Skip to Main Content

We have a new app!

Take the Access library with you wherever you go—easy access to books, videos, images, podcasts, personalized features, and more.

Download the Access App here: iOS and Android. Learn more here!



  • imageSpecial statistical tests are needed when more than two groups are studied or when a group is measured on several variables.

  • imageAnalysis of variance, or ANOVA, is a statistical method that divides the variance in an observation into the variance among groups and the rest of the variance, called the within-group or error variance.

  • imageThe F test used to compare two variances in Chapter 6 is used to compare the variance among groups to the error.

  • imageAn example of the way ANOVA is calculated from the definitional formulas is helpful in understanding the logic behind the test.

  • imageThe terms used in ANOVA are important, but the details of the computations are given for illustration only, and computer programs are used for all ANOVA procedures.

  • imageOne-way ANOVA is the appropriate method when more than two groups are studied on one variable.

  • imageAs with the t test, certain assumptions must be made to use ANOVA, and equal variances is one of the most important.

  • imageMaking many comparisons among groups increases the chances of a type I error, that a difference is concluded when there is none.

  • imageInvestigators can decide ahead of time what specific comparisons they want to make.

  • imageThe Bonferroni procedure is a common way to compensate for making many comparisons among groups; it works by reducing the size of α for each comparison, essentially increasing the difference needed to be significant.

  • imageSome multiple comparison methods, called post hoc, are done only if the ANOVA results are statistically significant.

  • imageTukey's test is one of the most highly recommended post hoc tests for comparing mean differences.

  • imageThe Scheffé post hoc procedure is the most conservative (requiring a larger difference to be significant), but it is also the most versatile.

  • imageThe Newman–Kuels post hoc procedure is used frequently in basic science research.

  • imageDunnett's procedure is the test of choice if the only comparisons being made are between the mean in a control group and the means in other groups.

  • imageTwo-way ANOVA analyzes two factors instead of just one, as in one-way ANOVA. It also permits the analysis of the interaction between two factors.

  • imageANOVA designs involving more than two factors are possible, generally called factorial designs.

  • imageConfounding variables can be accommodated by the ANOVA randomized block design.

  • imageRepeated-measures ANOVA is a common procedure in medical research; it is analogous to the paired t test with more than two groups and is also called the split-plot design.

  • imageNonparametric ANOVA methods include Kruskal-Wallis for one-way designs and Friedman two-way ANOVA for repeated measures. These methods are analogous to the Wilcoxon procedures and are used when the assumptions for ANOVA are not met.

  • imageThe chi-square test can be used to compare more than two proportions and to determine if there is an association between two factors, each of which can have two or more levels. It is a simple extension of the chi-square test we discussed in Chapter 6.

  • imageAs with research questions ...

Pop-up div Successfully Displayed

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