When conducting a structural equation model (SEM) or confirmatory factor analysis (CFA), it is often recommended to test for multivariate normality. Some popular SEM software packages (such as AMOS) assume your variables are continuous and produce the best results when your data are normally distributed. Here we discuss a few options for testing normality in SEM.
First, researchers can test for multivariate normality using a quantile (Q-Q) or probability (P-P) plot in SPSS through the Analyze > Descriptive Statistics menu. They can also create a quantile plot of Mahalanobis distances to check for normality. SPSS provides steps for calculating Mahalanobis distances, while Intellectus Statistics performs this method automatically. In all cases, the plot should show points following a relatively straight line. Marked deviations from a straight line suggest that the data are not multivariate normal.
In AMOS, the built-in normality test calculates Mardia’s coefficient, a multivariate kurtosis measure. AMOS provides this coefficient and a critical value for significance testing. A critical value of 1.96 corresponds to a p-value of 0.05. If Mardia’s coefficient is significant (critical ratio > 1.96), the data may not follow a normal distribution. However, this significance test on its own is not a practical assessment of normality, especially in SEM. These tests are highly sensitive to sample size. Larger samples are more likely to produce significant (non-normal) results.
In SEM, where your sample size is expected to be very large, this means that Mardia’s coefficient is almost always guaranteed to be significant. Thus, the significance test on its own does not provide very useful information. Researchers should use significance tests along with descriptive statistics, such as kurtosis values for individual variables (Stevens, 2009). Kurtosis values greater than 3.00 may indicate non-normal distribution (Westfall & Henning, 2013).
Researchers use many methods to test for normality, and SEM analysis use the most popular ones.
Need help conducting your analysis? Leverage our 30+ years of experience and low-cost same-day service to complete your results today!
Schedule now using the calendar below.
References
Stevens, J. P. (2009). Applied multivariate statistics for the social sciences (5th ed.). Mahwah, NJ: Routledge Academic.
Westfall, P. H., & Henning, K. S. S. (2013). Texts in statistical science: Understanding advanced statistical methods. Boca Raton, FL: Taylor & Francis.
Welcome, 2020! What are you going to do with this shiny, new decade? Will you complete your dissertation this year, or will you struggle for the next few years while you burnyourself out? Here are some tips on how to avoid the latter.
Inside Higher ED says setting deadlines early in the dissertation process is imperative to sustaining long-term motivation but making sure those deadlines are doable and flexible is key. Ask for feedback early on because the sooner you communicate with your committee about your work, the smoother collaboration and editing will be. Finally, remember that your dissertation is your work and you are the expert but it’s crucial to find out what your committee wants and expects from your work so open lines of communication are critical.
Before you dive into your dissertation this year, ask yourself how your journey can improve. What would help you complete your dissertation and how can you make that happen? The journey to completing your degree starts today, with the help of our dedicated team of dissertation experts.
What is dissertation assistance?
Dissertation assistance comes in the form of keeping you engaged and motivated to write with the backing and assistance of a mentor. Not only will our mentors help shape your chapter(s) until they’re submission-ready, but they will also help you address feedback so you can rest assured that there won’t be any surprise roadblocks along the way.
How do I get dissertation assistance?
The first step to getting dissertation assistance is to schedule your free initial dissertation consultation. During our call, we’ll discuss your project needs, talk about turn-around times, and project assistance cost. Scheduling your appointment is quick and easy! Simply select a date and time using the calendar to your right to reserve your spot.
The holiday season is upon us and our to-do list seems to be growing exponentially each day. In the midst of gift wrapping, dinner planning, and ugly holiday sweaters, are you achieving dissertation progress? Let’s take a moment to ground ourselves in the last few weeks of 2019 and then get ready to reach for the sky in 2020.
Find Support
If your 2019 New Year’s resolution was to finally complete your dissertation and you’re still stuck in a loop of countless revisions, it’s time to set a resolution that will actually stick. The American Psychological Association suggests that asking for support is key to ensuring one sticks with a New Year’s goal. With dissertation consulting from Statistics Solutions you’ll not only receive a team of seasoned mentors capable of helping you through each dissertation phase, but you’ll also receive friendly and consistent reminders to stay on track.
