Comparing Outcomes Across Predictor Groups

Why Compare Outcomes Across Predictor Groups?

A predictive analytics data set often contains an outcome of interest and a categorical predictor that divides observations into groups. For example, an insurer might want to describe claim amounts by payment channel, or a service team might compare resolution times across contact methods. A grouped summary makes the observed differences visible in a compact, interpretable form.

The purpose here is descriptive: summarize the observed outcome within each category, then state how the summaries differ. A difference between groups does not, by itself, show that the predictor caused the outcome to change. People or records in different categories may also differ in other ways, and the groups may not have been formed by random assignment.

The predictor defines the groups; the outcome is what is summarized within each group. State both explicitly before interpreting a result. If the predictor is “payment channel” and the outcome is “days to resolve,” a mean resolution time by channel answers a different descriptive question from the proportion of records marked “resolved” by channel.

Choose a Summary That Matches the Outcome

For a numeric outcome \(Y\), let \(G\) denote a categorical predictor. Within category \(g\), the group mean is the sum of the observed outcome values in that category divided by the number of observations in that category. The group median is the middle observed value after the category’s values have been ordered, or the average of the two middle values when there is an even number of observations.

Here, \(n_g\) is the number of observed records in category \(g\). The mean is sensitive to extreme values; the median is less sensitive to them. Reporting both can be useful when an unusual value makes the mean alone an incomplete description. The choice should serve the question and the shape of the observed data, rather than simply defaulting to one statistic.

If the outcome is categorical, summarize its distribution separately within each predictor group. For a binary outcome, such as “complete” versus “incomplete,” the within-group proportion marked “complete” is the number marked complete divided by the total number in that predictor category. The denominator is the group total, not the overall total.

A difference in group means or proportions is a descriptive contrast. For numeric outcomes, one useful convention is to define the contrast as the second named group’s summary minus the first named group’s summary. The direction then has a clear meaning: a positive value means the second group has the larger summary. For proportions, report the difference in percentage points when expressing the difference on a percentage scale.

Build and Read a Grouped Summary in R

With a data frame named records, a categorical predictor named channel, and a numeric outcome named days, dplyr can produce a summary for each channel. The command groups by the predictor, calculates statistics within each group, and then removes the grouping from the output.

R: records |> dplyr::group_by(channel) |> dplyr::summarise(n = dplyr::n(), mean_days = mean(days), median_days = median(days), .groups = "drop")

For a binary outcome stored as values such as “Complete” and “Incomplete,” first define exactly which outcome category is being counted. One direct approach is to summarize the number of records in each predictor-outcome combination and calculate the within-predictor proportion. The denominator for each proportion must be the total count across outcome categories for that predictor group. A percentage of all records in the data set answers a different question.

A grouped summary is only as meaningful as its inputs. The predictor categories should represent the intended groups, and the outcome should be recorded in a consistent unit and definition across categories. For example, comparing resolution times recorded in hours in one group with times recorded in days in another would not be a fair numerical comparison without first resolving the unit inconsistency.

Worked Comparisons for Different Outcomes

Why the Overall Mean Is a Weighted Average

A useful check on grouped means is that the overall mean can be recovered by weighting each group mean by that group’s share of the observations. This identity follows directly from how the means are calculated; it does not require a probability model.

To justify the identity, within group \(g\), the sum of the observed outcomes equals \(n_g\bar{y}_g\), by the definition of the group mean. Adding those sums across all groups gives the total of all observed outcomes. Dividing by the total number of observations, \(\sum_g n_g\), gives the overall mean:

For the first worked example, each group has four observations, so the overall mean is \((4\times11+4\times15)/(4+4)=104/8=13\) days. Simply averaging the two group means also gives 13 here because the group sizes are equal. If group sizes differ, an unweighted average of group means generally will not equal the overall mean.

Describe Differences Without Overstating Them

A careful comparison names the groups, the outcome, the statistic, the direction, and the units. For example: “In these records, the mean resolution time was 15 days for assisted service and 11 days for self-service, a difference of 4 days.” This is more informative than “assisted is worse,” which introduces a value judgment and can imply a causal conclusion not supported by a descriptive summary.

The predictor category may be associated with other characteristics of the records or people being compared. The observed group summaries alone do not separate those characteristics from the predictor. Therefore, describe what was observed and avoid language such as “caused,” “led to,” or “reduced” unless the study design and analysis justify a causal interpretation. A grouped summary is an exploratory description, not a substitute for an appropriate causal analysis.

When you report a proportion, make the denominator and outcome category clear. “60% were complete within the web-form group” identifies the group-specific percentage; “18 were complete” gives a count; “18 out of 50 were complete” uses the overall denominator. Those statements are not interchangeable.