A business researcher uses two-way ANOVA in a report for a client. The researcher does not check the assumptions of using the technique. Is this a problem? (Please explain and give examples.)
Yes, this can be a problem. A two-way ANOVA is used to check the statistical significance of the impact of 2 or more. For example your client may want to know if sex (male or female) impacts a particular buying trend but is also concerned that age may play a role in the buying trend (eg. Do woman of a certain age group buy more small purchases than men of all age groups or men of a certain age group or woman of different age group?). A two-way ANOVA would be used to determine if sex and/or age has a significant impact on the buying trend in question. If the client is only interested in examining the statistical significance of the relationship between one dependent variable and one independent variable (buying trend and sex or buying and age but not both) another statistical analysis must be performed (such as a one-way ANOVA, student T ...
Several paragraphs with examples and web references as to the proper use of a two-way ANOVA.