Break it Down
Harvard Medical School suggests breaking big New Year’s goals into small, manageable steps in order to not get discouraged and quit early on. For example, if the goal is to move onto the results chapter but you don’t know where to start – finding tutoring around that section is a good place. Search for and join free webinars or tutoring sessions on campus. We offer free Qualitative Methodology and Results Help Sessions along with free Quantitative Results Help Sessions online, and once you’re ready to take the plunge, our Accelerated Quantitative Results program can provide a draft of your chapter 4 in just 1-hour.
Reward Yourself
The same article from Harvard Medical also suggests that it’s important to give yourself recognition for healthy changes, even if you haven’t reached the end goal yet. If you sit down to write consistently, be proud of yourself (even if the chapter isn’t perfect yet)! Look for support from your peers and loved ones. Stay motivated and proud of yourself.
Learn from the Past
If last December your goal was to finish your dissertation and graduate in 2019, do something different in 2020. Reach out for help, change up your writing routine, explore online tutorials and webinars – Make 2020 your year of successful change. Make 2020 your graduating year! You’ve got this, we believe in you.
Looking to make a positive change now?
Schedule Your Consulting Appointment
Link to APA article: https://www.apa.org/helpcenter/resolution
Link to Harvard Medical School article: https://www.health.harvard.edu/staying-healthy/seven-steps-for-making-your-new-years-resolutions-stick
Structural equation modeling (SEM) is an increasingly popular choice for quantitative statistical analyses, as it allows researchers to model complex relationships while taking into account measurement error of latent variables. Although there are great advantages to using SEM, the complexity of the analysis can be daunting, especially for students or beginning researchers. One of the most troublesome issues students face is determining an appropriate sample size for structural equation modeling. For simple analyses like t-tests, ANOVAs, or regressions, reputable power analysis tools such as G*Power allow researchers to calculate an appropriate sample size using only a few basic parameters (i.e., power level, significance level, and effect size). For SEM, however, determining sample size is not as straightforward.
Assessing the Linear Relationship and Correlation
Most researchers agree that SEM requires “large” sample sizes, but what exactly does this mean? A number that gets tossed around a lot is 300 (see Comrey & Lee, 2013; Tabachnick & Fidell, 2013), but a one-size-fits-all answer like this probably will not fly with most reviewers. As there is no single correct or universally-accepted calculation or method for determining sample size for SEM, researchers and students alike often rely on “rules of thumb.”
Need help conducting your analysis? Leverage our 30+ years of experience and low-cost same-day service to complete your results today!
Schedule now using the calendar below.
For instance, some statistics scholars have recommended using the ratio of observations to estimated parameters (N:q) as a guide. Specifically, Kline (2015) recommended that the N:q ratio should be 20 to 1, or 20 observations (participants) for each estimated parameter in the model. Others have suggested that the N:q ratio can be as low as 10 to 1 (Schreiber et al., 2006) or 5 to 1 (Bentler & Chou, 1987). Clearly, there is a lot of variance and uncertainty even in guidelines proposed by SEM scholars.
So, what if your reviewers require some kind of hard calculation (rather than rules of thumb) to determine your sample size?
There are some easy-to-use online tools that have academic support (for an example see Daniel Soper’s sample size calculation tool based on the work of Westland, 2010). However, Monte Carlo simulation is becoming an increasingly preferred method (for an in-depth discussion, see Wolf et al., 2013). In short, the Monte Carlo simulation method allows you to construct a model to your exact specifications and then test the model on thousands of “random” datasets of varying sample sizes.
This lets you see approximately how often the effects in your model will be significant (i.e., statistical power) in a sample of any given size. The main advantage of this method is that it allows you to determine an appropriate sample size for the specific model you are testing. However, this method requires a high level of expertise in specific statistical software (such as Mplus) to conduct properly. Keep an eye out for future blogs where we may cover Monte Carlo methods in more detail!
References
Bentler, P. M., & Chou, C. P. (1987). Practical issues in structural modeling. Sociological Methods & Research, 16(1), 78-117.
