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2013 | OriginalPaper | Buchkapitel

6. Other Tests of Equal Pay

verfasst von : Stephanie R. Thomas

Erschienen in: Compensating Your Employees Fairly

Verlag: Apress

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Abstract

Although multiple regression analysis is the preferred statistical technique for examining questions of internal pay equity, a variety of other statistical and nonstatistical techniques are often used. Some common tools for examining disparate treatment in compensation include a comparison of means and medians, t-tests, cohort analyses, and tipping point and threshold tests.

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Vorheriges Kapitel Regression Models of Equal Pay

Nächstes Kapitel Analysis Follow-Up

In this case, we refer to the arithmetic mean, rather than the harmonic mean or geometric mean. Formally, the calculation of the arithmetic mean is given by the following:

$$ \overline{x}=\frac{1}{n}*\mathop{\sum}\limits_{i=1}^n{x_i} $$

Note that “similar” may or may not be equivalent to similarly situated. Means and medians comparisons are frequently performed on the basis of EEO-1 category, pay grade, or other broad grouping variable that may group together employees who are not similarly situated.

The examples shown in Tables 6-1 and 6-2 were excerpted from a sample compensation analysis report produced by Office of Federal Contract Compliance Programs (OFCCP). This sample report can be found at www.ofccp.com/PDF/Sample_Compensation_Analysis_Report.pdf.

The t-test was introduced in 1908 by William Sealy Gossett. Gossett developed the test as an inexpensive way to monitor the quality of stout while working as a chemist at the Guinness brewery in Dublin, Ireland. The test was published in Biometrika in 1908 under the pen name Student because his employer considered the fact that statistics were being used in Guinness brewing as a trade secret.

Note that this expresses the null and alternate hypotheses for a two-tailed test. In a one-tailed test, the alternate hypothesis is constructed such that the sample mean for the second group is either (a) greater than or (b) less than the sample mean for the first group:

$$ (a)\ {H_A}:\ \overline{{{X_1}}}<\overline{{{X_2}}} $$

$$ (b)\ {H_A}:\ \overline{{{X_1}}}>\overline{{{X_2}}} $$

The choice of one-tailed or two-tailed test depends on the question being addressed.

The assumption of paired samples is appropriate when comparing matched pairs of observations, or “before” and “after” observations on the same group of individuals. Paired samples are sometimes referred to as “dependent samples.” The assumption of overlapping samples is used in the case of paired samples with missing data in one of the samples.

The independent samples t-test is used when two separate sets of independent and identically distributed samples are drawn, one from each of the two populations under comparison. Within the context of internal pay equity, we are looking at, for example, annual pay rates for protected group members and nonprotected group members.

Levene’s test can be used to assess the equality of variances in different samples. Levene’s test statistic is given by:

$$ W=\frac{(N-k) }{(k-1) }*\frac{{\mathop{\sum}\nolimits_{i=1}^k{N_i}{{{({Z_{i. }}-{Z_{.. }})}}^2}}}{{\mathop{\sum}\nolimits_{i=1}^k\mathop{\sum}\nolimits_{j=1}^{{{N_i}}}{{{({Z_{ij }}-{Z_{i. }})}}^2}}} $$

As noted by Snijders, a common misinterpretation of the results of a t-test is that nonrejection implies support for the null hypothesis. Snijders argues that nonrejection should be interpreted as an undecided outcome; there is not enough evidence to reject the null hypothesis, but this does not mean that there is evidence for it. T. A. B. Snijders, “Hypothesis Testing: Methodology and Limitations,” International Encyclopedia of the Social & Behavioral Sciences (2001), 7125.

The exact format and layout of the output, including what summary statistics are included, varies by software. The sample output in Table 6-4 is intended to illustrate the nature of information commonly provided by most packages.

It is not uncommon for statistical software to generate results for both t-tests. Some also provide a calculation of Levene’s test to assist in interpreting which assumption is appropriate.

As discussed in Chapter 3, the p-value is the probability of obtaining a test statistic at least as extreme as the one actually observed, assuming that the null hypothesis is true.

Jana Moberg, “The New OFCCP Tipping Point Test,” DCI Consulting, available at http://ofccp.blogspot.com/2011/02/new-ofccp-tipping-point-test.html.

Here, comparators are defined as nonprotected individuals who receive greater compensation than the protected individual but have what appears to be less qualifying experience, time in job, education, and so on.

As discussed in Chapter 3, if the number of independent variables exceeds the number of observations, there are insufficient degrees of freedom and it is not mathematically possible to generate coefficient estimates.

The use of cohort analysis for follow-up is discussed in Chapter 7.

A dichotomous variable takes on one of two possible values (e.g., gender: male or female).

There are statistical tests designed to examine tables larger than two by two (e.g., three by three, two by n). The current discussion is limited to two-by-two contingency tables.

Ramona Paetzhold and Steven Willborn, The Statistics of Discrimination: Using Statistical Evidence in Discrimination Cases, Thompson/West (2006).

Dan Biddle, Adverse Impact and Test Validation: A Practitioner’s Guide to Valid and Defensible Employment Testing (Burlington, VT: Ashgate Publishing Company, 2006), 3.

If the eligibility for participation was determined after reviewing employees’ eligibility criteria—for example, to ensure that 25% of employees were eligible for participation—then the number of employees eligible for participation in the incentive compensation plan is fixed.

The binomial distribution is the discrete probability distribution of the number of successes in a series of independent yes/no experiments, each of which has a probability of success equal to p. One common example of the binomial distribution is coin-flipping. You flip a coin 10 times. What is the probability of getting 6 heads in 10 flips? The binomial distribution is used to calculate the likelihood of seeing x heads out of n flips.

The hypergeometric distribution is the discrete probability distribution that describes the probability of k successes in n draws without replacement. The common example used to illustrate the hypergeometric distribution is the “urn model”; you draw 10 marbles from an urn containing 5 red and 20 blue marbles without putting any drawn marbles back into the urn (without replacement). What is the probability that exactly 4 of the 10 marbles you draw are red? The hypergeometric distribution is used to calculate this probability.

A two-by-two contingency table has one degree of freedom. The number of values in the final calculation that are free to vary—that is, the number of independent pieces of information—is referred to as the degrees of freedom. In a two-by-two contingency table, if we know the row and column totals (in this case, the number of white and nonwhite employees and the numbers eligible and not eligible for participation), only one number—either A, B, C, or D—is required to fill in the remainder of the cells.

The translation of the chi square test statistic into a probability, and hence into units of standard deviation, is not discussed here. Readers are encouraged to consult any elementary statistics text for a discussion of this translation process.

In this context, a small sample size refers to an expected value in the contingency table cells of less than five.

Note that the symbol ! refers to the factorial. The factorial of a positive integer N is the product of all positive integers less than or equal to N. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

To reject the null hypothesis, the probability would have to be less than or equal to 0.05 under standard statistical assumptions.

A continuity correction is incorporated when a continuous function is used to approximate a discrete distribution. For example, if the normal distribution is used to approximate the binomial distribution, a continuity correction is used.

Titel: Other Tests of Equal Pay
verfasst von: Stephanie R. Thomas
Verlag: Apress
Buch: Compensating Your Employees Fairly
Print ISBN: 978-1-4302-5040-1

Electronic ISBN: 978-1-4302-5042-5

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-1-4302-5042-5_6

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