Category 2: Nominal Independent Variable(s) and a Scale Dependent Variable
If the research design includes one or more nominal independent variables and a scale dependent variable, then we have several choices. The next question pertains to the number of independent variables.
- If there is just one independent variable, then we ask ourselves how many levels it has.
- If there are two levels, but just one sample—that is, one level is represented by the sample and one level by the population—then we use either a z test or a single-sample t test. It is unusual to know enough about a population that we only need to collect data from a single sample. If this is the case, however, and we know both the population mean and the population standard deviation, then we can use a z test. If this is the case and we know only the population mean (but not the population standard deviation), then we use the single-sample t test.
- If there are two levels, each represented by a sample (either a single sample in which everyone participates in both levels or two different samples, one for each level), then we use either a paired-samples t test (if all participants are in both levels of the independent variable) or an independent-samples t test (if participants are in only one level of the independent variable).
- If there are three or more levels, then we use a form of a one-way ANOVA. We examine the research design to determine if it is a between-groups ANOVA (participants are in just one level of the independent variable) or a within-groups ANOVA (participants are in all levels of the independent variable).
- If there are at least two independent variables, we must use a form of ANOVA. Remember, we name ANOVAs according to the number of independent variables (one-way, two-way, three-way) and the research design (between-groups, within-groups).
The decisions about data that fall into category 2 and have one independent variable are summarized in Table E-2. For those with two or more independent variables, see Table 14-1.
Table : TABLE E.2 Category 2 Statistics When there are one or more nominal independent variables and a scale dependent variable, examine the data to see which test is appropriate to use. Begin by determining the number of independent variables. If there is just one independent variable, use the accompanying chart. (When there are two or more independent variables, we use a form of ANOVA; see Table 14-1.) The first two columns in the chart identify the number of levels of the independent variable and the number of samples. For two levels but one sample, choose either the z test and single-sample t test, depending on whether you know the population standard deviation; for two levels and two samples, choose either the paired-samples t test or the independent-samples t test, depending on the research design. For three or more levels (and the matching number of samples), choose either a one-way within-groups ANOVA or a one-way between-groups ANOVA, a decision that is also dependent on the research design.
| Number of Levels of Independent Variable |
Number of Samples |
Information About Population |
Research Design |
Hypothesis Test |
| Two |
One (compared with the population) |
Mean and standard deviation |
— |
z test |
| Two |
One (compared with the population) |
Mean only |
— |
Single-sample t test |
| Two |
Two |
— |
Within-groups |
Paired-samples t test |
| Two |
Two |
— |
Between-groups |
Independent-samples t test |
| Three (or more) |
Three (or more) |
— |
Between-groups |
One-way between-groups ANOVA |
| Three (or more) |
Three (or more) |
— |
Within-groups |
One-way within-groups ANOVA |