Comrey, A. L., & Lee, H. B. (2013). A first course in factor analysis. Psychology Press.
Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford publications.
Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. The Journal of Educational Research, 99(6), 323-338.
Soper, D.S. (2018). A-priori Sample Size Calculator for Structural Equation Models . Available from http://www.danielsoper.com/statcalc
Tabachnick, B. & Fidell, L. (2013). Using multivariate statistics. Boston: Pearson Education.
Westland, J.C. (2010). Lower bounds on sample size in structural equation modeling. Electronic Commerce Research and Applications, 9(6), 476-487.
Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73(6), 913-934.
Rejection hurts and failures are difficult to get over. As a PhD candidate, chances are, you have experienced rejection and failure at some point along your doctoral journey. Caitlin Kirby from Michigan State University wore her rejections from over the last 4 years as a badge of honor. Kirby entered her oral dissertation defense wearing a skirt made from 17 rejection letters she’d received.
Her committee found this both refreshing and humorous. Kirby explained the process of digging up the rejection letters and putting the skirt together as cathartic and therapeutic. How will you feel about your rejections on your defense day? Failure is necessary for growth and some can even use rejection as a motivator. As a society, many of us have become so used to instant gratification and persevering through a grueling processes such as getting your PhD can, at times, seem impossible. Nothing worthwhile comes easy and, by this point you’ve already overcome the rejection letters, so we are here to motivate you, and help you continue to persevere towards your goal of completing your dissertation.
Ultimately, going for your dreams of becoming a PhD gives you the opportunity to face your fears and see how strongly you persevere. Throughout the dissertation process, there will be a lot of rejections and it takes guts and confidence to carry on. Having a dedicated team of dissertation professionals keeps the pressure from being completely on your shoulders, so if you’ve been struggling, reach out and learn about the resources available to you. What have been some of the toughest rejections you’ve experienced on your dissertation journey thus far?
Need assistance with your research?
Schedule a time to speak with an expert using the link below.
What if your dissertation struggles didn’t have to be all-consuming? Instead of spending countless hours going back and forth with your committee feedback, what if you could spend that time constructively working with a seasoned mentor that knows how to get your chapter approved? That’s exactly the type of effective support you will find with one-on-one consulting at Statistics Solutions.
It’s time to reach out for academic help when you’re working hard but not seeing a reward, or even worse, when you begin to enter ‘shut-down mode.’ Many of our students come to us when they’re in year 5 or year 7 of their dissertation program. By then, they’ve wasted thousands of dollars in tuition and valuable years of their lives. Once they begin to constructively work on their research with us, they realize all of the time and money they could have saved by reaching out for help sooner.
Accelerate Your Dissertation Journey
It’s important to remember that you should be making significant dissertation progress every semester. So if you aren’t, ask yourself, why. What is holding you back from getting your chapter approved, getting IRB/URR approval, finishing your data collection? Is there something you can do to make the process a little smoother and kinder to yourself? The answer is a resounding, yes. There is something you can do and it’s simply asking for help.
Need assistance with your research?
Schedule a time to speak with an expert using the link below
A helpful exercise is to picture what graduation feels like. Picture yourself dressed in your graduation cap and gown, walking across the stage, about to accept your diploma. What does that feel like? Hold on to that feeling and use it to propel you forward. You can finish your dissertation and you will not be ABD forever. Take hold of your research and your future, merge into the dissertation fast-lane. You’ve got this and we’ve got you.
Yours in Dissertation Success,
The Intellectus Consulting Team
In the Discussion chapter of a dissertation, it is customary to discuss the limitations of your study and mention shortcomings that may have affected the results. However, students will often write about challenges they have had with their study rather than actual limitations. So, what is the difference between limitations and challenges, and what should you include in the Discussion section?
Limitations are shortcomings or weaknesses that may have affected your results. You should mention any limitation to your study in the Discussion chapter. This lets readers know they should interpret your findings with these limitations in mind. In quantitative studies, for example, having a small sample size is a limitation. If your sample size was smaller than expected, your statistical analyses may have been underpowered, meaning that you were less likely to find statistically significant results. Low sample sizes can also represent limitations in qualitative studies designed to collect in-depth information. Although sample sizes are usually considerably lower in qualitative studies than in quantitative studies, low sample sizes can represent a limitation because you may not have interviewed enough participants to have achieved saturation (the point at which no new ideas are emerging from the interviews). These are just a couple examples of limitations that can affect results.
