ASA = American Society of Anesthesiologists.

C. Descriptive statistics are intended to describe the sample of numbers obtained and to characterize the population from which the sample was obtained. The two summary statistics most frequently used are the central location and spread or variability (Table 9-2).

TABLE 9-2 Descriptive Statistics

Central Location for Interval Variables

Arithmetic mean (average of the numbers in the data set)

Median (middle most number or number that divides the samples into two equal parts; not affected by very high or low numbers)

Mode (number in a sample that appears most frequently)

Spread or Variability

Standard deviation (SD; approximates the spread of the sample data; 1 SD encompasses roughly 68% of the sample and population members, and 3 SDs encompass 99%)

Confidence Intervals

Standard error of the mean (approximates the precision with which the population center is known)

III. HYPOTHESES AND PARAMETERS

A. Hypothesis Formulation

1. The researcher starts the work with some intuitive feel for the phenomenon to be studied (biologic hypothesis).

2. The biologic hypothesis becomes a statistical hypothesis during research planning.

B. Logic of Proof

1. If sample values are sufficiently unlikely to have occurred by chance (alpha [P] <.05), the null hypothesis (which assumes there is no difference) is rejected.

2. Because statistics deal with probabilities rather than certainties, there is a chance that decisions made concerning the null hypothesis are erroneous.

a. A type I (alpha) error is wrongly rejecting the null hypothesis (false positive). The smaller the chosen alpha, the smaller the risk of a type I error.

b. A type II (beta) error is failing to reject the null hypothesis (false negative). Variability in the population increases the chance of type II error. Increasing the number of subjects (which is very important in research design for controlled clinical trials), raising the alpha value, and dealing with large differences between two conditions decrease the chances of a type II error.

C. Inferential Statistics. The testing of hypotheses or significance testing is the main focus of inferential statistics (Table 9-3).

TABLE 9-3 INFORMATION NECESSARY TO ACCEPT OR REJECT THE NULL HYPOTHESIS

Confirm that experimental data conform to the assumptions of the intended statistical test.

Choose a significance level (alpha).

Calculate the test statistic.

Determine the degree(s) of freedom.

Find the critical value for the chosen alpha and the degree(s) of freedom from the appropriate theoretical probability distribution.

If the test statistic exceeds the critical value, reject the null hypothesis.

If the test statistic does not exceed the critical value, do not reject the null hypothesis.

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