Bonferroni point

(noun)

how significant the best spurious variable should be based on chance alone

Related Terms

Examples of Bonferroni point in the following topics:

  • Stepwise Regression

    • The key line in the sand is at what can be thought of as the Bonferroni point: namely how significant the best spurious variable should be based on chance alone.
    • Several points of criticism have been made:

  • Pairwise Comparisons (Correlated Observations)

    • The standard practice for pairwise comparisons with correlated observations is to compare each pair of means using the method outlined in the section "Difference Between Two Means (Correlated Pairs)" with the addition of the Bonferroni correction described in the section "Specific Comparisons. " For example, suppose you were going to do all pairwise comparisons among four means and hold the familywise error rate at 0.05.
    • Using the Bonferroni correction for three comparisons, the p value has to be below 0.05/3 = 0.0167 for an effect to be significant at the 0.05 level.

  • Specific Comparisons (Independent Groups)

    • After the task, subjects were asked to rate (on a 10-point scale) how much of their outcome (success or failure) they attributed to themselves as opposed to being due to the nature of the task.
    • This inequality is called the Bonferroni inequality.
    • The Bonferroni inequality can be used to control the family wise error rate as follows: Id you want the family wise error rate to be alpha, you use alpha/c as the per-comparisson error rate.
    • This correction, called the Bonferroni correction, will generally result in a familywise error rate less than α.
    • The question of whether these four comparisons are testing different hypotheses depends on your point of view.

  • Elements of a Designed Study

    • The most conservative, but free of independency and distribution assumptions method, is known as the Bonferroni correction ${\alpha }_ {\text{per comparison}}=\frac { \bar { \alpha } }{ n }$.
    • Another procedure is the Holm–Bonferroni method, which uniformly delivers more power than the simple Bonferroni correction by testing only the most extreme $p$-value ($i=1$) against the strictest criterion, and the others ($i>1$) against progressively less strict criteria.
    • This is called the Bonferroni correction and is one of the most commonly used approaches for multiple comparisons.
    • Because simple techniques such as the Bonferroni method can be too conservative, there has been a great deal of attention paid to developing better techniques, such that the overall rate of false positives can be maintained without inflating the rate of false negatives unnecessarily.

  • Multiple comparisons and controlling Type 1 Error rate

    • The Bonferroni correction suggests that a more stringent significance level is more appropriate for these tests: α* = α/K, where K is the number of comparisons being considered (formally or informally).
    • Complete the three possible pairwise comparisons using the Bonferroni correction and report any differences.

  • Exercises

    • Test differences among the four levels of B using the Bonferroni correction.

  • Exercises

    • Make sure to control for the familywise error rate (at 0.05) by using the Bonferroni correction.
    • True/false: If you are making 4 comparisons between means, then based on the Bonferroni correction, you should use an alpha level of .01 for each test.

  • Glossary

    • When points in a graph are jittered, the are moved horizontally so that all the points can be seen and none are hidden due to overlapping values.
    • However, interval scales do not have a true zero point.
    • Ratio scales are interval scales that do have a true zero point.
    • Essentially a bar graph in which the height of each par is represented by a single point, with each of these points connected by a line.
    • A touchdown is worth 6 points and allows for a chance at one (and by some rules two) additional point(s).

  • Wilson's Fourteen Points

  • Point-Slope Equations

    • The point-slope equation is another way to represent a line; to use the point-slope equation, only the slope and a single point are needed.
    • The point-slope form is great if you have the slope and only one point, or if you have two points and do not know what the $y$-intercept is.
    • Then plug this point into the point-slope equation and solve for $y$ to get:
    • Write an equation of a line in Point-Slope Form (given two points)  Convert to Slope-Intercept Form
    • Plug this point and the calculated slope into the point-slope equation to get: $y-6=-2[x-(-3)]$.