Exercise 5—Anova

Points: 10

When an IV has only two values, as is the case with gender, a significant chi-square is sufficient to confirm that the two groups differ from one another beyond what one might anticipate due to chance. However, when an IV has more than two values, an Anova helps us decide which particular groups defined by the IV differ significantly on the DV.  Since Anova compares mean scores, however, most texts say that the dependent variable in an Anova analysis should be measured at the interval level. This understanding is considered in the following analyses.

Part 1—California results
Note in questions Cal 1-9, the DV (RawImm4) is a raw index scored between 0-4. It measures Californians’ attitudes toward immigrants.

Cal 1. How many categories are there in the dependent variable RawImm4?

Cal 2. At what level is this dependent variable measured?

Cal 3. Which ethnic groups differ significantly in California on RawImm4?

Cal 4. Which age group differs significantly from all except one other?

Cal 5. Is this result reflected in the means plot?

Cal 6. Is the overall Anova for the Coastal IV significant?

Cal 7. Which groups on the Coastal IV do not differ significantly?

Cal 8. Do those of different levels of interest differ significantly?

Cal 9. Which partisan groups differ significantly?

Cal 10. Referring to the following code, at which level is ImmCal3 measured? 

recode RawImm4 (0,1=0) (2,3= .5) (4 =1) into ImmCal3.
value labels ImmCal3 0 'low' .5 'med' 1 'high'.

Cal 11. Although not generally advised, an analysis of variance can be run using a recoded version of an index, such as ImmCal3. Using some artistic licence (and the syntax in Cal10), run an Anova with ImmCal3 as the DV and ethn the IV. According to this analysis, which California ethnic groups differ significantly?

Part 2—Texas results
Working with the December 2023 Texas data, two distinct measures of attitudes toward immigrants are used as dependent variables (DVs). The first (ImmIncl) asks about inclusive attitudes. The second (ImmExcl) asks about exclusionary attitudes. In questions Tex1-9, both DVs (ImmIncl & ImmExcl) are measured through raw indices scored between 0-3. Note that Anova calculations for both of these DVs are use a single Anova command for each IV. This permits the ready comparison of results for ImmIncl and ImmExcl in the output.

Tex 1. How many categories are there in each of the DVs ImmIncl and ImmExcl?

Tex 2. At what level are each of these two variables measured?

Tex 3. Which ethnic groups do not differ significantly on these variables?

Tex 4. Do Hispanics score higher or lower than whites on ImmIncl?

Tex 5. Do Blacks score higher or lower than whites on ImmExcl?

Tex 6. On which DV do urban and suburban Texans not differ?

Tex 7. Do rural Texans score higher or lower than urban Texans on ImmExcl?

Tex 8. On which dependent variable and between which groups do those of different levels of interest differ significantly?

Tex 9. Which partisan groups differ significantly?

Tex 10. Referring to the following code, at which level is ImmIncl3 measured? 

recode immIncl (0 thru 1.33=0) (1.65 thru 2=.5) (2.32 thru 3=1) into ImmIncl3.
value labels ImmIncl3 0 'low' .5 'med' 1 'hi'.

Tex 11. Using some artistic licence (and the syntax in Tex 10), run an Anova with ImmIncl3 as the DV and ethn the IV. According to this analysis, which Texas ethnic groups differ significantly?