Recognizing commonly used statistical symbols: greek, latin and mathematical

Statistical greek symbols, latin symbols and mathematical symbols

Recognizing commonly used statistical symbols

  • In statistics, you will come across many symbols. Most of the statistical symbols are greek, latin and mathematical symbols and each has a different meaning in statistics.
  • On this page you will find the most commonly used statistical symbols in alphabetical order with their name and meaning for a quick reference.

 

Commonly used greek symbols

SignDescriptionMeaning in statistics
\[\huge{\alpha}\]Alpha

Chance of type I error

\[\huge\beta\]Beta

Chance of type II error

\[\huge\beta_i\]Beta of i

Standardised regression coëfficiënt

\[\huge\epsilon\]Epsilon

Error

\[\huge\eta^2\]Eta squared

Measurement of effect size

\[\huge\mu\]Mu

Mean of scores of population

\[\huge\rho\]Rho

Correlation in population

\[\huge\sigma\]Sigma

Standard deviation

\[\huge\sigma^2\]Sigma squared

Variance of population

\[\huge\sigma_x\] 

Standard error

\[\huge\tau\]Kendall’s Tau

A non-parametric correlation coefficient

\[\huge\varphi\]Phi

Association between two categorical variables

\[\huge \chi^2\]Chi-square

Association between two categorical variables

\[\huge\omega^2\]Omega squared

Measurement of effect size

 

Commonly used latin symbols

SignMeaning in statistics
\[\huge b_i\]Regression coefficient
\[\huge df\]Degrees of freedom
\[\huge e_i\]Error associated with variable i
\[\huge F\]F-statistic
\[\huge H\]Kruskall-Wallis test statistic
\[\huge k\]Number of levels of variables
\[\huge ln\]Natural logarithm
\[\huge MS\]Mean squared error
\[\huge N, n, n_1\]Size of sample of population
\[\huge P\]Probablity
\[\huge r\]Pearson’s correlationcoefficient
\[\huge r_s\]Spearman’s rank correlationcoefficient
\[\huge r_b\]Biserial correlationcoefficient
\[\huge r\]Multiple correlationcoefficient
\[\huge R^2\]Determination coefficient
\[\huge s\]Standard deviation of sample of population
\[\huge s^2\]Variance of sample of population
\[\huge SS\]Sum of squares
\[\huge SSA\]Sum of squares of variable A
\[\huge SS_M\]Model of sum of squares
\[\huge SS_R\]Rest sum of squares
\[\huge SST\]Total sum of squares
\[\huge t\]Test statistic for t-test
\[\huge t\]Test statistic for Wilcoxon’s matched-pairs signed-rank test
\[\huge U\]Test statistic for Mann-Whitney test
\[\huge W_s\]Test statistic for Wilcoxon’s rank-sum test
\[\huge\bar{x}\]Mean of sample scores
\[\huge z\]Point of data expressed in units of standard deviation

 

Commonly used mathematical symbols

SignDescriptionMeaning in statistics
\[\huge\bar{\small[value]}\]Bar notationMean of: [value], or everything directly below the bar sign
\[\huge\hat{\small[value]}\]Hat operator notationEstimator (or predicted value of a sample) of: [value], or everything directly below the hat operator sign
\[\LARGE\prod \small[value]\]Product notationMultiplying of: [value], or everything directly after the product sign
\[\LARGE\sum \small[value]\]Sigma notationSummification of: [value], or everything directly after the sigma sign
\[\huge\sqrt{\small[value]}\]Square root notationSquare root of: [value], or everything directly after the square root sign

More knowledge and assistance for recognizing statistical symbols

See below for

  • What is the difference between Greek and Latin letters in statistics?
  • Video for basic statistical symbols
  • Glossary, video
  • Related topics for encountering and understanding and applying statistics
  • Updates for WorldSupporter Statistics
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How to triumph over the theory of statistics (without understanding everything)?

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  • The first years that you follow statistics, it is often a case of taking knowledge for granted and simply trying to pass the courses. Don't worry if you don't understand everything right away: in later years it will fall into place, and you will see the importance of the theory you had to know before.
  • The book you need to study may be difficult to understand at first. Be patient: later in your studies, the effort you put in now will pay off.
  • Be a Gestalt Scientist! In other words, recognize that the whole of statistics is greater than the sum of its parts. It is very easy to get hung up on nit-picking details and fail to see the forest because of the trees
  • Tip: Precise use of language is important in research. Try to reproduce the theory verbatim (i.e. learn by heart) where possible. With that, you don't have to understand it yet, you show that you've been working on it, you can't go wrong by using the wrong word and you practice for later reporting of research.
  • Tip: Keep study material, handouts, sheets, and other publications from your teacher for future reference.

