Do smartphones harm teenagers? If so, how much? In this blog, I've written before about the quasi-experimental and correlational designs used in research on screen time and well-being in teenagers. In that post you can practice identifying the different designs we can use to study this question.

Today's topic is more about the size of the effect in studies that have been published. A recent *Wired* story tried to put the effect size in perspective.

One side of the argument, as presented by Robbie Gonzalez in *Wired, *scares us into seeing social media as dangerous.

For example, first

...there were the books. Well-publicized. Scary-sounding. Several, really, but two in particular. The first, *Irresistible: The Rise of Addictive Technology and the Business of Keeping Us Hooked*, by NYU psychologist Adam Alter, was released March 2, 2017. The second, *iGen: Why Today's Super-Connected Kids are Growing Up Less Rebellious, More Tolerant, Less Happy – and Completely Unprepared for Adulthood – and What That Means for the Rest of Us*, by San Diego State University psychologist Jean Twenge, hit stores five months later.

In addition,

...Former employees and executives from companies like Facebook worried openly to the media about the monsters they helped create.

But is worry over phone use warranted? Here's what Gonzalez wrote after talking to more researchers:

When Twenge and her colleagues analyzed data from two nationally representative surveys of hundreds of thousands of kids, they calculated that social media exposure could explain 0.36 percent of the covariance for depressive symptoms in girls.

But those results didn’t hold for the boys in the dataset. What's more, that 0.36 percent means that 99.64 percent of the group’s depressive symptoms had nothing to do with social media use. Przybylski puts it another way: "I have the data set they used open in front of me, and I submit to you that, based on that same data set, eating potatoes has the exact same negative effect on depression. That the negative impact of listening to music is 13 times larger than the effect of social media."

In datasets as large as these, it's easy for weak correlational signals to emerge from the noise. And a correlation tells us nothing about whether new-media screen time actually *causes* sadness or depression.

There are several things to notice in the extended quote above. First let's unpack what it means to, "explain 0.36% of the covariance". Sometimes researchers will square the correlation coefficient *r* to create the value R^{2}. The R^{2 } tells you the percentage of variance explained in one variable by the other (incidentally, they usually say "percent of the variance" instead of "percent of covariance."). In this case, it tells you how much of the variance in depressive symptoms is explained by social media time (and by elimination, it tells you what percentage is attributable to something else). We can take the square root of 0.0036 (that's the percentage version of 0.36%) to get the original *r* between depressive symptoms and social media use. It's *r* = .06.

**Questions**

a) Based on the guidelines you learned in Chapter 8, is an *r* of .06 small, medium, or large?

b) Przybylski claims that the effect of social media use on depression is the same size as eating potatoes. On what data might he be basing this claim? Illustrate your answer with two well-labelled scatterplots, one for social media and the other for potatoes. Now add a third scatterplot, showing listening to music.

c) When Przybylski states that the correlation held for the girls, but not the boys, what kind of model is that? (Here are your choices: moderation, mediation, or a third variable problem?)

d) Finally, Przybylski notes that in large data sets, it's easy for weak correlation signals to appear from the noise. What statistical concepts are being applied here?

e) Chapter 8 presents another example of a large data set that found a weak (but statistically significant) correlation. What is it?

f) The discussion above between Gonzalez and Przybylski concerns which of the four big validities?

g) Finally, Przybylski mentions that "a correlation tells us nothing about whether new-media screen time actually *causes* sadness or depression". Why not?

**Suggested answers:**

a) An r of .06 is probably going to be characterized as "small" or "very small" or even "trivial." That's what the "potatoes" point is trying to illustrate, in a more concrete way.

b) One scatterplot should be labeled with "potato eating" on the x axis and "depression symptoms" on the y axis. The second scatterplot should be labeled with "social media use" on the x axis and "depression symptoms" on the y axis. These first two plots should show a positive slope of points with the points very spread out--to indicate the weakness of the association. The spread of the first two scatterplots should be almost the same, to represent the claim the two relationships are equal in magnitude. The third scatterplot should be labeled with "listening to music" on the x axis and "depression symptoms" on the y axis, and this plot should show a much stronger, positive correlation (a tighter cloud of points).

c) It is a moderator. Gender moderates (changes) the relationship between screen use and depression.

d) Very large data sets have a lot of statistical power. Therefore, large data sets can show statistical significance for even very, very, small correlations--even correlations that are not of much practical interest. A researcher might report a "statistically significant' correlation, but it's essential to also ask about the effect size and its practical value (the potatoes argument). Note: you can see the *r* = .06 value in the original empirical article here, on p. 9.

e) The example in Chapter 8 is the one about meeting one's spouse online and having a happier marriage--that was a statistically significant relationship, but *r* was only .03. That didn't stop the media from hyping it up, however.

f) Statistical validity

g) The research on smartphones and depressive symptoms is correlational, making causal claims (and causal language) inappropriate. That means that we can't be sure if social media is leading to the (slight) increase in depressive symptoms, or if people who have more depressive symptoms end up using more social media, or if there's some third variable responsible for both social media use and depressive symptoms. As the *Wired* article states,

...research on the link between technology and wellbeing, attention, and addiction finds itself in need of similar initiatives. They need randomized controlled trials, to establish stronger correlations between the architecture of our interfaces and their impacts; and funding for long-term, rigorously performed research.

Finally, the *Wired* article quotes (the seemingly skeptical) Pyrbylski as saying,

"Don't get me wrong, I'm concerned about the effects of technology. That's why I spend so much of my time trying to do the science well," Przybylski says.

Good science* is* the best way to answer our questions.