# Chapter 6. Research Questions About Two Separate or Independent Groups

- Research questions about two independent groups ask whether the means are different or the proportions are different.
- Confidence intervals using the
*t*distribution determine the confidence with which we can assume differences between two means will vary in future studies. - A pooled standard deviation is used to form the standard error of the differences.
- An “eye-ball” test is helpful when reports present graphs of the mean with 95% confidence intervals.
- Using the
*t*distribution requires the two groups to be independent from each other as well as the assumptions of normality and equal variances in the two groups. - Tests of hypothesis are another way to test the difference between two means.
- The assumption of equal variances can be tested with several procedures.
- The nonparametric Wilcoxon rank sum test is an excellent alternative
to the
*t*test when the assumptions of normality or equal variances are not met. - Both confidence intervals and statistical tests can be used
to compare two proportions using the
*z*test, again using a pooled standard deviation to form the standard error. - The chi-square test is a very versatile statistical procedure used to test for differences in proportions as well as an association between two variables.
- Fisher’s exact test is preferred to chi-square when two characteristics are being compared, each at two levels (ie, 2 × 2 tables) because it provides the exact probability.
- The relative risk, or odds ratio, is appropriate if the purpose is to estimate the strength of a relationship between two nominal measures.
- When two groups are compared on a numerical variable, the
numerical variable should not be turned into categories to use the
chi-square test; it is better to use the
*t*test. - It is possible to estimate sample sizes needed to compare the means or proportions in two groups, but it is much more efficient to use one of the statistical power packages, such as PASS in NCSS, nQuery, or SamplePower.

Kline and colleagues (2002) published a study on the safe use of d-dimer for patients seen in the emergency department with suspected pulmonary embolism (PE). We used this study in Chapter 3 to illustrate descriptive measures and graphs useful with numeric data. In this chapter we continue our analysis of some of the information collected by Kline and colleagues. We will illustrate the t test for two independent samples and learn whether there was a significant difference in pulse oximetry in patients who did and those who did not have a PE. The entire data set is in a folder on the CD-ROM [available only with the book] entitled “Kline.”

Cryosurgery is commonly used for treatment of cervical intraepithelial neoplasia (CIN). The procedure is associated with pain and uterine cramping. Symptoms are mediated by the release of prostaglandins and endoperoxides during the thermodestruction of the cervical tissue. The most effective cryosurgical procedure, the so-called 5-min ...

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