How to score points with formulas of statistics (without learning them all)?

  • The direct relationship between data and results consists of mathematical formulas. These follow their own logic, are written in their own language, and can therefore be complex to comprehend.
  • If you don't understand the math behind statistics, you don't understand statistics. This does not have to be a problem, because statistics is an applied science from which you can also get excellent results without understanding. None of your teachers will understand all the statistical formulas.
  • Please note: you will probably have to know and understand a number of formulas, so that you can demonstrate that you know the principle of how statistics work. Which formulas you need to know differs from subject to subject and lecturer to lecturer, but in general these are relatively simple formulas that occur frequently, and your lecturer will likely tell you (often several times) that you should know this formula.
  • Tip: if you want to recognize statistical symbols, you can use: Recognizing commonly used statistical symbols
  • Tip: have fun with LaTeX! LaTeX code gives us a simple way to write out mathematical formulas and make them look professional. Play with LaTeX. With that, you can include used formulas in your own papers and you learn to understand how a formula is built up – which greatly benefits your understanding and remembering that formula. See also (in Dutch): How to create formulas like a pro on JoHo WorldSupporter?
  • Tip: Are you interested in a career in sciences or programming? Then take your formulas seriously and go through them again after your course.

How to practice your statistics (with minimal effort)?

How to select your data?

  • Your teacher will regularly use a dataset for lessons during the first years of your studying. It is instructive (and can be a lot of fun) to set up your own research for once with real data that is also used by other researchers.
  • Tip: scientific articles often indicate which datasets have been used for the research. There is a good chance that those datasets are valid. Sometimes there are also studies that determine which datasets are more valid for the topic you want to study than others. Make use of datasets other researchers point out.
  • Tip: Do you want an interesting research result? You can use the same method and question, but use an alternative dataset, and/or alternative variables, and/or alternative location, and/or alternative time span. This allows you to validate or falsify the results of earlier research.
  • Tip: for datasets you can look at Discovering datasets for statistical research

How to operationalize clearly and smartly?

  • For the operationalization, it is usually sufficient to indicate the following three things:
    • What is the concept you want to study?
    • Which variable does that concept represent?
    • Which indicators do you select for those variables?
  • It is smart to argue that a variable is valid, or why you choose that indicator.
  • For example, if you want to know whether someone is currently a father or mother (concept), you can search the variables for how many children the respondent has (variable) and then select on the indicators greater than 0, or is not 0 (indicators). Where possible, use the terms 'concept', 'variable', 'indicator' and 'valid' in your communication. For example, as follows: “The variable [variable name] is a valid measure of the concept [concept name] (if applicable: source). The value [description of the value] is an indicator of [what you want to measure].” (ie.: The variable "Number of children" is a valid measure of the concept of parenthood. A value greater than 0 is an indicator of whether someone is currently a father or mother.)

How to run analyses and draw your conclusions?

  • The choice of your analyses depends, among other things, on what your research goal is, which methods are often used in the existing literature, and practical issues and limitations.
  • The more you learn, the more independently you can choose research methods that suit your research goal. In the beginning, follow the lecturer – at the end of your studies you will have a toolbox with which you can vary in your research yourself.
  • Try to link up as much as possible with research methods that are used in the existing literature, because otherwise you could be comparing apples with oranges. Deviating can sometimes lead to interesting results, but discuss this with your teacher first.
  • For as long as you need, keep a step-by-step plan at hand on how you can best run your analysis and achieve results. For every analysis you run, there is a step-by-step explanation of how to perform it; if you do not find it in your study literature, it can often be found quickly on the internet.
  • Tip: Practice a lot with statistics, so that you can show results quickly. You cannot learn statistics by just reading about it.
  • Tip: The measurement level of the variables you use (ratio, interval, ordinal, nominal) largely determines the research method you can use. Show your audience that you recognize this.
  • Tip: conclusions from statistical analyses will never be certain, but at the most likely. There is usually a standard formulation for each research method with which you can express the conclusions from that analysis and at the same time indicate that it is not certain. Use that standard wording when communicating about results from your analysis.
  • Tip: see explanation for various analyses: Introduction to statistics
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  • Understand statistics with knowledge and explanation about a topic of statistics
  • Practice with questions and answers to test your statistical knowledge and skills
  • Watch statistics practiced in real life with selected videos for extra clarification
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  • Share your knowledge and experience and see other WorldSupporters' contributions about a topic of statistics