The one sample t-test requires the sample data to be numeric and continuous, as it is based on the normal distribution. Continuous data can take on any value within a range (income, height, weight, etc.). The opposite of continuous data is discrete data, which can only take on a few values (Low, Medium, High, etc.). Occasionally, discrete data can be used to approximate a continuous scale, such as with Likert-type scales.

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1. The dependent variable must be continuous (interval/ratio).
2. The observations are independent of one another.
3. The dependent variable should be approximately normally distributed.
4. The dependent variable should not contain any outliers.

Assumptions

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Level of Measurement

Independence of observations is usually not testable, but can be reasonably assumed if the data collection process was random without replacement. In our example, we would want to select laptop computers at random, compared to using any systematic pattern. This ensures minimal risk of collecting a biased sample that would yield inaccurate results.

Independence

Bell-shaped distribution, often referred to as Gaussian. To test the assumption of normality, a variety of methods are available, but the simplest is to inspect the data visually using a histogram or a Q-Q scatterplot. Real-world data are almost never perfectly normal, so this assumption can be considered reasonably met if the shape looks approximately symmetric and bell-shaped. The data in the example figure below is approximately normally distributed.

Normal Distribution

An outlier is an extreme score that falls significantly above or below the rest of the scores within a distribution. While these extreme values can represent genuine cases on the variable being measured—such as a single clinically depressed individual in an otherwise happy sample—they can also result from equipment malfunctions, participant misunderstandings, or researcher errors.

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