Video Tutorial: CFA in MPlus

Bonferroni Correction

• 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: α_critical = 1 - (1 – α_altered)^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 (α_altered =.05/13) = .004 (rounded), but α_critical = 1 - (1-.004)¹³ = 0.051, which is not less than 0.05.  But with the non-rounded version: (α_altered =.05/13) = .003846154, and α_critical = 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 (α_original = .05) divided by the number of comparisons (9):  (α_altered = .05/9) = .006.  To determine if any of the 9 correlations is statistically significant, the p-value must be p < .006. 

Recoding

Survey items can be worded with a positive or negative direction:

·         Positively worded: e.g., I know that I am welcomed at my child’s school, I feel that I am good at my job, Having a wheelchair helps, etc…

·         Negatively worded: e.g., I feel isolated at my child’s school, I am not good at my job, having a wheelchair is a hindrance, etc…

·         Likert scaled responses can vary: e.g., 1 = never, 2= sometimes, 3 = always; OR

1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, 5 = strongly agree

·         When creating a composite score from specific survey items, we want to make sure we are looking at the responses in the same manner.  If we have survey items that are not all worded in the same direction, we need to re-code the responses. E.g.: I want to make a composite score called “helpfulness” from the following survey items :  

o   5-point Likert scaled, where 5 = always   4 = almost always  3 = sometimes, 2 = almost never  1 = never

1.      I like to tutor at school   

2.      I am usually asked by my friends to help with homework

3.      I typically do homework in a group setting

4.      I do not go over my homework with others

In this example, survey items 1 – 3 are all positively worded, but survey item 4 is not.  When creating the composite score, we wish to make sure that we are examining the coded responses the same way.  In this case, we’d have to re-code the responses to survey item 4 to make sure that all responses for the score “helpfulness” are correctly interpreted; the recoded responses for survey item 4 are: 1 = always, 2 = almost always, 3 = sometimes, 4 = almost never, 5 = never.

Now, all responses that are scored have the same direction and thus, can be interpreted correctly: positive responses for “helpfulness” have higher values and negative responses for “helpfulness” have lower values.

·         Also, you may wish to change the number of responses.  For example, you may wish to dichotomize or trichotomize the responses.  In the example above, you can trichotomize the responses by recoding responses “always” and “almost always” to 3 = high, “sometimes” to 2 = sometimes, and “almost never” and “never” to 1 = low.  However, please be advised to make sure that you have sound reason to alter the number of responses.

Dissertation Data Analysis

In order to receive their doctoral degrees, students must first successfully complete a dissertation. Part of this dissertation involves dissertation data analysis. Dissertation data analysis consists of all of the data that accompanies the dissertation and the interpretation of that data. Dissertation data analysis, then, is a crucial part of the dissertation.

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The dissertation is a difficult thing to complete because it is extremely time consuming and laborious. Part of what makes it so time consuming is the accumulation of all of the data that is necessary for the dissertation. Further, once this data is actually accumulated, it must be interpreted properly. This dissertation data analysis must follow proper methodology and this is where many students need help as they are not trained in dissertation data analysis.

Dissertation data analysis involves the breaking down of complex statistics and numbers in order to prove a student’s thesis. Dissertation data analysis is done by following very precise methodologies. Dissertation data analysis can only be done after the data for the dissertation data analysis has been collected by also following very precise methodologies. If the data that is collected is not accurate or valid, the dissertation data analysis will not be valid or precise either. Therefore, before beginning the dissertation data analysis, it is important for the researcher (or student) to make sure that he or she follows the proper methodologies while collecting the data.

Dissertation data analysis is very technical and follows strict rules, tests, and methodology. These tools for dissertation data analysis include t-tests, ANOVA, descriptive statistics, etc. Unfortunately, most doctoral students are not trained to do proper dissertation data analysis because it is so technical and because dissertation data analysis requires the understanding of the tests and methodology of statistics.

Fortunately however, there is help for dissertation data analysis as students can seek dissertation consultants for dissertation data analysis help. Dissertation consultants are trained in all things regarding statistics and dissertation consultants are therefore proficient in dissertation data analysis. Additionally, getting the help of dissertation consultants will save students much time and energy. This is true because dissertation consultants will help students complete the dissertation and dissertation consultants will help students understand all aspects of the dissertation—from the proposal phase to the dissertation data analysis. Not only will dissertation consultants help students in terms of finishing on-time, dissertation consultants will also explain everything carefully to the student. This is important because students need to understand their research and methodology in order to complete the oral defense of their dissertation. Dissertation consultants know this and dissertation consultants make sure that they explain every single aspect of the dissertation to the student. Dissertation consultants do this by going over every step of the dissertation with the student—including reviewing the dissertation data analysis. As mentioned earlier, the dissertation data analysis can be very technical and the dissertation data analysis can be one of the most complicated aspects of the dissertations. Dissertation consultants will guide students through this difficult dissertation data analysis and dissertation consultants will make sure that everything that the student does in terms of the dissertation data analysis is accurate, precise and related to the dissertation. What’s more, dissertation consultants will go out of their way to make sure that the student understands every single component and aspect of the dissertation data analysis.

Dissertation consultants, then, can be extremely valuable to anyone writing a dissertation. Dissertation consultants have themselves obtained their doctoral degrees and therefore dissertation consultants know exactly what the student needs to do. Additionally, dissertation consultants know how to explain the complex procedures and methodologies of statistics to each and every student—and dissertation consultants will do so regardless of the student’s statistical abilities.