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Measures of variability are used to describe the degree of dispersion of observations around a central tendency index.

In other words, measures of variability allow us to assess how data are spread around a central value, which may be represented, for example, by the mean or the median. They provide valuable information about the distribution of data, enabling a better understanding of the phenomenon under observation.

The techniques for measuring the variability of datasets are numerous. Among them, the most widely known (and most commonly used) are:

• the range
• the mean deviation and the variance
• the standard deviation
• the coefficient of variation

We will also visualise the concepts of central tendency and dispersion by revisiting skewness and introducing the concept of kurtosis.

Continue reading “Standard Deviation and CV: when the mean alone deceives you (SEO case studies)”

A random variable (also called a stochastic variable) is a variable that can take on different values depending on some random phenomenon. In many statistics textbooks it is simply abbreviated as r.v. It is a numerical value.

When probability values are assigned to all the possible numerical values of a random variable x, the result is a probability distribution.

In even simpler terms: a random variable is a variable whose values are each associated with a probability of being observed. The set of all possible values of a random variable and their associated probabilities is called a probability distribution. The sum of all probabilities is 1.

Continue reading “Probability Distributions: Discrete Distributions and the Binomial”

We are running an A/B test on two title tags for a product page. Variant A gets 127 clicks out of 4,000 impressions (CTR 3.17%), variant B gets 152 clicks out of 4,000 impressions (CTR 3.80%). A difference of 25 clicks. Is this a real lift, or just random noise?

Questions like this — is this difference due to chance? — arise constantly in any data-driven activity. Hypothesis testing is the statistical procedure that allows us to answer with a methodical approach, distinguishing results that reflect a real phenomenon from those that are merely sampling noise.

In the article on hypothesis testing we saw how to check whether a sample mean is compatible with a hypothesis about the population. In the examples we proposed, however, we knew the population standard deviation, sigma — which allowed us to use the normal distribution and the Z-score.

In practice this is a rather rare case. If we do not know the population sigma, or if we are working with small samples, we need a different distribution: the t distribution, or Student’s distribution.

In the article on hypothesis testing we saw how to check whether a sample mean is compatible with a hypothesis about the population. But in practice the most common case is comparing two groups.

Does a new drug lower blood pressure more than a placebo? Does a training course improve test scores? Does a new landing page produce a higher CTR? In each case we have two groups (treatment vs control, before vs after, variant A vs B) and we want to know whether their means differ. The right tool is the two-sample t-test.