V9.9 - Three-Way (2x2x2) Between-Subjects ANOVA in SPSS

in this video I'm going to show you how to do a between-subjects factorial ANOVA with three independent variables and the presence of three independent variables opens up the opportunity for a three-way interaction and that's the furthest I'm going to go in the Foundation's section of the chapter with respect to evaluating interactions in the factorial design three independent variables once you get beyond that it really does start to get quite complicated to try to interpret and communicate the effect to a reader so in this example study the dependent variable is intention to wear a seatbelt and basically the researchers provided scenarios to the participants to read and after they read the scenario they provided the chances that the person would be inclined to wear a seatbelt or not in that circumstance so what they manipulated was whether the person liked wearing a seatbelt or where the person didn't like wearing the seatbelt presumably you'd expect somebody who dislikes wearing a seatbelt to be less inclined to wear a seatbelt then the next scenario they manipulated was the riskiness level associated with where they were driving so in one scenario was a safe driving circumstance and then the other scenario it was a risky driving scenario and the final variable was whether the person was rating for themselves or whether they were rating intention to wear seatbelt for somebody else a third person so with these three independent variables all scored on one to two scale so it's a nominal scale only two levels and a continuously scored dependent variable that yes goes into negative values because the researchers measured it in such a way that scores negative suggests a very low level of inclination to wear a seatbelt and positive values were an inclination to wear a seatbelt so we've got a two by two by two between subjects factorial ANOVA now the principles associated with conducting the analysis are exactly the same as a two by two factorial ANOVA the distinction is how to unpack a three-way interaction if one is observed so all other principles are the same in terms of interpreting main effects in the presence of an interaction you have to conduct simple main effect analyses and hope to see that they're all in the same direction I'm not going to go into those details here I'm just going to assume that you learn that from the other examples in the textbook the key point I'm interested in here is unpacking the three-way interaction so in order to analyze the data going to analyze general in your model univariate intention to where goes in the dependent variable box and you put all three independent variables in the fixed factors box click on options and you'll probably want descriptive statistics estimates of effect size homogeneity tests click continue you'll want to plot the results this is going to be very important when it comes to interpreting the three-way interaction it's important when interpreting a two-way interaction it's even more important for a three-way interaction so I'm going to put like dislike as a horizontal axis safety risky safe risky in the separate lines box and self-other in the cell a separate plots box so basically what's going to happen here is SPSS is going to produce two plots of the means depicting a two-way interaction and I'll show you what that looks like in a minute click Add you can click on include air bars and maybe in the final result you would do that for the purposes of the report but for the purposes of actually interpreting the may the interaction I'm going to leave it out because it's a little too messy click continue and we would probably want estimated marginal means there's gonna be a lot of them here and I'm just gonna throw them all in so click continue I've only got two levels so there's no need to compare main effects if I had three levels in any of the independent variables maybe I would look at that and then click OK so here are the results we can see that the sample sizes were slightly different across the conditions and so the estimated marginal means are going to be a bit different then the total means reported in the descriptive statistics table again if you don't understand what I'm talking about now go back to the two-by-two between-subjects factorial ANOVA the video game example I go into some detail about the difference between the descriptive observed means and the estimated marginal means so here are the descriptive statistics associated with the analysis here's Levine's test of homogeneity of variance and we can see that we have not violated the assumption of equal variances based on and on the mean approach which I recommend you do for most cases it produced a net value of 0.4 3 with 7 and 124 degrees of freedom P of 0.8 8 0 satisfy the assumption which is a good thing because the sample sizes are not equal across all levels so dodged a bullet there here is the table with the key results associated with the main effects and the interaction let me just fix this up a little bit so that everything is all on one row and we can see that we could ignore corrected model and intercept rows just like we did in a two-by-two here we have like dislike main effect and it was statistically significant so without considering the possibility of a significant interaction and having to do simple main effect analyses the like/dislike main effect appears to be statistically significant whether can be interpreted as a separate question but with an F value of 141 very large and a p-value of less than point zero zero one partial a the square root of 0.5 3 4 it looks like like vs. dislike is statistically significant and where would we get those means we have the means right here 2.49 is the like intention to wear seat belt value mean and the disliked intention to wear seat belt mean is 0.41 7 so a higher number suggests a greater likelihood to wear a seat belt that's what you'd expect now that's based on the descriptive statistics and the sample sizes are a little bit unequal 65 and 67 and so you'd want to consult the estimated marginal means because technically that is what the between subjects ANOVA is based on so if we look at it here here's the estimated marginal means 2.5 versus 0.44 is the difference between the means that's producing this man effect over here with an F of 140 1.91 and P less than point zero zero one zero one yes so next we've got safe versus risky not quite significant P equal point zero nine to two point eight eight so you know based on these data it looks like whether the situation is more dangerous or not it doesn't impact people's perception of their intention to wear a seatbelt when