Computing
Texts
Tuesdays are set up as lectures/discussion, and Thursdays as lab
Office Hours
. This will be tricky this year, because I am temporarily going to be housed across campus until flood damage is replaced. Send me a message if you can't reach me, and we'll set a time.By appointment (I’m usually in) but NOT before class
First Assignment
because of the way they presented their data, I was not able to include sex as a variable in my example.This example is based on Klesges, R. C., et al. (1998) The prospective relationship between smoking and weight in a young, biracial cohort: The coronary artery risk development in young adults study. Journal of Counseling and Clinical Psychology, 66, 987-993.
The study looked at weight changes over a seven year period in subjects who did, and did not, stop smoking. The authors broke down subjects by smoking condition, race, and sex, but
One reason for choosing this example is that it involved very large samples. We usually use small samples for examples, and I thought it would be useful to look at a case with thousands of subjects.
At baseline, data were collected on weight, smoking behavior (Never, Former, and Smoker), and other variables for over 5000 subjects. Seven years later data were obtained from 3868 subjects on their smoking status (Never, Former, Quitter, Intermittent, Initiator, and Continuous), their weight, and their weight gain. Data were also collected on alcohol use and caloric intake..
For this example I am going to run one-way analyses for smoking behavior on the pretest and the posttest data separately. I will ignore race and sex. I'll may come back to those variables later.
The data are found in Klesges.sav for 3868 subjects. The variables are Race, Basesmoke, Endsmoke, Alcohol, Basewt, Endweight, WtChange, and Fatpercn, in a different order. I generated these myself based on their data. Weight is given in kilograms.
First we'll look at differences in weight of the three smoking conditions at the beginning of the study. What would students predict?
The results:
First look at the outliers. With this many observations, it would be very surprising if there weren't a bunch of outliers. These seem reasonable.
It looks as if the smokers weighed slightly less than the other two groups, though it is not clear whether the other two groups differ. The differences are small, (2.5 kilograms at most) but with these sample sizes, there is a lot of power. The analysis of variance follows, along with the Bonferroni test.
Notice that the overall anova is significant, but when we run the multiple comparisons the only significant difference is the 2.58 kilogram difference between Nonsmokers and Smokers. Interestingly, the Ex-smokers fall in the middle and don't differ from either group. So it is not true that quitting smoking led to weight gain--at least over the long term.
I spoke last semester about effect size measures and their importance. I talked about three different approached. One was an r2 type measure, one was d, and the last was a confidence interval.
h2 and w2
There are two measures related to squared correlation, the first (h2) is biased by simple, the second (w2) is much less biased, but slightly more complicated. For the one-way analysis of variance,
and
The answers are virtually the same because of rounding and because there is relatively little error variance relative to the rest of the variance.
This doesn't look like much of an effect, but it is hard to evaluate percentages of variance--What would a large one be?
d
The recently more popular measure of effect size is Cohen's d, which expresses the difference between or among means in terms of standard deviation units. This is a direct extension of the d we encountered when we talked about t tests.
How do we interpret this?
Notice that the numerator in the above equation is essentially the variance of the cell means. (The divisor is k, instead of (k-1), but that is ok--see the discussion of fixed effect designs.) So what we have is the ratio of the variance of group means relative to the within group variance. We take the square root of that, but that doesn't really change anything. It is just the standard deviation of group means relative to the standard deviation within groups.
So we can conclude that the variability (read standard deviation) of means is about 5% of the error variability. That is not a very large amount to be attributed to smoking.
In class I made the observation that when the dependent variable is a meaningful measure, it probably makes sense to report the effect size in raw score units. For example, we all have a pretty good idea what it means to say that there is a 5 pound difference between two groups. Of course, whether 5 pounds if large or small depends on the size of a standard deviation, but we can probably get by with raw units.
However, if the units are not particularly meaningful--e.g. a 5 point difference on the Howell scale of personality--there is little to be gained by using raw score units. Here we would be far better off with scaled units--i.e. scale by the size of a standard deviation. APA would generally go along with this general idea.
Small, medium, and large effects
Cohen (1988) very roughly defined a small effect as one with d (he called it f) = .15, a medium effect as one with d = .25, and a large effect as one with d = .40. What we have here is a very small effect, even though it is significant. Smoking does not seem to affect weight in any important way.
In Contrast:
Spilich et al (1992) Compared smokers, nonsmokers, and "delayed smokers" on a cognitive task. The dv was the number of errors, so 'small is good.' The results are shown below:
Variable
ERRORS
By Variable SMOKEGRP
Analysis of Variance
Sum of
Mean
F
F
Source D.F.
Squares
Squares
Ratio Prob.
Between
Groups 2
2643.3778 1321.6889
4.7444 .0139
Within
Groups 42 11700.4000 278.5810
Total
44 14343.7778
Standard Standard
Group
Count Mean
Deviation
Error 95 Pct
Conf Int for Mean
Grp 1
15 28.8667
14.6866 3.7921
20.7335 TO
36.9998
Grp 2
15 39.9333
20.1334 5.1984 28.7838
TO 51.0828
Grp 3
15 47.5333
14.6525 3.7833
39.4191 TO
55.6476
Total
45 38.7778
18.0553 2.6915 33.3534
TO 44.2022
Here we see that smoking has a very important effect on cognitive behavior.
I could go off and calculate various measures of effect, but they would all be low, and I won't take the time here.
These data have something different to tell us. First of all, noticed that everyone gained weight over the course of the study. It is relevant that they had a mean age of 24.8 years at baseline, so we aren't talking about a bunch of middle-aged folks who just moved into senility. But the other thing that the original study tells us is that the mean caloric intake of these people at baseline was 2962.3 calories (and black males had a mean intake of over 4000 calories). It is not a big surprise that they gained weight. Interestingly, the mean "calories from fat" was 37% with a standard deviation of 6%, and that did not vary by race or gender by more than 1 percentage point. (I have added fatpercn to the data file.)
In terms of weight gain, the people who quite smoking gained more than any other group. The only other difference that came close to being significant was the difference between those who smoked continuously and those who never smoked (p = .061).
With 6 groups it would be a real pain in the neck to calculate the relevant statistics for power. Instead, I used G*Power. It took a lot of trial and error to get all the answers in the right places, but when I was finally done I had
Notice that the power is virtually 1.00, which again comes from the fact that we have huge sample sizes.
On Thursday
I will take a little time to answer questions on the material above (especially since I don't think that I can cover it all in class), and then we will use different data to look at alternative multiple comparison techniques. We are using different data there because I want an example where there are several differences among the treatments. We will meet in Waterman.Last revised: 01/15/02
