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Are Active Sentences More Lexically Dense?

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Say what you will about using the passive voice, we pose the question of whether or not there is any connection between its use and lexical density.
We googled "examples of active and passive voice" and found many examples of pairs of sentences written in both active and passive voice and compared their average lexical density to see if we could detect any significant differences. Our sentences contained examples of past, present, and future of the simple, continuous and perfect tenses. We then ran the analysis...

A Thought Experiment

Before we look at the results of our analysis, let's perform a small thought experiment. Will the lexical density differ between active and passive versions of an ideal model sentence? Let's find out.
A typical active super simple sentence has a Subject + Verb + Object form. (We are assuming the verb takes an object. Otherwise, how would we form the passive?) We consider the following as a model sentence:
The dog chased the cat.
This sentence has a lexical density of (3 lexical words)/(5 total words), or 60% which is about the same as an informative article.
Writing our super simple sentence in passive form we have:
The cat was chased by the dog.
This sentence has a lexical density of (3 lexical words)/(7 total words), or 42.86%. The extra grammatical, non-lexical baggage has lowered the lexical density of our ideal super simple sentence to a mere 42.86%, a lexical density typical of the spoken word.
Thus, in theory, we can expect a general decrease in lexical density on the order of about 17 percentage points.
Let's now look at the results of the analysis of the active passive sentence pairs we found online.

The Results

The active sentences had an average lexical density of 58.17%, whereas, the passive sentences had an average lexical density of of 47.62%.
So in practice, by converting an active sentence to passive, we can expect an approximate reduction in lexical density of about 10.55%.

Concluding Remarks

It is clear that the passive voice introduces more function words with a consequent drop in lexical density. We are fairly convinced that in most, if not all, cases the active voice is more lexically dense. But we impress upon the reader that the degree to which lexical density is reduced by converting an active sentence to passive depends on how dense the active sentence is to begin with. Suppose we make our super simple model sentence more descriptive:
The naughty, mean dog gleefully chased the poor, defenseless cat.
This sentence clocks in at (8 lexical words)/(10 total words) for a whopping 80% lexical density. Rewriting this sentence in passive voice we get
The poor, defenseless cat was gleefully chased by the naughty, mean dog.
for a lexical density of (8 lexical words)/(12 total words) or, 66.67%. Despite a reduction of about 13 percentage points, this passive sentence still retains a high lexical density.
This is perhaps one explanation for why expository writing, such as newspaper and Wikipedia articles, can still be quite lexically dense despite frequent use of passive constructions.
If we are to follow the advice of David Didau, when our prose is wonky or bloated and we want to start trimming the fat by shedding "extraneous grammatical garbage," our passively constructed sentences may be a good place to start looking. If the reader would like some help tagging the lexical words in their text as in our model sentences above, they use our lexical density calculator on our homepage.
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Links and References

Didau, David, Black space: improving writing by increasing lexical density, from The Learning Spy: Brain Food for the Thinking Teacher
Article on this Website: Lexical Density.
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