Part II – ANOVA through regression

Part II – ANOVA through regression

On the midterm, you addressed the vital issue of whether different cookie types lead to more or less milk consumption among children enrolled in public elementary schools in the Los Angeles Unified School District (LAUSD) in order to generate knowledge that would help to prevent LAUSD from going bankrupt due to excessive spending on milk (imagine a tax increase for this reason…).

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You conducted a test of the hypothesis that cookie type (a 3-category EV) is associated with milk consumption (measured in ounces) in the population of LAUSD elementary school students using a sample of students obtained from LAUSD, in which each student was randomly assigned to eat 1 of 3 cookie types (chips ahoy, oreos, fig newtons).  You recorded how much milk each child consumed while eating the cookies.  The hypothesis-testing method you used was analysis of variance (ANOVA) with follow-up tests of differences in milk consumption between all possible pairs of cookie categories using Tukey’s multiple comparison procedure.

Since the midterm, you have learned that you can test the association between a 3-category EV and a quantitative RV using multiple linear regression.  This requires creating g-1 dummy variables (where g is the number of groups, or categories of the EV) and including the dummy variables as EVs in a multiple regression.  This “ANOVA through regression” is preferred to traditional ANOVA with follow-up tests if 2 conditions are met:

-you can test your hypothesis while limiting the number of comparisons of pairs of group means among the set of 3 group means to g-1, or 2 comparisons.

-each of the comparisons you test has the same reference group, or comparison group

So you are going to repeat the analysis you completed on the midterm testing for differences in milk consumption between/among cookie types.  This time, you will assume that school district administrators hypothesized that children who ate fig newtons would consume significantly less milk than children who ate chips ahoy and children who ate oreos.  So these are the 2 comparisons that you will test statistically, and you will do so by creating 2 dummy variables and including them as EVs in a multiple linear regression analysis.

Here are the sample means for each cookie type (not all of these will appear in your regression output), and the null and alternative hypothesis statements:

H₀: µ_{1 (chips ahoy)} = µ_{2 (oreo)} = µ_{3 (fig newton)}

H_a:  at least one µ ≠ another µ

Use  α = .05

Using the data from the original midterm problem #8 on the course website, create two dummy variables from the 3-category COOKIETYPE variable.  Be very careful when deciding which cookie categories should receive values of 1 on each of the two dummy variables, and which cookie categories should receive values of 0 on the two dummy variables.  Also think carefully about which cookie represents the reference category.  This is the cookie that should receive codes of 0 on both dummy variables.

It should be noted that you did not complete a lab exercise in which you created dummy variables and included them as EVs in a multiple linear regression.  But you can create these dummy variables using either the GENERATE (GEN) or RECODE functions in STATA.  You have instructions from previous lab sections that will help you to do this.  After creating the 2 dummy variables:

• Run the multiple linear regression analysis with milk consumption as the RV and the 2 dummy variables included as EVs using STATA. Paste your output below.

• Interpret the value of the y-intercept in your output

• Interpret the value of the slope measuring the association between your FIRST dummy variable and milk consumption. Does the t-test for this slope indicate a significant difference in milk consumption between the fig newton group and another group?  Report the t-statistic and p-value in support of your answer.

• Interpret the value of the slope measuring the association between your SECOND dummy variable and milk consumption. Does the t-test for this slope indicate a significant difference in milk consumption between the fig newton group and another group?  Report the t-statistic and p-value in support of your answer.