Adapted Bar Charts

Histograms and bar charts were introduced in the previous lesson as depicting the distribution of numeric and categorical variables, respectively, with the height (or length) of bars indicating the number of data points that fell within each bar's range of values. These plots can be adapted for use as bivariate plots by, instead of indicating count by height, indicating a mean or other statistic on a second variable.

For example, we could plot a numeric variable against a categorical variable by adapting a bar chart so that its bar heights indicate the mean of the numeric variable. This is the purpose of seaborn's barplot function:

base_color = sb.color_palette()[0]
sb.barplot(data = df, x = 'cat_var', y = 'num_var', color = base_color)

Different hues are automatically assigned to each category level unless a fixed color is set in the "color" parameter, like in countplot and violinplot.

The bar heights indicate the mean value on the numeric variable, with error bars plotted to show the uncertainty in the mean based on variance and sample size. The Delta bar dips below the 0 axis due to the negative mean.

As an alternative, the pointplot function can be used to plot the averages as points rather than bars. This can be useful if having bars in reference to a 0 baseline aren't important or would be confusing.

sb.pointplot(data = df, x = 'cat_var', y = 'num_var', linestyles = "")
plt.ylabel('Avg. value of num_var')

By default, pointplotwill connect values by a line. This is fine if the categorical variable is ordinal in nature, but it can be a good idea to remove the line via linestyles = "" for nominal data.

The above plots can be useful alternatives to the box plot and violin plot if the data is not conducive to either of those plot types. For example, if the numeric variable is binary in nature, taking values only of 0 or 1, then a box plot or violin plot will not be informative, leaving the adapted bar chart as the best choice for displaying the data.

plt.figure(figsize = [12, 5])
base_color = sb.color_palette()[0]

# left plot: violin plot
plt.subplot(1, 3, 1)
sb.violinplot(data = df, x = 'condition', y = 'binary_out', inner = None,
              color = base_color)
plt.xticks(rotation = 10) # include label rotation due to small subplot size

# center plot: box plot
plt.subplot(1, 3, 2)
sb.boxplot(data = df, x = 'condition', y = 'binary_out', color = base_color)
plt.xticks(rotation = 10)

# right plot: adapted bar chart
plt.subplot(1, 3, 3)
sb.barplot(data = df, x = 'condition', y = 'binary_out', color = base_color)
plt.xticks(rotation = 10)

Adapted Histograms

Matplotlib's hist function can also be adapted so that bar heights indicate value other than a count of points through the use of the "weights" parameter. By default, each data point is given a weight of 1, so that the sum of point weights in each bin is equal to the number of points. If we change the weights to be a representative function of each point's value on a second variable, then the sum will end up representing something other than a count.

bin_edges = np.arange(0, df['num_var'].max()+1/3, 1/3)

# count number of points in each bin
bin_idxs = pd.cut(df['num_var'], bin_edges, right = False, include_lowest = True,
                  labels = False).astype(int)
pts_per_bin = df.groupby(bin_idxs).size()

num_var_wts = df['binary_out'] / pts_per_bin[bin_idxs].values

# plot the data using the calculated weights
plt.hist(data = df, x = 'num_var', bins = bin_edges, weights = num_var_wts)
plt.xlabel('num_var')
plt.ylabel('mean(binary_out)')

To get the mean of the y-variable ("binary_out") in each bin, the weight of each point should be equal to the y-variable value, divided by the number of points in its x-bin (num_var_wts). As part of this computation, we make use of pandas' cut function in order to associate each data point to a particular bin (bin_idxs). The labels = False parameter means that each point's bin membership is associated by a numeric index, rather than a string. We use these numeric indices into the pts_per_bin, with the .values at the end necessary in order for the Series' indices to not be confused between the indices of df['binary_out'].

This plot shows that the average outcome of the y-variable "binary_out" generally increases across values of the x-variable "num_var".

More commonly, you'll see plots summarizing one numeric variable against values of a second numeric variable not as adapted histograms, but instead as line plots. These are covered on the next page.