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Assumption of normality

Definition

The assumption of normality in a t-test states that the population being sampled should follow a normal distribution. This assumption allows for accurate inference about parameters such as means and variances based on sample data.

Analogy

Imagine you have collected data on how much time high school students spend studying per day. If this data follows a bell-shaped curve resembling a normal distribution, it satisfies the assumption of normality needed for certain statistical tests, just like when your favorite music streaming service suggests songs based on what others with similar tastes listen to.

Related terms

Central Limit Theorem (CLT): This theorem states that, regardless of the shape of the population distribution, if we take a sufficiently large random sample from it and calculate the means of those samples, those sample means will be approximately normally distributed.

Skewness: This term refers to the asymmetry or lack of symmetry in a probability distribution. A normal distribution has zero skewness.

Kurtosis: This term measures the "tailedness" or peakedness/flatness of a probability distribution. A normal distribution has a kurtosis value of 3 (mesokurtic).