- Three factors help determine whether an observed estimate,
such as the mean, is different from a norm: the size of the difference,
the degree of variability, and the sample size.
- The t distribution is similar to the z distribution, especially
as sample sizes exceed 30, and t is generally used in medicine when
asking questions about means.
- Confidence intervals are common in the literature; they are
used to determine the confidence with which we can assume future
estimates (such as the mean) will vary in future studies.
- The logic behind statistical hypothesis tests is somewhat
backwards, generally assuming there is no difference and hoping
to show that a difference exists.
- Several assumptions are required to use the t distribution
for confidence intervals or hypothesis tests.
- Tests of hypothesis are another way to approach statistical
inference; a somewhat rigid approach with six steps is recommended.
- Confidence intervals and statistical tests lead to the same
conclusions, but confidence intervals actually provide more information
and are being increasingly recommended as the best way to present
- In hypothesis testing, we err if we conclude there is a difference
when none exists (type I, or α, error), as well
as when we conclude there is not difference when one does exists
(type II, or β, error).
- Power is the complement of a type II, or β,
error: it is concluding there is a difference when one does exist.
Power depends on several factors, including the sample size. It
is truly a key concept in statistics because it is critical that researchers
have a large enough sample to detect a difference if one exists.
- The P value first assumes that the null hypothesis is true
and then indicates the probability of obtaining a result as or more
extreme than the one observed. In more straightforward language, the
P value is the probability that the observed result occurred by
- The z distribution, sometimes called the z approximation to
the binomial, is used to form confidence intervals and test hypotheses
about a proportion.
- The width of confidence intervals (CI) depends on the confidence
value. 99% CI are wider than 95% CI because 99% CI
provide greater confidence.
- Paired, or before-and-after, studies are very useful for detecting
changes that might otherwise be obscured by variation within subjects,
because each subject is his or her own control.
- Paired studies are analyzed by evaluating the differences
themselves. For numerical variables, the paired t test is appropriate.
- The kappa κ statistic is used to compare
the agreement between two independent judges or methods when observations
are being categorized.
- The McNemar test is the counterpart to the paired t test when
observations are nominal instead of numerical.
- The sign test can be used to test medians (instead of means)
if the distribution of observations is skewed.
- The Wilcoxon signed rank test is an excellent alternative
to the paired t test if the observations are not normally distributed.
- To estimate the needed sample size for ...
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