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Introductory Stats Definitions I Should Know

I have a PhD in statistics, yet it is over 15 years ago since I took my first introductory statistics course. So sometimes, I find myself being rusty on some of the fundamental concepts of statistics. It didn’t help that I didn’t have to teach during my doctoral studies so I didn’t have to prepare the course materials, which I think was a missed opportunity to revise the concepts I had learned a long time ago.

Since I am currently revising introductory statistics using OpenIntro Statistics, I have decided to create a note of some of the fundamental concepts and definitions (I’d like to come back to reference) as I encounter them in the book. So here they are:

Definitions

  • Statistics: Statistics is the study of how best to collect, analyze and draw conclusions from data.

  • Summary Statistic:A summary statistic is a single number summarizing a large amount of data.

  • Numerical Variable: are variables that can take on a wide range of numerical values (numbers) and it is sensible to add, subtract, take averages with those values. Numerical variables can be discrete or continuou

    • Continuous Numerical Variable: are numerical variables that can take on any value within a given range, meaning there are infinitely possible values they can take on.
    • Discrete Numerical Variable: are numerical variables that can take on only specific, separate values (often integers), meaning the values “jump” and there are no meaningful intermediate values between two possible outcomes.

  • Categorical Variable: are variables whose values fall into groups or categories rather than along a numeric scale. The possible categories of the variable are called ‘levels’.

    • Ordinal Categorical Variable: the levels of the categorical variable have a meaningful natural order to them, but the spacing between levels isn’t necessarily equal.
    • Nominal Categorical Varible: the levels of the variable have no natural order to them.

  • Associated Variables: Two variables are said to be assoicated or correlated if they vary together in a pattern, either in the same direction (positive correlation/association) or in opposite directions (negative correlation/association). Associated variables are said to be dependent variables.

  • Independent Variables: Two variables are independent if they’re not associated/ccorrelated. This means that information about one variable, doesn’t provide any information about the other variable.

  • Observational Study: A study in which data is collected in a way that does not interfere with how the data arise. Can only be useful to prove association, but not causation.

    • Retrospective study: data is collected after events have taken place.
    • A Prospective study: data is collected as events unfold.

  • Experimental Study A study in which the researcher acively intervenes in the way data is generated, usually by assigning treatments/exposures to participants. When the assignment is randomized, the study is called a randomized experiment,

  • Population: The entire group of observational units that a study deals with.

  • Sample: A representative subset of the population.

  • Anecdotal evidence: is evidenced based on data collected in a haphazard fashion, like individual stories, personal accounts, or isolated examples, rather than systematic data collection.