# Statistical Symbols and Jargon

As with any area of study, statistics has developed its own vocabulary and sets of symbols that you must know in order to understand what you see in books and journal articles.  Because statistics makes use of so many letters as symbols, some statistical material can seem incredibly complicated at first glance.

Let us say, for example, that your professor has given you four quizzes, and you made the following grades:  100, 90, 80, and 90.  He then asks you to figure out your average.  No problem, right?  All you have to do is add up the scores and divide that by how many quizzes there were (4 in this example).

## Some Jargon and Symbols

Now let us say our hypothetical professor is having a bad day and asks you to compute something called the arithmetic mean.  However, to make it easier, he is going to provide you with a formula:

If you are not familiar with statistical symbols, then that equation can look intimidating, and you still do not know what an arithmetic mean is!  If we break it down into everyday language, it becomes easy, because it is just the average that you already knew how to get.  The arithmetic mean is what most people would refer to as the “average.”

The letter X with the bar on top (pronounced “X bar” or “bar X”) is the symbol for the mean of X.  In statistics, X usually stands in for a group of scores rather than a particular value as it usually does in algebra.  Therefore, “bar X” stands for the mean of a group (a column) of scores labeled X.  The Greek letter sigma is known as the summation symbol that we considered in the math review.  When it appears next to X as it does in the formula above, it tells us to add up all the numbers in the X column.  The letter n stands for the number of elements being considered (the number of quizzes in our example).  As we introduce new procedures, we will introduce new jargon and symbols that simply must be memorized.  Without knowledge of these terms and symbols, you will not be successful in your statistics course.

## It’s Greek to Me

### Uppercase Greek Letters

1. Sigma (Σ)
• Statistical Meaning: Represents the sum of a series of values.
2. Phi (Φ)
• Statistical Meaning: In some contexts, it can represent the cumulative distribution function of a standard normal distribution.

### Lowercase Greek Letters

1. alpha (α)
• Statistical Meaning: Significance level in hypothesis testing, e.g., α = 0.05 for a 5% significance level.
2. beta (β)
• Statistical Meaning: Represents regression coefficients in a linear regression model.
3. sigma (σ)
• Statistical Meaning: Standard deviation of a population.
4. rho (ρ)
• Statistical Meaning: Population correlation coefficient, often used in non-parametric statistics.
5. epsilon (ε)
• Statistical Meaning: Represents the error term or residuals in regression models.

### English Alphabet Letters

1. t
• Statistical Meaning: Represents the t-value in a t-test.
2. F
• Statistical Meaning: Represents the F-value in an F-test, used in analysis of variance.
3. r
• Statistical Meaning: Pearson correlation coefficient, indicating the linear relationship between two variables.
4. p
• Statistical Meaning: P-value, a measure used to help determine the significance of an observed effect.
5. N
• Statistical Meaning: Total number of subjects or observations in a sample.
6. n
• Statistical Meaning: Number of subjects or observations in a specific category or group.
7. X̄ (X-bar)
• Statistical Meaning: Represents the sample mean.
8. s
• Statistical Meaning: Sample standard deviation.
9. b
• Statistical Meaning: Represents the slope in a simple linear regression.
10. Ŷ (Y-hat)
• Statistical Meaning: Predicted score or value based on a regression equation.

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`Last Modified:  08/18/2023`

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