Wage Differentials Among Occupations: Why we need ANOVA (Part I)
- Due May 17, 2024 by 11:59pm
- Points 0
- Available until May 17, 2024 at 11:59pm
Wages in Different Sectors of the Economy
Do some occupational categories (or sectors) pay more than others? This chart lists median hourly wages for samples of detailed occupations within five categories. Data from US Bureau of Labor Statistics. Links to an external site.
Note: The detailed occupations were not chosen randomly, because of the wide variation in the sizes of occupations within a category. Instead, the largest ones were chosen. This violates the criteria for statistical tests, but we will ignore those criteria for now in order to illustrate the concepts.
Management Occupations (sample) |
|
Business & Financial Occupations (sample) |
|
Community and Social Service Occupations(sample) |
|
Health practitioner & Technician occupations (sample) |
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Healthcare Support Occupations(sample) |
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|---|---|---|---|---|---|---|---|---|---|
|
11-1011 |
88.68 |
13-1071 |
29.77 |
21-1012 |
27.42 |
29-1141 |
35.24 |
31-1131 |
14.26 |
|
11-1021 |
48.45 |
13-1111 |
40.99 |
21-1015 |
17.38 |
29-1051 |
61.58 |
31-9091 |
19.27 |
|
11-3021 |
70.37 |
13-1198 |
35.37 |
21-1018 |
22.23 |
29-1122 |
43.00 |
31-9092 |
16.73 |
|
11-3031 |
62.45 |
13-2011 |
34.40 |
21-1021 |
22.78 |
29-1127 |
38.04 |
31-9011 |
20.59 |
|
|
|
|
|
21-1093 |
16.85 |
29-1021 |
74.81 |
|
|
|
|
|
|
|
|
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29-1171 |
52.80 |
|
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- How can we compare the population means of three or more groups if we have a sample from each group?
- One idea would be to compare them two at a time and test for whether there is a difference between each pair. Can you see what the problem would be?
Risk of Making a Type-I Error
The problem is that this would drastically increase the chance of making a Type-I error.
For example, someone might create a test and give it to independent samples of people from ten different states (or ethnic groups, or religions, or whatever). And maybe there would be no difference at all among the population mean scores on this test. If we tested them by pairs, there would be 10 nCr 2= 45 pairs and therefore 45 tests.
Using a 5% level of significance for each test, about 5% of the tests would incorrectly tell us there was a difference between the two population means. The expected number of type-I errors would be (.05)(45) = 2.25 .
Universities in the US often put tremendous pressure on faculty to "publish or perish." This can encourage "Question Trolling." That means searching through large numbers of results to find the ones that are "statistically significant" and then choosing those topics to write about. In our example, someone doing that might produce two "research papers" based entirely on type-I errors.
Is this a real problem? See http://hermanaguinis.com/JBPharking.pdf Links to an external site.
- What if we had independent samples from all 50 states plus Puerto Rico, Guam, the Virgin Islands and the District of Columbia: How many tests of two means would be possible? If there were really no differences among population means. and we used a 1% level of significance , how many type-I errors should we expect?
Solution: ANOVA
Instead, when we have independent samples from three or more populations, we use a method called ANalysis Of VAriance, or ANOVA. Since the TI 83 and 84 calculators and many apps have a built-in one-way ANOVA function, this isn't hard to do.
(A more powerful method called two-way ANOVA requires more powerful software. We will look at how it is used and interpreted in research.)
Post final comments, answers to questions, etc. in the Wage Differentials Among Occupations: Why we need ANOVA (Part I) EC only Discussion.
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