S is for Scatterplot

Visualizing your data is incredibly important. I talked previously about the importance of creating histograms of your interval/ratio variables to check the shape of your distribution. Today, I'm going to talk about another way to visualize data: the scatterplot.

Let's say you have two interval/ratio variables that you think are related to each other in some way. You might think they're simply correlated, or you might think that one causes the other one. You would first want to look at the relationship between the two variables. Why? Correlation assumes a linear relationship between variables, meaning a consistent positive (as one increases so does the other) or negative (as one increases the other decreases) relationship across all values. We wouldn't want it to be positive at first, and then flatten out before turning negative. (I mean, we might, if that's the kind of relationship we expect, but we would need to analyze our data with a different statistic - one that doesn't assume a linear relationship.)

So we create a scatterplot, which maps out each participants' pair of scores on the two variables we're interested in. In fact, you've probably done this before in math class, on a smaller scale.

As I discussed in yesterday's bonus post, I had 257 people respond to a rather long survey about how they use Facebook, and how use impacts health outcomes. My participants completed a variety of measures, including measures of rumination, savoring, life satisfaction, Big Five personality traits, physical health complaints, and depression. There are many potential relationships that could exist between and among these concepts. For instance, people who ruminate more (fixate on negative events and feelings) also tend to be more depressed. In fact, here's a scatterplot created with those two variables from my study data:

And sure enough, these two variables are positively correlated with each other: r = 0.568. (Remember that r ranges from -1 to +1, and that 1 would indicate a perfect relationship. So we have a strong relationship here, but there are still other variables that explain part of the variance in rumination and/or depression.)

Savoring, on the other hand, is in some ways the opposite of rumination; it involves fixating on positive events and feelings. So we would expect these two to be negatively correlated with each other. And they are:

The correlation between these two variables is -0.351, so not as a strong as the relationship between rumination and depression and in the opposite direction.

Unfortunately, I couldn't find any variables in my study that had a nonlinear relationship to show (i.e., has curves). But I could find two variables that were not correlated with each other: the Extraversion scale from Big Five and physical health complaints. Unsurprisingly, being an extravert (or introvert) has nothing to do with health problems (r = -0.087; pretty close to 0):

But if you really want to see what a nonlinear relationship might look like, check out this post on the Dunning-Kruger effect; look at the relationship between actual performance and perceived ability.

As I said yesterday, r also comes with a p-value to tell whether the relationship is larger than we would expect by chance. We would usually report the exact p-value, but for some these, the p-value is so small (really small probability of occurring by chance), the program doesn't display the whole thing. In those cases, we would choose a really small value (the convention in these cases seems to be 0.001) and say the p was less than that. Here's the r's and p-values for the 3 scatterplots above:

1. Rumination and Depression, r = 0.568, p < 0.001
2. Rumination and Savoring, r = -0.351, p < 0.001
3. Extraversion and Health Complaints, r = -0.087, p = 0.164

Marriage, Anniversaries, and the Striking Down of DOMA

Today is a very special day. Today I celebrate my third anniversary of marriage. Today is also the day that the Supreme Court ruled the Defense of Marriage Act (DOMA) unconstitutional. I feel very privileged to share my anniversary with a day that I hope signals massive change in how we view the construct of marriage.

In the distant past, a wedding was a luxury generally afforded to the wealthy. Common law marriages were established so that the poor could still be considered married, even if they could not afford to go through the ritual of marriage. Even in more recent centuries, when the United States was expanding Westward, many towns did not have a church, and so couples would move in together and start their families, and have the wedding when a circuit rider (a pastor, usually of a Protestant denomination, who rode around preaching to the settlements) came around and could perform the ceremony - sometimes months or years later.

Today, weddings are still an expensive undertaking, but there are many options for people. Small wedding chapels, justice of the peace ceremonies - hell, you can even have Elvis marry you in Vegas, something I half-jokingly referenced multiple times while my fiance and I complained about wedding planning and its costs. A wedding, and marriage, is no longer a luxury of the very wealthy.

Instead, it is the luxury of the straight. It has been used as a new form of division,  this time not between the wealthy and the poor, but between the heterosexual and the homosexual. Say what you will about the religious underpinnings of the concept of marriage - the way we think of marriage today is as a contract between two willing parties. Two people who wish to be bound together in some way, whether that be under God, under the State, or all of the above. Even among people who generally think of marriage in the same way (say, as a contract under God), the definition of marriage will still vary widely. I'm sure my idea of marriage differs very much from others who share my faith and religious practice. It's a very personal concept and decision.

So even in the face of all that variability - as well as all the variability in opinions on gender roles (don't even get me started on that one - this blog post would be way too long) - why do so many people still insist that marriage is only to occur between a man and a woman? And further, why is there this belief that allowing a man to marry another man, or a woman to marry another woman, will somehow change the definition and meaning of a given couple's marriage? Like I said, the definition and meaning is a very personal thing. And nothing anyone else does can alter it.

I'm happy that I was able to marry my husband. And I'm happy that others, who have been denied this privilege in the past, will hopefully soon be able to share this institution.

Thoughtfully yours,
~Sara