Interaction Contrast Analysis - Mixed-Design ANOVA in SPSS

in a previous video I demonstrated how to conduct an interaction contrast analysis in SPSS which involved a context that was factorial between subjects in nature and somebody asked if it's possible to do this on repeated measures data and the answer to that question is yes and in fact an article that was part of the inspiration of my video which talks about contrast analyses for factorial designs and a fair amount of detail says that it's possible to do one for like a mixed design anova but they don't give very many details but I figured out a way how to do it fairly easily in any program but I'm gonna show you how to do it in SPSS and the key to doing this is actually calculating different scores but before I do so I'm gonna show you these data basically it's a two by two design mix design ANOVA with a grouping variable where the groups equal to two where there's one placebo and two treatment group and let's just say the treatment is relevant to something like enhancing short-term memory and weight so we have IQ scores relevant to memory and the drug is supposedly going to help improve people's memory in old age who might end up suffering from dementia or something like that so if I analyze these data with a mix design and OVA in a conventional way go to general linear model repeated measures ANOVA and I'm just going to change this to time and two levels I just want to show you what these data look like before I actually do the contrast analysis and so what's gonna happen is I'm just barely gonna not reject the null hypothesis with these data which is where the power of the contrast analysis comes in and I'm gonna plot the means so I want group in two separate lines time or as on toll axis could continue and options I descriptors effect size and that's all I'll look and homogeneity test one leave boxes M tests and click OK and so I'm just gonna scroll down quickly to the the chart of the means because that's really where the story is told and we can see that the means for the treatment group is actually increasing cognitive performance for the treatment group from pretest to post-test and the means for the no group is actually decreasing at least numerically now the key to testing this hypothesis and getting support for it is to observe a statistically significant interaction and when I look at the test of within-subjects effects table the time by group interaction is actually not statistically significant with an F of three point one nine five and a P equal point zero eight three that's with one and thirty four degrees of freedom so I haven't rejected the null hypothesis here and it looks like there should be evidence in favor of the effect it's just not quite strong enough on the basis of a two-tailed test now a lot of people would be stuck at this point not knowing what to do it's not even close to point zero five or less it's way too high and there's no such thing as a one tailed test in the context of an ANOVA because an F distribution actually only has one tail to it so there's no possibility of a one tailed test so you're stuck so a possible solution to this scenario is to do the planned comparison because these data are consistent with what was hypothesized theoretically the treatment group was supposed to increase and presumably the placebo group over time older people's memory cognitive functioning decreases over time so everything is consistent with theory and previous data you just don't have a statistically significant effect so to do this as a contrast analysis the first thing you need to do is calculate different scores between your time one and time two data so I'm gonna do that transform compute I'm gonna call that difference and pretest minus post-test and click OK and that created a different score variable so what I'm gonna do first I'm going to show you that when I do just a regular independent sample t-test on these different scores I get exactly the same result as I did with the time by group interaction effect through the mix design ANOVA so let me just show you that quickly analyze compare means independent sample t-test I'm going to use the different scores here and I'm gonna use the grouping variable as my independent variable defining the groups I think it's one and two for the placebo and treatment groups and okay and here is the analysis with the tests of the differences between the two group means of the different scores and so a positive difference score here implies that the first mean was larger than the second mean which is the case for the placebo group the first mean was larger than the second mean and so I get a positive mean different score for the placebo group and the opposite is true for the treatment group going from time one to time two pretest post-test this is going to be a negative mean different score value and in fact that's what I got and the tests of the difference between the different scores the mean different scores is exactly the same result as the mix design ANOVA with a p-value equal to point zero eight three which is exactly what I got here in the mix design ANOVA and that is not a coincidence it's because it's exactly the same test so let me just prove that to you a little bit more by pushing out this T value to five decimal places and once I square that T value I will get exactly the F value now doing this will open up the possibility of a contrast analysis that's three point nine five two and when I scroll up over here three point one nine five and it's a two if I were to push the decimal place so by squaring the T value of