Estimating population parameter

what is an estimation procedure?

• point estimate = one sample stat is used to estimate a population value

• interval estimate (confidence interval) = a range of values estimating the population

• margin of error = how far the interval extends around the point estimate

what are indicators for choosing estimators?

bias and efficiency

what is bias?

an estimator is unbiased if the mean of its sampling distribution is equal to the population value of interest → sample means and proportions are always unbiased estimators

what is efficiency?

the extent to which the sample distribution is clustered around the mean → larger sample have greater clustering around the means and thus more efficiency

• as sample size increases, the standard deviation of the sampling distribution decreases

what are confidence levels?

because the sampling distribution is normal, we can predict how likely the sample mean is to fall near the population mean

•   ± 1 Z = 68.26% chance the sample mean is within that sampling distribution mean

• ± 1.96 Z = 95% chance the sample mean is within that sampling distribution mean

• ± 2.58 Z = 99% chance the sample mean is within that sampling distribution mean

since the sampling distribution mean equals the population mean, these ranges also tell us how likely the sample mean is to fall within that distance of the population mean

higher confidence = wider range = greater chance of capturing the population mean

how do we point estimate?

• draw an EPSEM sample

• calculate a mean

• estimate that the population parameter is the same as the sample stats based on the sampling distribution of outcomes

• when the sample is larger

how do we construct confidence intervals for means if we know the population standard deviation?

• determine the alpha level (probability of error)

  • the level depends on the research situation but 0.05 probability is more common in social research

• find the z-score associated with alpha

  • if alpha is equal to 0.05 we would place half (0.025) of the probability in the lower tail and half in the upper tail and find the corresponding z-score

  • if the tail is equal to 0.01 we would place half (0.005) of the probability…. and find the corresponding score

  • if alpha is equal to 0.10 do the same thing

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• calculate the confidence interval

  • c.i. = confidence interval

  • X = sample mean

  • z = the score determined by the alpha level

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