Hello Fadhli,

I recommend you use ANCOVA, and certainly not use pre- and post- fatigue scores because ANCOVA will take those scores into account appropriately because of different baseline scores.

I hope that helps - and all the best with your research.

Robt.

Dear Robert Trevethan,

From my understanding, you refer to the score of prefatigue minus postfatigue as outcome variable, am i right?

Example:

Prefatigue score: 8.5

Postfatigue score: 6.5

Recovery score: 8.5 - 6.5 = 2.0

Then, the prefatigue score will be one of the covariate, isnt it?

Thanks for your kind response.

Hello again, Fadhli,

Sorry, it seems I didn't make myself clear. No, I think that the difference between the scores should not be regarded as an outcome variable. If you use ANCOVA, you should be able to avoid that kind of situation. In fact, there are recommendations that the difference between pre and post scores should not be used at all, partly because of differences in baseline scores.

Are you familiar with ANCOVA? There are some good YouTube presentations about it that might be helpful.

Robt.

Visual analog scale measures have an upper and a lower boundary. Hence, you should build a model with a response distribution that has two boundaries. ANCOVA is inappropriate as it uses Normal response distribution (no boundaries).

In my online book I recommend beta regression for visual analog scales (see chapter 7.6.2): https://bookdown.org/schmettow/NewStats/GLM.html#beta-regression

@Martin S, thanks for contributing to this thread. May I check with you please, concerning whether or not ANCOVA really requires that data be normally distributed. I used to think that normality of data was highly desirable, but I am increasingly suspecting that this is not so. For example, I found the following article by Geoffrey Norman to be enlightening: Adv in Health Sci Educ (2010) 15:625–632. DOI 10.1007/s10459-010-9222-y. What do you think? I'd appreciate your comments. Robt.

Robert Trevethan ANCOVA is a (general) linear model and as such it makes the assumption of Normal distribution of the response variable (not the predictors!) You have to look no further than Wikipedia (or any statistics introductory text) to check this.

Another assunption is that the variance of the response distribution is constant. Most likely this is violated by VAS responses as well, because when responses get closer to the lower or upper boundary (0cm, 10cm), the distribution typically gets more narrow. In contrast, Beta distributions behave exactly like that, with the response distribution being widest when it is centered (x = .5).

@Martin S, thanks for getting back regarding this. I'll explore it further, but unfortunately I'm accumulating contradictory evidence. RT.

Dear Robert Trevethan and Martin Schmettow,

Thank you for your input. I realized me myself suggesting inapproriate statistical method.

For clarification, my study is a observational two-wavel panels study involving one group samples with different levels of baseline pre-outcome measures.

There are three outcome measurements that will be measured two times (pre-rest and post-rest):

1. Subjective fatigue level (measured by visual analog score)

2. Work engagement level (measured by Likert scale - ordinal data)

3. Objective fatigue level (mean reaction time in miliseconds)

The independant variables consist of different type of data i.e. continous (age, hours, etc), categorical (yes/no, role, etc) and ordinal type (likert scale).

To represent the concept of recovery i.e. unwinding of initial fatigue level, i decided to measure recovery by substracting pre-measure with post-measure for each outcome, and the score differences are operationally defined as recovery level (subjective recovery level, objective recovery level and engagement recovery level).

I would like to determine whether the independant variables would significantly predict each outcome (subjective fatigue, work engagement and objective fatigue).

Currently i am thinking of these statistical strategies:

1. Multiple linear regression, however one outcome measure i.e. work engagement is ordinal data.

2. Hierarchical regression or hierarchical linear modelling or multilevel modelling, but i am not quite familiar with the concept, assumption or other aspect of these method

3. I would consider reading on beta regression (sorry, this is my first time reading on this method).

4. Could i consider Structural Equation Modelling with this type of data?

Thanks for your kind assistance.

Regards,

Fadhli

Hello Fadhli,

Thank you for the additional information. It reveals that your investigation in considerably more complex than you first indicated. As a result, I now suspect that my original recommendation that you use ANCOVA might well not be appropriate, as Martin S had indicated was the case, anyway.

Unfortunately, I'm not sufficiently familiar with the ins and outs of structural equation modelling to give you advice about that. It's also a bit difficult, from a distance, to know exactly the nature of your research questions and therefore how best to address them.

Here is one comment, however: If your work engagement variable is composed of a number of Likert items that all measure the same construct, I think you could regard that variable as being equal interval for the purpose of statistical analyses, even if the data are not, strictly speaking, equal interval.

In addition, I recommend that you ensure that any assumptions concerning the technique(s) you use have been met.

Robt.

Dear Robert Trevethan,

Thank you for your kind response and valuable advice.

I will try my best to share the end product with you once the research completed for the purpose of learning.

Regards,

Fadhli

Thanks for your thanks, Fadhli. I'd be interested to see what you come up with. If you decide to do ANCOVA, I might be able to provide some advice / recommendations. However, I realise that ANCOVA might not be the best for what you need to do statistically.

Robt.

Dear @Nesrine Amor,

If I am not mistaken, ANCOVA is a statistical test to compare two groups. However my study consists of only one-group.

Regards,

Fadhli

Hello again Fadhli,

I think you are correct in thinking that ANCOVA will not be appropriate for your analyses. I have now read your initial question again and realise that I misinterpreted the design of your research. In the main question, you did indeed refer to a "one group sample", but in the expansion of your question you referred to "one group samples" (plural) - and that second reference made me think that you had two (or more) samples for comparison.

Now, I think that something such as regression or SEM would be more appropriate. I think you should consider those prospects - and, in doing so, consider whether the assumptions pertaining to those procedures and be met. It would also be necessary to ensure your sample (singular!) is sufficiently large.

All the best as you forge ahead!

Robt.

Dear Robert Trevethan,

I am really sorry for my bad grammar.

Thank you for your response and suggestion.

1. Sample size

In response to your suggestion on sample size, my sample size would be around 350 to 400 randomly chosen participants. Currently i already had around 250 participants who completely completed the questionnaires. I calculated the sample size based on correlation efficient: alpha two tails 0.05, beta 0.80, and expected correlation efficient 0.15 would require 347 participants. ( Calculator link http://www.sample-size.net/correlation-sample-size/ ). However, i am not quite sure whether the decision to calculate based on correlation coefficient is correct.

In your opinion, how large is sufficiently large?

2. Work engagement

As for your previous query on work engagement, it originally contains 3 constructs, but numerous research, including by original developer, shown that it can be used as single construct, and my initial intention is to measure as single construct. So, your suggestion to treat it as single construct and assume equal interval is really helpful, but i have to find literatures to support this 'equal-interval assumption'.

Regards,

Fadhli

Hello Fadhli,

Don't worry about your grammar. I should have been more careful, too.

I think you have enough people for your analyses.

I am attaching an article from a highly respected methodologist / statistician that should reassure you about your work engagement variable being able to be regarded as at the equal-interval level for purposes of analysis. It has some highlighting that I placed in it. I hope that's OK.

Robt.

Dear @Robert Trevethan,

Thank you for your the reference. You save my time and greatly relief my preoccupied thought on Likert scale ordinal data.

Regards,

Fadhli