Hello everyone,
Thank you for your help in advance.
I am working on a journal revision. The reviewers ask me to do a mixed procedures analysis because my experiment was a multiple-period task in which a participant repeated a task over several periods, and all periods observations were used in the analysis.
The reviewers also provided a reference for rerunning the analysis. When I was reading the reference paper, the results table is reported as in the picture attached.
My question is how do I conduct an ANOVA or mixed procedure and report results similar to the table attached. Specifically, do I need to conduct two ANOVA analyses to report one for between subjects and one for within-subjects? Or one analysis is enough. If so, how do I find the two Errors (one for between subjects and one for within-subjects)?
BTW, I use SPSS.
Thank you very much for your help!
As far as I understand from the info you provide, your reviewer recommended to perform a mixed-effects model, not repeated measures ANOVA. A mixed-effects model may provide similar/identical results with a repeated measures ANOVA if the design is simpler, but for more complex designs, a mixed-effects model is usually more appropriate (for a summary of the differences, see for instance https://www.theanalysisfactor.com/six-differences-between-repeated-measures-anova-and-linear-mixed-models/). You should read an introduction to the theory of mixed-effects model, then find a tutorial on building mixed-model effects in SPSS, for instance https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjKpN3HvtrxAhXQ_KQKHZumD7YQFjAGegUInQEQAw&url=https%3A%2F%2Fcsass.ucsc.edu%2Fself-study%2520courses%2FSPSSMixed.pdf&usg=AOvVaw2rr_UlXKWlxQ_Q7QGzODOB
I would submit both models and say why one is slightly better than the other.
There is a terminology issue here (and the terminology is confusing). They reviewers might have meant:
1) a mixed ANOVA with a combination of within (repeated measures) and between (independent measures factors). This is relatively easy to run via the repeated measures ANOVA commands in SPSS (e.g., see https://www.discoveringstatistics.com/repository/mixed_2020.pdf ). This is a single model that handles all the error terms etc.
2) They could have meant a linear mixed model (or multilevel model). If you have a completely balanced design with no missing cells and no time-varying covariates then this is essentially equivalent to the mixed ANOVA (assuming a single random factor for participants and a nested design). Generally this approach is useful because you have imbalance or complex random effects that you want to model (and the mixed ANOVA is a special case of this kind of model). The mixed term here is a mixture of random and mixed effects being modelled. Its a highly flexible approach. You can run this in SPSS but it isn't straightforward if you are new to these models.
The table you show appears to be from a mixed ANOVA. Your description isn't sufficient to tell what the reviewers meant.
Thank you Bruce Weaver! The reference paper is Cardinaels, E. 2016. Earnings benchmarks, information systems, and their impact on the degree of honesty in managerial reporting. Accounting, Organizations and Society 52: 50-62.
I used a similar experimental design. The reviewers ask me to run the analysis similar toTABLE 1 on p. 56 in Cardinaels (2016).
Thank you Robert Ancuceanu ! It is what I thought I should've used. The attached table is from the reference paper (Cardinaels 2016). I am confused by that how I can run the ANOVA model (model 1) and the mixed module procedure (model 2) and report the results for the between subjects and the within-subjects effect.
The reference paper is Cardinaels, E. 2016. Earnings benchmarks, information systems, and their impact on the degree of honesty in managerial reporting. Accounting, Organizations and Society 52: 50-62.
The table is reported on p.56.
Thank you Béatrice Marianne Ewalds-Kvist ! The methods report similar results and p-values. So, at least, I don't have to worry about cleaning data again :)
Thank you Thom Baguley ! I believe they ask me to do the mixed linear model because it is the method used in the "reference paper'.
OK. This is the text from the paper: "Because there is less room to misrepresent costs at high levels of the actual cost, I also control for the actual cost in a second model (see also Brüggen & Luft, 2011). Table 1 presents the results of the full-factor ANOVA (Model 1) and a mixed model procedure (Model 2) with the actual cost as a time-varying covariate (i.e., 41 possible values between 4.00, 4.05, 4.10, …, 5.95, and 6.00). In both models, the reporting period is treated as a within-subject effect."
So they do both. Model 1 is a mixed ANOVA (though they may have run it as a multilevel model) and Model 2 is a linear mixed model because it includes the time-varying covariate. That makes sense. So you should adopt a similar approach if you have a time varying covariate.
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