PRDV420: Introduction to R Programming

After plotting the data, mean and variance are some of the basic summaries that we want to know. R has built-in functions to calculate mean, sd, var, and median. This video demonstrates the calculations and, using the plot, shows how the results relate to the sample data.

Even one variable can tell a story. For example, sample data on personal incomes might show distinct clusters of high- and low-paid workers, and time series of average temperatures may show trends and seasonal cycles. Here you will learn R tools for working with such data by combining your experience with plots and simple statistical summaries.

As you already know, for each base-R operation, there are user-contributed alternatives. This video demonstrates the function describe from the package psych, which outputs more statistics than the standard function summary. (You already know how to install and load the package to your R environment.) Be careful, as user-contributed packages might use the same names for their functions. For example, the package Hmisc also has a function describe that produces a different output.

Functions for individual quantities like mean or median are convenient when we want to use that specific number in further analysis or visualizations, but the function summary and its alternatives are great for exploratory analysis. In the exercise, you can practice both approaches. This exercise does not count toward your grade. It is just for practice!

Finally, the function table can count the number of observations per group. It is most useful when applied to factors, integers, logical values, or strings. It allows you to study group counts, proportions, and identify outliers. This section demonstrates the application of this function and how it can be applied to more than one variable.

The t-test is quite simple, and the base-R functionality will likely be sufficient for all your related calculations. This section introduces the plots and testing functions that help us to conduct the inference based on the t-test and its nonparametric alternative, the Wilcoxon (or Mann-Whitney) test.

Fortunately, the t-test calculations can be modified for the cases when the assumption of equal variances across groups is violated. In other words, Welch's version of the t-test accounts for unequal variances. This video demonstrates the test application in R and the relevant options for implementing it.

The greater the difference between compared quantities and the more observations we have, the more confident we (the t-test) are that the observed differences are not just due to a random chance but are true, statistically significant differences. Even if the means of two populations are different, the t-test might not detect it if the difference or the sample is small. The probability with which the t-test would detect the difference under the given sample size and variability is the power of the test and can be calculated in R. We prefer high power and often use the desired power, confidence level, and expected variability to identify the required sample size.

In this exercise, you will use the t-test and Wilcoxon test to compare the Examination rates across the two groups. This exercise does not count toward your grade. It is just for practice!

This section introduces base-R functionality for the one-way ANOVA. "One-way" means that only one factor variable is used, such as in the case of BloodPressure ~ ExerciseLevel. Be aware that when two or more factors are used the contributed functions like car::Anova are preferred because they have the option to apply different types of the F-test and conduct inference without depending on the order the factors are introduced in the R formula.

This video shows the implementation of ANOVA in the packages car and afex. It probably makes sense to start using one of these packages for ANOVA analysis instead of the base-R functions aov and anova, even if you have only one factor variable to start with. The video also covers a range of post-hoc tests used to find which groups the statistically significant differences occur between. These tests are useful, but the global ANOVA test is not needed for the analyst to start using these tests – just remember to use an adjustment for multiple testing.

In this practice exercise, you will use the built-in dataset iris to test whether the Sepal.Length differs by Species. This exercise does not count toward your grade. It is just for practice!

Models are simplified representations of reality based on available observations. Both the observations and our assumptions about the form of the existing relationships affect the model we get as an outcome of the analysis. Here you will learn the general approach for specifying and estimating a linear model in statistics.

While R makes the model fitting process extremely easy, several steps or implicit decisions go into it. For example, one may choose to keep or remove extreme observations (outliers) and select the optimization algorithm. This exercise demonstrates the effects of these decisions on the modeling outcomes.

One of the best tools to check the quality of a model is to plot things. This section shows how to visualize modeling results and the unmodeled remainder (residuals) to diagnose the model. Remember that residuals should not have any remaining pattern and should look randomly scattered. If there is a remaining pattern, try to include it in your model (that is, respecify the model), then reestimate the model and visualize the new residuals.

You should get used to checking model quality visually. Look for inconsistencies between the data cloud pattern and the fitted lines for patterns in residuals and outlying observations. These exercises give examples and suggest R functions you can use for these tasks. This exercise does not count toward your grade. It is just for practice!

We often keep the intercept in the model even if it is not statistically significant because our main focus is usually on the effect of other variables expressed in their coefficients. However, there are cases when we need to remove the intercept to obtain the so-called "regression through the origin". Also, we might need to model the combined effect of two factors using the interaction term (for example, to model how light and water conditions affect plant growth). These exercises let you practice these cases and suggest you compare alternative models. It does not count toward your grade and is just practice!