rated by the participants and then we have self other and that is statistically significant P less than point zero zero one with a partial a two squared at point two six six have an F value of 45 and there's one and one hundred and twenty four degrees of freedom in fact there's a hot one and one hundred twenty four degrees of freedom for all the main effects now the descriptive statistics let's actually just go to the estimated marginal means self other two point zero five self and other point eight nine so it looks like people are more likely to suggest that they're going to wear their seatbelt if they're rating for themselves versus other people's that's a bit interesting people view that other people are less likely to wear their seatbelt than themselves whether that's really true or not we don't know these are just their perceptions based on them responding to these scenarios then we have the interactions two-way not significant like dislike interacting with safe risky P equal point three one not significant the like dislike self other interaction however is significant and they say frisky versus self other two-way interaction is not significant so I would recommend that you not interpret the two-way interactions until you've solved the issue of interpreting the three-way interaction and I would even suggest that probably the three-way interaction will be enough for you to tell the story you need to say and not have to talk about the two-way interactions so you might talk about the main effects and you might talk about the three-way interaction I don't know if you would go so far as to try to explain the two-way interaction that was significant in the presence of a three-way interaction I'm not saying you can't do it but I don't think it's really recommendable so in this case you got to try to find the best way to present the data to represent how this variable the third variable is moderating is interacting with the actual interaction of two other variables and in these data it turns out that I think the best way to present that is by isolating the interaction between like and self-other across safe and risky so I'm gonna isolate across safe and risky because that's not actually part of this two-way interaction is it but I'm going to separate it because it this three-way interaction is telling me that the nature of the interaction is being moderated by another variable and I think in this case it's best to split it so go into data and split far and then click on compare groups and then add safe risky to the groups based on safe risky click ok and then redo the analysis and make sure that your plots are consistent with what you want to do so in this case you need to make sure that you have liked disliked self-other in the separate lines box and then add it and I've already got that there so you need to have make sure that it looks like that click continue so these are the two variables that are interacting with each other and I'm gonna be looking at that across safe scenario and risky scenario and I don't have to write that in separate plots here because I've told SPSS to separate to split the group in that previous step click continue make sure your display means for estimated marginal means if you wanted to get that that you have to make sure that it's clear and here sometimes there's an error in SPSS it just triples up if you've ran the analysis already the previous three way factorial ANOVA it'll jumble up version 25 it'll jumble up things here and you got to throw it out it'll tell you it's got an error I don't need that for right now I really just need to make sure that I'm gonna run the separate two-way factorial ANOVA across a third variable which is that three-way interaction taking place and make sure I've got a fixed size yes so click continue and here are the results that are going to help me interpret this three-way interaction so first of all when we look at the the two-way interaction and we can see that there is no significant interaction of self dislike and self other when I'm isolating at less risky scenarios but there is a significant effect for the risky scenario so if I wanted to interpret that two-way interaction I would be kind of wrong doing so because the presence of that interaction is dependent upon a third variable that's what a three-way interaction is so it's dependent in this case on the riskiness of the driving scenario so stated alternatively the interaction of like/dislike and self other on intention to wear seatbelt depends on the riskiness of their driving scenario so let's look at the plots we can see here this is the one that wasn't significant it kind of looks like it's heading towards that direction looks like there's a bigger drop when the person's rating another person's intention to wear a seatbelt from like to dislike it drops more than the blue line in by comparison but this is not significant this is still you know I'm not significant interaction P point 133 and this one here though in the risky scenario when people write intention to wear a seatbelt there's a much more substantial drop in comparison to the blue line from like to dislike for self when they're rating their the intention to wear seatbelt for the self versus the other it's a much steeper drop when they're rating another person so basically people think other people are less likely to wear their seatbelt than themselves and that becomes even more pronounced in a risky driving scenario the difference in the differences is more substantial in the risky driving scenario so this is how you can interpret a three-way interaction basically you got to decompose the two-way interaction in such a way that you're isolating across another the third one and then you say look the interaction looks different the magnitude of the interaction is different now the fact that it came out significant in one and non significant in the other is not necessarily relevant to the observation of a three-way interaction this could have been statistically significant and this could be significant even in the presence of a three-way interaction the three-way interaction is just saying that the magnitude of the interaction is unequal across the levels of a third independent variable and that's what we're seeing here the magnitude of the interaction it's the ADA squared is point zero three six versus 0.279 that's the ADA squared interaction effect effect size associated with the two isolated levels so that is how you can go about interpreting a three-way interaction in the context of it between subjects factorial ANOVA

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Length: 14min 19sec (859 seconds)

Published: Mon Feb 25 2019