Need help with your dissertation? Leverage our 30+ years of experience and low-cost service to make progress on your project!
Schedule now using the calendar below.
However, students will often write about challenges they encountered when conducting their studies. If something was difficult about your study but did not affect the results, it probably was a challenge. But not a limitation. As such, challenges should not mention in your Discussion chapter. For example, if you had trouble getting participants but ultimately obtain enough for your study to adequately powered, this would be a challenge not a limitation. If you had trouble contacting certain parties or agencies for permission, for example, but finally contacted them, this too would be a challenge and not a limitation.
All studies have challenges, and all studies have limitations. So, it is important to know the difference. Limitations can affect your results and, consequently, should be mentioned in your Discussion chapter. Challenges are difficulties. If they did not affect your results, you do not need to mention them.
Computer assisted qualitative data analysis software is very helpful for researchers when analyzing data. Programs like NVivo, Atlas.ti, and Dedoose help researchers organize and catalogue qualitative data, but they can be pricey. Even at student rates, many students do not have the money to shell out for such a program. So, what do you do when you cannot afford one of these programs, or you do not have access to them? Well, you can do what qualitative researchers have done for a long time – make do without! There are lots of ways to perform qualitative analysis without a specialized program. For example, qualitative analysis can be done using common text editing or word processing programs. Here, I will talk about how you can perform qualitative data analysis in Microsoft Word.
Discover How We Assist to Edit Your Dissertation Chapters
Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.
- Bring dissertation editing expertise to chapters 1-5 in timely manner.
- Track all changes, then work with you to bring about scholarly writing.
- Ongoing support to address committee feedback, reducing revisions.
Once you have finished data collection and transcription, the next step is analyzing your data. Your transcripts should be in Word document format. I would recommend saving a copy of the raw transcripts, then save the document as a separate file as well with a label indicating that it is a coded transcript. This is the document you will be working with.
There are several features in Word that you may use to code your transcripts. The one that I find the most helpful is the highlighting feature, found in Home section of Word. The default color is yellow, but if you click the dropdown button next to the highlighting tool, more color options become available. As you start line-by-line coding you will use the different colors for different codes, so make sure that you keep a key for these. You will use this key across all your transcripts. Continue using this color-coding system until you have generated codes for all of your transcripts. If you run out of colors, you can use the Underline, Bold, or Italic functions to denote new codes.
When you finish coding your transcripts, you will begin to compile the codes based on color. For this, you can use Microsoft Word or Microsoft Excel. Begin with the first transcript and, in a new Word document or Excel spreadsheet, copy and paste all of the yellow-highlighted passages from the transcript into the new document. If you are using a spreadsheet, you can put each item into a different cell. Do this for all yellow-highlighted passages from all transcripts, and then do the same for the other colors you have used. When you are done, you will have a list of all coded passages assigned to one code, making them easy to retrieve for further review in later analysis stages.
The other feature of Word that can be helpful is the New Comment function, found in the Review section of Word. This feature allows you to highlight text passages and add notes in the margin. As you are coding your transcripts, you will likely have thoughts and ideas about what your participants said in their interviews. Using the New Comment feature will help you make annotations in the margin that are assigned to a certain passage, so you can pull these up quickly in the document and remember what was important about that passage.
While dedicated qualitative data analysis programs have their advantages, they are not necessary to perform good and thorough qualitative data analysis. Using the tools already available to you, this can be accomplished quite easily. Using this system can help you stay organized so you can easily visualize your data and results.
Take the course: Coding and Memoing
In Part 1 of this series on focus groups, we discussed preparing to run a successful focus group, a powerful method of qualitative data collection. In this blog, we will talk about running a successful focus group.
