2x2x2 ANCOVA

Nem

Feb 2015
7
0
Canada
Hi all

I'm not entirely sure this would be the correct place to ask, but Im in the process of analyzing data for my thesis and realized that I need to conduct an ANCOVA on my data. While I've taken a number of statistics courses, I have never come across ANCOVAs and I wanting to get some feedback on the correct way to conduct this analysis.

I have 3 2level factors (2x2x2):
var1 - within subjects
var2 - within subjects
var3 - between subjects
and a covariate that is continuous

Im expecting to find a significant 3 way interaction once the effect of the covariate has been removed, and then be able to assess the 2 2ways within the same analysis

In SPSS, I can go to analyze > GLM > repeated measures, add all the within, between variables and covariate

Onto my questions:
1. In the output, I assume I look at var1*var2*var3 to assess my 3 way interaction? Is this with the effect of the covariate removed?

2. In the same output, what does var1*var2*covariate tell me? Is that relevant to my question?

3. Assuming I look at the var1*var2*var3 row, I do in fact get a significant 3 way interaction. Now I need to assess whether there are significant 2 way interactions between var1*var2 at the different levels of var3. I understand that there are going to be alpha issues if I just split the file by var3 and run some 2 way ANCOVAS - what is the correct way to conduct these analyses, ideally at the same time as conducting the initial 3 way? Can SPSS give me all that output in one go?

4. How do I then go on to assess the simple main effects of those 2 way interactions?

5. Are there assumptions that ANCOVA makes that I should be testing prior to doing any of this? And how are those assumptions tested in SPSS?

Basically, Im trying to get a bunch of information: 3 way, 2 ways, simple main effects, main effects, all in a single analysis without having to do any file splitting and without inflating/deflating my alpha level

thanks!
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey Nem.

If you are doing a GLM with all possible factor combinations then yes - the a*b*c coefficient will be used to test whether there is a statistically significant three way interaction.\

Two way interactions come from look at var1*var2 for var1 and var2 being any variable but different to each other.

When it comes to two way interactions you will have to look at the coefficients of the regression for x*y where x and y are the variables. Note that this is only a linear model - if you are looking at further associations that are non-linear then you will need to add terms like (var1*var2)^2 or something of that nature. Understanding this will require you to understand the nature of the stochastic process as well as your output and statistical assumptions.

The two way interactions are assessed by assessing the coefficient and what it relates to - along with trying to interpret what it really says about the question you are trying to answer.

There are assumptions for ANCOVA:

Analysis of covariance - Wikipedia, the free encyclopedia

You ultimately need to say what question you are trying to answer and then understand how you can use statistics and your expert knowledge to answer it. The best results are based on getting the most accurate, representative, unbiased, and useful answer to a very well defined question that can be answerable in some useful manner.

I think before doing these analyses you need to provide the well defined question you are trying to answer and then use the statistics and expert knowledge to decide how both of these impact the kind of analyses that you can do as well as the kinds of analyses that you should do. Sometimes the could is not the same as the should.

Note that even if you do get statistically significant (or insignificant) results, you always need to put them into perspective. If they go against intuition then check them. If they don't make sense in expert knowledge, then check them. If the relations used in your assumptions to do statistical analyses don't make sense then check them.

It may also turn out that your expert beliefs are also false - or better yet, not accurate to the specifics of your experiment and process and if after checking your models many times over don't seem to yield any sort of easy fault (including when others check it) then you may need to change your existing beliefs of what you think you already know.

Anyway - get the question right and the answer will be much easier to obtain.
 
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Nem

Feb 2015
7
0
Canada
My research question is the following: Does being placed under high (or low) cognitive load (factor 1) impact how well we can memorize map routes and map landmarks (factor 2). In other words, I expect there to be a significant interaction between load*map type, specifically such that high load will hinder landmark learning more than route learning (with no difference between route/landmark under low load). I expect this interaction to be moderated by a third factor: sex

Due to the way I'm testing participants, I believe their mental rotation ability might impact their performance, so I want to use that as a covariate

When I use GLM > repeated measures in SPSS, I do in fact find a significant 3 way interaction (map*load*sex) when using mental rotation as a covariate. So the (alt) hypothesis appears to be supported thus far. When reporting the results for the 3-way interaction I can pull the numbers straight from the SPSS output. No problem here.

My problem now, is I also need to report the 2-way interactions (map*load for males, and map*load for females - both with mental rotation as a covariate still). However, the standard SPSS output does not give me the numbers for these 2 2-way interactions

One way around this is to split the file by sex, and then just test the map*load interaction for each gender separately, but I believe this will be incorrect as it will affect my alpha level. My question is how do I correctly get the numbers for these 2 2-way interactions, while still using a covariate?

If the covariate were not in the picture then I would know how to calculate the interactions by hand, but alas that is not the case here
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
If you are doing a GLM then you will have the opportunity of setting the model and obtaining the coefficients.

I haven't used SPSS for a very long time but I do know from experience that R and SAS will fit complex GLM's and output the coefficients along with the uncertainty (standard error) for the estimation thus giving a confidence interval and provided you meet the requirements of the Central Limit Theorem then it should be a useful estimate.

R is free but SAS usually costs money - but they have released a free virtual machine that allows you to do things for educational purposes (but it will be a big download).

If you can specify a GLM model then you would have to tell me what you can specify.

I think you should start by telling us the data types you use and what variables you are fitting the response to along with the structure (integers, positive real numbers, all real numbers, etc).

Once you get that sorted then it's a matter of opening SAS and R preparing the data tables and then using a command to fit the right GLM and get the output. Both SAS and R do a decent job of this.