Wage Differentials Among Occupations: Why we need ANOVA (Part II)

See the note about this table from Part I:

(Reminder:  these are not truly random samples, but we will ignore that for this exercise)

We will use a method called ANalysis Of VAriance, or ANOVA.  This type of hypothesis tests uses the F distribution (which you may have seen before in conducting a hypothesis test on two variances or standard deviations).  But the F sample statistic is calculated differently for ANOVA.  

The data values within each group vary.  The data values between the groups also vary.  In ANOVA,  .  If F is "large"  then we can conclude that the mean values for the groups really differ.  The null hypothesis in an ANOVA test is always that "all the population means are equal."  The alternative hypothesis is that "at least two population means are different."  (ANOVA does not tell us which ones.)  It is always a right-tail test.

The  OpenStax  e-text  (Ch.13)  explains  the  theory  and  the  computations in more  detail.  Most calculators and apps with statistical functions will automate the calculations.   The important thing is how to interpret the results.

1. Conduct an ANOVA hypothesis test to investigate whether different occupational categories have different average hourly wages (among the detailed occupations).  Remember to include all steps and use a 1% level of significance.

NOTE:  The format of your output might vary, but it should include the following:

F = 13.3398     p = .0011       (What does p tell you?)

Factor (relating to the numerator of the F statistic)

df = 2  ( k - 1  where k is the number of groups being compared)

SS = 611.02   (technical calculation - see text)

MS = 305.51   (Variance between groups  -  "mean square between") 

Error (not a mistake!  relating to the denominator of the F statistic)

df = 11 (N - k where N is the total sample size in all categories and k is the number of categories)

SS = 251.92 (technical calculation - see text)

MS = 22.90  (Variance  within groups - "mean square within")  

Sxp = 4.786  (pooled standard deviation)

2. Since we have found that at least two means are different, we probably want to know which ones.  One method is to create side-by-side box plots for the groups.  Use technology to do this.  What do you find?  Look back at the table and see why this is reasonable.

3. The table below gives the actual jobs instead of the numerical codes.  Why do you think our society rewards some categories of jobs more than others?   What question(s) do the data raise for you?  Post a comment in the Wage Differentials Discussion.