Question: The Age Discrimination in Employment Act mandates that workers 40 years of age or older be treated without regard to age in all phases of employment (hiring, promotions, firing, etc.). Age discrimination cases are of two types: disparate treatment and disparate impact. In the former, the issue is whether workers have been intentionally discriminated against. In the latter, the issue is whether employment practices adversely affect the protected class (i.e., workers 40 and over) even though the employer intended no such effect. A small computer manufacturer laid off 10 of its 20 software engineers. The ages of all engineers at the time of the layoff are shown below. Analyze the data to determine whether the company may be vulnerable to a disparate impact claim.

Welch's two-sample t-test with the T distribution (DF=17.7198) (two-tailed) (validation)

The mean population of Not laid off is believed to be equivalent to the average population of Laid off: In other words, the variation in averages between the Not laid off and laid off groups is not statically important.

2. The p-value: The p-value is 0.230356 (p(xT) = 0.115178). This suggests that if we refuse H0, the likelihood of a type I mistake (rejecting a valid H0) is excessively high: 0.2304. (23.04 percent). The greater the p-value, the more strongly it confirms H0.

3. The figures:T = -1.242191, within the 95 percent critical value allowed range: [-2.1033: 2.1033].

x1-x2 = - 4.40 is within the 95% acceptable range: [-7.4500: 0.06226].

The statistic S' is 3.542.

4. Size of the effect: The standardized effect size found is modest (0.56). That means the size of the difference between the average as well as the average is moderate.

Outliers: Tukey Fence, k=1.5, outlier detection technique

Not laid off: contains one probable outlier, accounting for 10% of the data.

Laid off: contains one probable outlier, accounting for 10% of the data.

The Shapiro-Wilk Test was used to validate the assertion. (α=0.05)

It is believed that not laid off: is distributed normally (p-value = 0.803), or more precisely, that the assumption of normality cannot be rejected.

Laid off: is expected to be non-normally distributed. The p-value is 0.0361. For modest violations of the normality criterion, the test is deemed sturdy.

Power of testing: Because the prior strength is low (0.1849), the test may fail to reject an inaccurate h0. The assumption of variation equality. A two-tailed F test indicates that 1 is equivalent to 2 (p-value = 0.713). The F test implies equal mean and standard deviation, which the analysis does not.

Check to see if the data sample is appropriately symmetrical around the mean. If it isn't, you should verify the data processing, such as log transformation and square-foot transition. If none of the modifications work, a non-parametric test should be performed. Mann Whitney is the applicable non - parametric test. To do the U test, click the 'Determine Mann-Whitney' option.

It is advised that the test power be increased by:

The sample size should be increased.

σ: Determine if the standard error may be lowered by removing sounds irrelevant to the tested value.

Effect size: It was feasible to raise the impact factor when designing the research, but this came at the expense of the capacity to discover lower effect sizes.

If just one of the positive or detrimental alterations is meaningful, go to a one-tailed test.

α*: It was feasible to boost the significance level () while designing the research, but this increased the likelihood of a type I mistake.

*Note: Before collecting data, determine the test power, response rate, significance level, as well as meaningful scale ().

R Code

The R code below must get similar outcomes:

x1<-c (29,32,34,38,40,40,42,42,46,55)

x2<-c (35,39,40,40,40,41,44,47,52,64)

t. test (x1, x2, alternative = "two-sided", paired = FALSE, var. equal = FALSE, confidence level = 0.95)