Based on the results below, I should accept the null hypothesis of equal variances: bartlett.test(y ~ Treatment) Bartlett test of homogeneity of variances data: y by Treatment Bartlett's K-squared = 95.877, df = 3, p-value

Question

Based on the results below, I should accept the null hypothesis of equal variances:

> bartlett.test(y ~ Treatment)

Bartlett test of homogeneity of variances

data:  y by Treatment

Bartlett's K-squared = 95.877, df = 3, p-value < 2.2e-16

BlackTom AI · Accepted Answer

The question presents the Bartlett test for homogeneity of variances and asks whether, based on the results, we should accept the null hypothesis of equal variances.
Option 1: True. This statement would claim that the data support equal variances across groups. In reality, the test output shows Bartlett's K-squared = 95.877 with df = 3 and a p-value < 2.2e-16. Such an extremely small p-value provides very strong evidence against the null hypothesis of equal variances, meaning we should not accept equal variances. Therefore, describing the result as accepting equal variances is incorrect.
Option 2: False. The p-value is far below any conventional alpha level (e.g., 0.05, 0.01), so we reject the null hypothesis of equal variances. This indicates that the variances differ across Treatment groups, or at least that there is sufficient evidence to doubt homogeneity of variances. It’s also worth noting that Bartlett’s test is sensitive to departures from normality, but with such a minuscule p-value the conclusion about unequal variances remains warranted under typical assumptions.
In summary, the claim that we should accept equal variances is contradicted by the tiny p-value and large test statistic, which collectively point toward heterogeneity of variances rather than equality.

ENVX2001 (ND) End of Week 4 Quiz

Based on the results below, I should accept the null hypothesis of equal variances: > bartlett.test(y ~ Treatment) Bartlett test of homogeneity of variances data: y by Treatment Bartlett's K-squared = 95.877, df = 3, p-value < 2.2e-16

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