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Questions and Answers
What is the primary purpose of conducting a Bonferroni correction?
What is the primary purpose of conducting a Bonferroni correction?
- To confirm the null hypothesis more accurately
- To reduce the inflated chance of Type I errors (correct)
- To avoid Type II errors
- To enhance the likelihood of significant results
What effect does the Bonferroni correction have on Type II errors?
What effect does the Bonferroni correction have on Type II errors?
- It does not influence Type II errors
- It increases the risk of Type II errors (correct)
- It decreases the likelihood of Type II errors significantly
- It eliminates Type II errors completely
When reporting the adjusted p-value after a Bonferroni correction, which of the following is typically true?
When reporting the adjusted p-value after a Bonferroni correction, which of the following is typically true?
- The adjusted p-value is commonly reported without rounding
- Exact values beyond three decimal places are typically used
- Only unrounded values are accepted by statistical software
- The rounded p-value is usually presented, despite not being technically correct (correct)
In the context of ANCOVA, if the original p-value is 0.05 and there are two covariates, what is the adjusted p-value after applying Bonferroni correction?
In the context of ANCOVA, if the original p-value is 0.05 and there are two covariates, what is the adjusted p-value after applying Bonferroni correction?
How is the critical value determined when applying the Bonferroni correction?
How is the critical value determined when applying the Bonferroni correction?
What is the adjusted p-value when the original p-value is 0.05 and there are 2 dependent variables?
What is the adjusted p-value when the original p-value is 0.05 and there are 2 dependent variables?
In a study using a one-way ANCOVA, how many independent variables are involved?
In a study using a one-way ANCOVA, how many independent variables are involved?
Which test is specifically used to assess the homogeneity of covariance in MANCOVA?
Which test is specifically used to assess the homogeneity of covariance in MANCOVA?
Which of the following assumptions is NOT required for ANCOVA?
Which of the following assumptions is NOT required for ANCOVA?
In detecting univariate outliers for MANCOVA, which method is commonly used?
In detecting univariate outliers for MANCOVA, which method is commonly used?
What is a key assumption regarding observations in ANCOVA?
What is a key assumption regarding observations in ANCOVA?
What is the purpose of using covariates in ANCOVA?
What is the purpose of using covariates in ANCOVA?
How can outliers be assessed in ANCOVA according to Cook's distance?
How can outliers be assessed in ANCOVA according to Cook's distance?
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Study Notes
Bonferroni Correction
- Protects against inflated Type I error, which is the chance of a false positive.
- A Type I error is rejecting the null hypothesis when you should not
- Conducting multiple analyses on the same dependent variable increases the chance of a Type I error.
- Corrects for this by making the significance level more stringent.
When to Use
- When conducting multiple analyses on the same dependent variable.
Limitations
- Can increase the chance of a Type II error which occurs when failing to reject the null hypothesis when you should.
Applications
- ANCOVA (Analysis of Covariance):
- Uses Bonferroni Correction to adjust the significance level.
- Involves one independent variable, multiple covariates and one dependent variable.
- MANCOVA (Multivariate Analysis of Covariance):
- Uses Bonferroni Correction to adjust the significance level.
- Involves one independent variable, multiple covariates and multiple dependent variables.
Assumptions
- Independent Variable: Categorical, with two or more groups.
- Dependent Variable: Continuous.
- Covariate/Control Variables: Continuous.
- Study Design: Independent observations (different participants in each group).
- Outliers:
- No significant outliers.
- Outliers can be detected by inspecting studentized residuals, leverage values, and Cook's distance.
- Normality: Data should be normally distributed, tested using Shapiro-Wilk test.
- Homogeneity of Variance: Assumes equal variances between groups.
- ANCOVA/ MANCOVA: Use Box's M Test of Equality of Covariance Matrices
- ANCOVA: Levene's Test of Equality of Variances.
- Homogeneity of Covariance: Assumes equal covariances between groups.
- ANCOVA/MANCOVA: Use Box's M Test of Equality of Covariance Matrices.
- ANCOVA: Levene's Test of Equality of Variances.
- Homoscedasticity: Assumes equal variances between groups.
- Tested using Shapiro-Wilk test.
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