Bonferroni Correction


Posted November 12, 2012

Bonferroni Correction is also known as Bonferroni type adjustment

Made for inflated Type I error (the higher the chance for a false positive; rejecting the null hypothesis when you should not)

When conducting multiple analyses on the same dependent variable, the chance of committing a Type I error increases, thus increasing the likelihood of coming about a significant result by pure chance. To correct for this, or protect from Type I error, a Bonferroni correction is conducted.

Bonferroni correction is a conservative test that, although protects from Type I Error, is vulnerable to Type II errors (failing to reject the null hypothesis when you should in fact reject the null hypothesis)

Alter the p value to a more stringent value, thus making it less likely to commit Type I Error

To get the Bonferroni corrected/adjusted p value, divide the original α-value by the number of analyses on the dependent variable. The researcher assigns a new alpha for the set of dependent variables (or analyses) that does not exceed some critical value: αcritical= 1 – (1 – αaltered)k, where k = the number of comparisons on the same dependent variable.

However, when reporting the new p-value, the rounded version (of 3 decimal places) is typically reported. This rounded version is not technically correct; a rounding error. Example: 13 correlation analyses on the same dependent variable would indicate the need for a Bonferroni correction of (αaltered =.05/13) = .004 (rounded), but αcritical = 1 – (1-.004)13 = 0.051, which is not less than 0.05. But with the non-rounded version: (αaltered =.05/13) = .003846154, and αcritical = 1 – (1 – .003846154)13 = 0.048862271, which is in-fact less than 0.05! SPSS does not currently have the capability to set alpha levels beyond 3 decimal places, so the rounded version is presented and used.

Another example: 9 correlations are to be conducted between SAT scores and 9 demographic variables. To protect from Type I Error, a Bonferroni correction should be conducted. The new p-value will be the alpha-value (αoriginal = .05) divided by the number of comparisons (9): (αaltered = .05/9) = .006. To determine if any of the 9 correlations is statistically significant, the p-value must be p < .006.


Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. The services that we offer include:

Data Analysis Plan

Edit your research questions and null/alternative hypotheses

Write your data analysis plan; specify specific statistics to address the research questions, the assumptions of the statistics, and justify why they are the appropriate statistics; provide references

Justify your sample size/power analysis, provide references

Explain your data analysis plan to you so you are comfortable and confident

Two hours of additional support with your statistician

Quantitative Results Section (Descriptive Statistics, Bivariate and Multivariate Analyses, Structural Equation Modeling, Path analysis, HLM, Cluster Analysis)

Clean and code dataset

Conduct descriptive statistics (i.e., mean, standard deviation, frequency and percent, as appropriate)

Conduct analyses to examine each of your research questions

Write-up results

Provide APA 6th edition tables and figures

Explain chapter 4 findings

Ongoing support for entire results chapter statistics

Please call 727-442-4290 to request a quote based on the specifics of your research, schedule using the calendar on t his page, or email [email protected]


Pin It on Pinterest

Shares
Share This