Homework Assignment

Factorial Analysis of Variance: Week 6 Factorial Analysis of Variance: Week 6 Program Transcript MATTHEW JONES: This week, we're going to be exploring factorial ANOVA.

Factorial ANOVA is an extension of one-way ANOVA. We're still doing a comparison of means test. But rather than having one factor, we now have\ two or more factors. And the designs can get quite comple x.

But for this week's example, we're just going to look at the differences\ in fear of asking for help between gender, which is a binary variable, and responde\ nt's type of undergraduate degree, which is also a binary variable.

To perform a factorial ANOVA, we click on Analyze, General Linear Model,\ because it's part of the general linear model family, Univariate. And ou\ r dependent variable is going to be the variable that we're interested in \ comparing a mean on, so that is fear of asking for help at time 1. And our fixed factors are gender, binary coded as male and female, and also type of undergraduate \ degree, which is coded as natural science and social science.

So under Options, we want to go ahead and move gender over to display me\ ans for-- again, remember, we're doing a comparison of means test here-- degree.

And you'll see this new term in here, this gender multiplied by degree. \ So in a factorial ANOVA, not only can we look at these main effects of, OK, is o\ ur difference in fear of asking for help between gender and degree-- is there some interaction between the two? So just like we did in moderation analysis,\ we want to make sure and move that over as well.

So we want to click on Compare Main Effects, and this downmenu will high\ light.

And I'm going to go ahead and click on Bonferroni as a comparison of mai\ n effects. And we also want to click on estimates of effect size and homog\ eneity tests. Click Continue. I'm also going to click on Plots. Because if ther\ e is an interaction, a picture is really worth a thousand words here.

So on the horizontal axis, I'm going to enter Gender. And degree I'm goi\ ng to go ahead and put under separate lines. Be sure and click that Add. Otherwis\ e, if you click Continue, nothing will really happen. So click Add. And once you click Add, you can see there it's added. So continue.

And one thing-- I want to talk about this briefly, and we'll come back to it. But under this model, when SPSS is performing this calculation, it's default\ ing to this - - you see here type 3 sum of squares. You see there are a number of differ\ ent sum of squares calculations.

And a type 3 sum of squares assumes that our design is orthogonal. That \ has to do with balance and equal cell size. So we'll come back and revisit that\ issue in just a moment. But for now, let's just assume that we have an orthogonal design.

1 Factorial Analysis of Variance: Week 6 Click Continue. And we'll click OK. Here we should get our results. So w\ e see our test of between subjects here. And this is probably familiar to you, loo\ king at a one-way ANOVA table. It's just slightly expanded. And we see, looking at ou\ r statistical significance, that gender is statistically significant. So t\ here's some difference there, some statistically significant difference in fear of a\ sking for help.

Degree also statistically significant. So something is going on there, and there is some difference somewhere. And then our interaction, gender by degree-- and this was sort of a tough one, because we see a significance level of 0.0\ 55. So this is a question that comes up a lot if you get one of those borderlin\ e results, statistically significant results.

So you have a couple of options, really. You can go ahead and interpret \ this interaction, say, OK, this is close to 0.05. It's just too close. I want\ to go ahead and interpret it if 0.05 is your threshold. Or you could say, well 0.050\ is my threshold. And although it's just slightly above it, nonetheless, it is \ above it, so I'm not going to interpret.

So for the purposes of our demonstration here, since it is so close, let\ 's go ahead and i nterpret this interaction. Moving down, we have some of our basic descriptive statistics here. You'll see for gender, females on average a\ re more fearful of asking for help at time 1 than males. And we have a pairwise \ comparison here between those, and it is statistically significant.

And then moving down to undergraduate degree, we see that those in the n\ atural sciences are more fearful of asking for help than those in the social sc\ iences.

Again, it's performing this pairwise comparison with our mean difference. And it's statistically significant, as we saw in the overall omnibus model above,\ the tested between subjects.

And now we're looking down here at the interaction here. So we see that \ males who have a natural science degree are more fearful of asking for help than males with a social science degree. And females with a natural science degree \ are more fearful of asking for help than females with a social science degre\ e. Those with a natural science degree seem to be more fearful.

So looking at our plots, indeed we can see this. So you can see these sl\ opes are quite different. So males with a social science degree have the least am\ ount of fear, and females with a natural science degree have the highest level o\ f fear.

So males with the natural science degree are less fearful than females, and males with a social science degree are less fearful than females with a \ social science degree. But again, overall, those with a natural science degree \ are more fearful than those with a social science degree.

2 Factorial Analysis of Variance: Week 6 So I talked a little bit earlier about orthogonal and balance and design\ . So there's one way we can quickly test for that. So we can go back to our good old \ friend, the cross tab, and see if there's any difference or any relationship bet\ ween degree and gender. So if we go back to Analyze, and I'll explain why we're doing that.

So I'll entered gender into the row. I'm going to enter degree, listed a\ s undergraduate degree, into the column. And I'm going to go to Cells and \ enter percentages within the column. I'll click Continue, and I'm also going t\ o click on Statistics Chi-Square. So you've done this before in a previous course. \ I'm just looking at my descriptive statistics. 34% of males-- just looking at my descriptive statistics, 34% of those with a natural science undergrad degree are males, and 66% are females. And 32% of males-- and 32% of those with a social science degree are males, and 67% of those with a social science degree \ are females.

So we have approximately the same year-- 34 and 66 and 32 and 66. So there's obviously some unequal cell size there. But the question comes up of whe\ ther there's balance.

So if there was a statistically significant relationship between these t\ wo, then perhaps there might not be some balance. So looking here at the chi-square, I can see I have a really low chi-square value. And this is definitely not\ statistically significant. In a perfect world, it would be completely balanced and equ\ al cell size.

But of course, that doesn't always happen. So this is a good, important \ step here.

So I'm going to go ahead and assume that it's orthogonal and use the typ\ e 3 sum of squares, which was the default.

Factorial Analysis of Variance: Week 6 Additional Conte nt Attribution FOOTAGE:

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