval

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estimate; a range of values that are likely to cover the true population parameter with a level of confidence attached, such as 95% confidence that the interval contains the unknown parameter.

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Point estimate +/- margin of error

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the general form of confidence interval.

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Two types of estimates that can be produced for any population parameter.

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Point estimate and confidence interval.

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For estimation, classifying the key study variable (outcome or endpoint) ...

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Dichotomous or continuous.

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The number of comparison groups in the investigation...

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dictate the appropriate estimation technique.

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Usual confidence intervals chosen.

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90%, 95%, and 99%. Although any level can be chosen between 0 & 100%.

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What is determined first when calculating the confidence interval?

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Point estimate

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What does it mean when we choose a confidence level of 95%?

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There is a 95% probability that a confidence interval will contain the true population mean.

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Confidence Interval Formula for a continuous outcome.

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(for 95% confidence level) X +/- (z)1.96 Ïƒ/âˆšn

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Margin of error formula

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(for 95% confidence level) 1.96 Ïƒ/âˆšn

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The higher the confidence level, the larger the

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z values - which translate to larger margins of error and wider confidence intervals.

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To be 99% confident that a confidence interval contains the true unknown parameter, we need

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a wider interval.

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t values for confidence intervals are larger for

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smaller samples, resulting in larger margins of error. There is more imprecision with small samples.

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What does it mean when we take an estimate of a population using a 95% confidence level with a sample of 100 people?

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95 out of 100 confidence intervals will contain the true mean value Î¼, and 5 out of 100 will not include the true mean value.

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Sample standard deviation sign

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s

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Statement when confidence interval is made for continuous outcome.

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We are 90%, 95%, 99% confident that the true mean in the population is between a and b.

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Confidence interval formula for a dichotomous outcome.

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pÌ‚ +/- zâˆšpÌ‚1 (1-pÌ‚)/n

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Standard error

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SE(pÌ‚) = âˆšpÌ‚1 (1-pÌ‚)/n

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Statement when confidence interval is made for dichotomous outcome.

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We are 90%, 95%, 99% confident that the true proportion is between a and b.

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What is the middle of the interval?

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The sample mean

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The size of the confidence interval is determined by three (3) things:

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1. how confident you want to be in the estimate, 2. standard deviation in the underlying population, 3. the size of the sample

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The more confident or the higher your confidence level

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the wider your confidence interval will be.

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The larger the standard deviation...

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the farther the confidence interval will deviate from the mean which means a wider interval.

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The larger the sample...

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the higher the accuracy.

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Margin of error is determined by three (3) things:

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1. level of confidence (z or t, the bigger the confidence level the higher the margin of error), 2. standard deviation (bigger the sigma, the higher the margin of error), 3. sample size (the smaller the sample, the larger the margin of error).