Hopefully you will have chosen a quiet, private space to conduct your focus group. Comfortable seating is a plus! Arrange the chairs into a circle if possible. Doing this will ensure participants can look at each other when talking and take cues – both verbal and nonverbal – off other participants. This will also provide the best angle for you to observe participants as they speak. It is a good idea to bring light refreshments and maybe coffee and water for your participants. Food goes a long way to keeping participants happy and comfortable!
Before beginning the focus group, introduce yourself to everyone and explain the purpose of your research and the purpose of the focus group. Also make sure all participants have given their consent and confirm with them that it is okay to audio record the session. Remember that ethical guidelines require transparency.
You are the moderator of the focus group, which means that you will be following your protocol and not contributing. Do not interrupt participants as they speak and avoid inserting yourself into the discussion more than necessary. You are there to learn from your participants. Encourage participants to speak openly and freely. If participants get derailed, try to steer them back on topic by referring to your protocol. Try to encourage participants who have not spoken to talk – you want data from everyone! You may take notes during the session, but make sure that you pay attention to what participants are saying. You do not want to be looking down and writing notes during the entire session.
After the focus group is over, thank people for their participation! They have shared their valuable free time with you, so let them know that you appreciate this. Close by highlighting some of the “big ideas” that came out of the focus group and ask if participants have other ideas for what the takeaways of the session were. Let participants know that you will follow up with them by providing each with a copy of the transcript for them to verify for accuracy. Confirm that you have the participants’ contact information to do this.
After the focus group, transcribe the recording of the session. Then, contact your participants with the transcript. You can do this either by providing the entire transcript to all participants or by sending participants their respective contributions to the focus group. Ask them to verify the accuracy of their statements and to let you know if amendments need to be made. If so, make the necessary changes to the transcripts prior to data analysis. If not, the transcripts are ready for data analysis.
One of the most fundamental components of a study is the research problem. In fact, this drives the entire study; if you do not have a research problem, you do not have a study. Yet, beginning researchers sometimes do not understand the importance of the research problem or understand exactly what a research problem is. This blog is intended to shed light on the nature and purpose of the research problem.
It is exactly what it sounds like: a problem or issue in or with the research. Although it stems from a social or organizational issue, the actual research problem itself is developed by looking into the literature. I cannot emphasize this point enough. The research problem is developed by diving into the research on the topic to see what is there and what research is needed. It does not come from what we think is important, from our opinion about what needs to be studied, or from our desire to study something. This is exists in and is developed from the literature.
Identifying areas for further investigation through existing literature
For example, let’s say there is a problem with special education teachers leaving the profession. The first thing to do is to go to the research to see what is already known about the topic. So, the research says they are leaving because they are not satisfied in their jobs, jobs demands are high, and pay is commensurately low. They also leave because they do not feel adequately prepared and feel they are not supported by administration. So now, where do we go from here? You can review the “Recommendations for Further Research” sections of recent studies. These are recommendations for future research suggested by researchers based on their findings. These recommendations may be developed into research problems.
Need help with your project? Leverage our 30+ years of experience and low-cost service to make progress on your results!
Schedule now using the calendar below.
Identifying gaps and opportunities for further exploration
To develop a this, you should delve into the issue further. Look at how we know what we know about teachers leaving special education. Maybe the research is primarily quantitative, necessitating qualitative inquiry to gain in-depth information on teachers’ perceptions and experiences. Or, maybe it is the reverse. Maybe we have lots of information on teachers’ experiences but little quantitative research confirming the relationships between factors and constructs. Or, maybe we do not have comprehensive information about the topic, necessitating the views of other stakeholders such as administrators, or more comprehensive study designs such as case studies with multiple data sources. These shortcomings in the research represent gaps in what we know or problems with the research that, if addressed, can enhance understanding of the topic and uniquely contribute to the research.
I sometimes hear beginning researchers say, “I want to study” or “I think it’s important to study” such-and-such. These are good places to start, but they do not represent legitimate research problems. From these starting points, go to the literature. See what is there. Notice what the shortcomings, weaknesses, and gaps are in the research on your topic. See what the issues or problems are in the research and how you can uniquely contribute to it. Then, you will be on your way to developing a true research problem to support a study.