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
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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