Part of what makes R such a popular language for data science is the ease with which it can perform more advanced calculations. For example, in a very basic language you’d have to manually multiply numbers within the code for the specified number of times to get that value’s power. But with R you can quite literally do so with a single character. And this ease of use translates into more advanced usage scenarios with numeric powers. You’ll soon discover how to raise values to powers in R and then take that concept to the next level.
An Overview of R’s Relationship to Exponentiation
Raising values to powers is a fairly simple process in any language. Even within those that don’t have built-in functions to do so. You essentially just need to multiply a base number against the exponent (power). So if we started with 2, and wanted to raise it to the power of 3, we’d essentially work through the following.
or if we wanted to raise 2 to the power of 2 it’d look like this.
Of course, the problem is that while massive multiplication is simple, it becomes time-consuming when done in this manner. So we have shorthand in the form of powers. Instead of 2*2, we can just write 2 squared to show that it’s the number 2 multiplied by itself. Or, 2^3 for 2 to the power of 3. An R script can easily perform that type of operation without the need for any special libraries or excessive computing time. And what’s especially remarkable is that the process is easy to extend into R structures like a data frame. The end effect is that R can be used to adapt these calculations into power analysis. For example, by using a pipe to essentially channel data to find the standard deviation, the significance level, or statistical power, within a study’s dataset.
Though note that the terminology can change depending on context. For example, in a T test the term would refer to the probability of significance values effectively rejecting a null hypothesis. Likewise, you might see the term used as a way to measure whether or not there’s a meaningful difference in multiple subjects with a particular sample size and effect size. These calculations use a type, for example type I, set at a particular level. The effect size is then determined as an interplay of the variables where subjects are compared and predictors determined.
The two concepts can overlap, but they should be considered distinct from each other. Think of it as similar to hammering a nail and working on housing construction. Tasks involving the latter will typically involve the former. But they’re not intrinsically linked. There are a lot of tasks involved with building a house that don’t require hammering nails. The same holds true of these two methods of R pow. The respective powers used in the basic multiplication operation and statistical plotting might coincide. But there’s no guarantee of it.
A Deeper Dive Into Raising Values to a Power
With all of that in mind, the simplicity of R’s calculations for powers can be most easily seen by simply diving into a quick example. Take a look at how the R pow syntax can be used to generate two to the third power.
ourPower <- 2^3
In this example, the generation essentially just comes down to expressing the math as you would in standard notation and then assigning the result to a variable. The “^” is used as the exponentiation operator. So as an exponent, 3 is the number of times the base number is multiplied by itself in the R code. Or in other words, 3 is the exposure in this equation. The ourPower variable is then explicitly printed to the screen. This is a very basic example, but we can build on it by using some of R’s other features related to data analysis.
Fleshing Out the Calculation
You’ve seen just how easy R makes these calculations. But part of what makes R so powerful is the ease with which you can mix and match data-related tools together. As an example of this concept, take a look at the following code. Though keep in mind that you’ll also need the dplyr R package installed. It’ll provide a special mutate function to best illustrate the system’s flexability.
ourDataFrame <- data.frame(ourNumber = c(1, 2, 3, 4, 5))
ourDataFrame <- ourDataFrame %>% mutate(postPowerCalculation = ourNumber^2)
In this example, you create and populate a simple data frame called ourDataFrame. Then the code will print it to the screen so that you can get a look at its structure. Next, the data frame is run through a mutate function from dplyr. This changes the structure to hold a new “postPowerCalculation” column and fills it with each of the “ourNumber” values raised to the second power. Next, the code writes the results to the screen. And you’ll see how easily R can iterate through a data frame while generating the powers of every value.
This basic concept can be expanded into any of R’s various structures or methodologies. You could even transition from the result of one loop, use related products as a base, and generate new structures from them. This highlights one of the strongest elements of the R language. All of the mathematical concepts, abstractions, and structures flow into each other. Combined with the mutability seen in the prior example it’s easy to chain generative events into each other. You can pipe the results of an operation’s powers into any other equation or structure.