What are dt qt pt rt in R for Marketing Analytics

In marketing analytics, we rarely get perfect data.

Most of the time, we work with small samples, short campaign windows, and noisy customer behaviour.

How I used Student t distribution to evaluate campaign performance with limited data

In marketing analytics, we rarely get perfect data.

Most of the time, we work with small samples, short campaign windows, and noisy customer behaviour.

Early in my consulting work with a consumer internet business, I realised that normal distribution assumptions break down when sample sizes are small.

Why Student t distribution matters in marketing analytics

In many marketing problems, we try to estimate an average metric.

Conversion rate, daily revenue per user, average order value, email click rate.

The challenge is that campaigns often run for a short duration. Sample sizes remain small and population variance stays unknown.

In such situations, assuming a normal distribution leads to overconfidence.

Student t distribution corrects this by accounting for additional uncertainty.

From a business point of view, this prevents false confidence and bad rollout decisions.

The wider curve you see here is exactly what protects decision makers from aggressive conclusions based on limited data.

Marketing analytics scenario I worked on

The client was an online subscription based education platform.

They launched a new paid ad creative and wanted to know whether it genuinely improved daily conversion rate or whether the improvement was random.

The campaign ran for 10 days. Each day we tracked conversion rate from paid traffic.

This is realistic marketing data. Small sample, daily fluctuations, and pressure to decide quickly.

Hypothetical dataset similar to what I received

The question was simple.

Is the average conversion rate truly higher than the historical benchmark of 2.8 percent.

Using dt in R to understand distribution shape of campaign performance

Before calculating probabilities, I like to understand how uncertain my estimate really is. This is where dt helps conceptually.

The dt function gives the height of the Student t probability density at a given value.

In simple words, it tells us how likely a particular t value is, given our sample size.

In this campaign, we had 10 observations. Degrees of freedom become 9.

dt(0, df = 9)

I do not use dt to answer business questions directly.

I use it to explain uncertainty to stakeholders.

When I plot the density using observed t values derived from real data points, the message becomes clear.

With small samples, the distribution stays wide.

That means we should expect volatility and avoid aggressive conclusions.

This explanation alone helped the marketing head accept a cautious rollout plan.

Using pt in R to calculate probability of campaign uplift

pt is the function I use most in client work.

Conceptually, pt returns the probability that a random value from a Student t distribution is less than a given value.

In marketing terms, it helps answer probability style questions.

First, I compute the sample mean and standard deviation.

conv <- c(0.028,0.031,0.030,0.027,0.032,0.029,0.033,0.030,0.031,0.029)
xbar <- mean(conv)
s <- sd(conv)
n <- length(conv)

Then I calculate the t statistic comparing it with the historical benchmark.

benchmark <- 0.028
t_stat <- (xbar - benchmark) / (s / sqrt(n))

Now comes pt.

pt(t_stat, df = n - 1)

This value gives me the probability that the campaign performs better than the benchmark, considering uncertainty.

When I explain this to marketing teams, I say this.

This number tells us how confident we should feel that the improvement is real and not just random noise.

Using qt in R to build confidence intervals marketers understand

Decision makers rarely like yes or no answers. They prefer ranges.

qt helps find the cutoff points of the Student t distribution. These cutoffs allow us to build confidence intervals.

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