## KEY CONCEPTS

KEY CONCEPTS

• 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 backward, 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 results.

• 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 a difference when one does exist (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 chance alone.

• 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 their 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 ...

### Pop-up div Successfully Displayed

This div only appears when the trigger link is hovered over. Otherwise it is hidden from view.