the difference between the different scores the mean difference I get exactly the mix design ANOVA effect now i t-distribution has two tails to it unlike the F distribution so now I have the possibility of doing a one-tailed planned comparison or a planned contrast which means that I could split the p-value in half if I get the effect in direction that was hypothesized and to specify the hypothesis in a contrast context I've got to specify the contrast weightings and that is easy enough to do in a two-by-two mix design ANOVA I just have to specify which one I think is going to be positive and which one I think is going to be negative or in more general sense which mean is going to be larger than the so let me just click on analyze compare means and one-way ANOVA this is where I can do a planned comparison with contrast weightings in SPSS so I'm going to use the different scores again as the dependent variable and the grouping variable as my factor variable and I'm going to click on contrast here and so I need to specify the coefficients in such a way that a couple of rules are satisfied one of which is the coefficients must total to 0 and the coefficients must correspond to the pattern of means that you expect so in this case here I expect the placebo mean to be larger than the treatment group mean and the placebo group is actually specified as a 1 so placebo is group 1 and treatment is group 2 so I keep that in mind so the placebos Group 1 and I expect that mean difference to be lower or negative than the treatment group so if I go in to analyze compare means and create this contrast analysis with that information in mind I can go into contrast and specify this so the mean of the different scores for the placebo group is expected to be positive so I'm gonna put a positive coefficient of 1 by contrast for the treatment group pretest to post-test if I subtract those two means it's going to be negative minus 1 is what I had put here and so my coefficient total is 0 and I have a pattern of coefficients that's consistent with the pattern of means that I expect so I'm not gonna do this whole video on contrast weightings I might do another video in the future that talks about that a little bit more but in the context of a 2 by 2 mix design ANOVA there's really only two possibilities a positive one and a negative one and you have to figure out the pattern of the means that's consistent with your effect so with my contrast weighting specified I've click continue and click OK and so here is the test the contrast weighting so here's placebo with a plus one and treatment a negative one and in fact that's consumed with the placebo being positive here plus 1.88 and treatment is negative negative three point four six so I've allocated those contrast weightings in a way that's consistent with the pattern of the means I will point out briefly here that the mean different scores do not have to be one positive in one negative very often you'll have two different scores that are the means are negative and that's fine you just have to specify the negative one for the mean different score in that context that is smaller than the other one and so the treatment group should always be producing the larger effect and so the treatment group should be taken into consideration that way in order to specify your contrast weighting so basically the take-home messages look at the pattern of the means or if you've hypothesized this to begin with specify your contrast weightings in such a way that they will be consistent with the pattern and means that you hypothesize and if it's consistent with the hypothesis in mind the contrast T value which is produced here is going to be positive and direction so a positive T value says that it is consistent with the coefficients that you've specified here had I specified negative one for placebo and plus one for treatment I would have got a negative T value here which would not have been consistent with the hypothesis and so that in that context I haven't rejected the null hypothesis and so therefore I haven't supported the idea that the treatment worked but in this case I've got a T value of one point seven eight eight and with 34 degrees of freedom and a one tailed test because in this case I have planned this comparison and I'm allowed to do a one tailed test in that context there are references to support that strategy I can divide this p-value by two point zero eight three divided by two equals point zero four one five so now the mix design I know of a p-value that I was stuck on which is exactly the same that I've just obtained now in the planned contrast analysis can be overcome and suggested to be statistically significant because the contrast T value is associated with a p-value that I can divide into which produce point zero four one five and because that's less than point zero five I can reject the null hypothesis and suggest that my treatment work now in a lot of cases you will be stuck with a mixed design on over two by two and not get a significant result and if you're less than point one zero zero you have the opportunity to do a contrast analysis and get a significant result now of course this assumes that you have in fact planned this comparison that there is empirical research and or theory to support your one tailed test so that is how you can do a mixed design and OVA in a contrast analysis context which will afford you more power if you evaluate the p-value from a one-tailed perspective

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Id: 1NEmDyXNwLA

Length: 11min 51sec (711 seconds)

Published: Sun Jun 16 2019