Symbol/Formula

Description

2 to the k formula

2k > n. Formula used to determine the number of categories, classes, buckets, or bins in a Frequency Distribution

Class Interval or Width, i

Class Midpoint

f

Frequency or the number of observations

H

The highest value in a distribution

k

Number of categories, classes, buckets, or bins in a Frequency Distribution

L

The smallest value in a distribution

N

Number of observations, or items, in a population

n

Number of observations, or items, in a sample

% or RF

Relative frequency or the proportion of the total number of observations

Symbol/Formula

Description

Coefficient of Variation as a percentage

Coefficient of Variation as an index

D

Stands for Decile. Deciles divide a distribution into ten groups of equal frequency

Interquartile Range (IQR)

Location of a Decile

Lower Outlier (Extreme Lower Outlier)

Location of a Percentile

Location of a Quartile

X̅ (The Sample Mean, X-Bar)

, where X are the random variables

μ (The Population Mean, mu)

where X are the random variables

X̅W (Weighted Mean)

where X are the random variables and w are the weights

Sample Mean, Grouped Data

Mean Deviation (MD) or Mean Absolute Deviation (MAD)

where “| |” means the absolute value, the distance of a positive or negative number from zero, or the value of a number regardless of its negative or positive sign.

Median

M or Med or “x-tilde”

Mode

Mo

P

Stands for Percentile. P75 or P75 means the 75th percentile. Percentiles divide a distribution into a hundred groups of equal frequency.

Range

Range = H (Highest Value) – L (lowest Value)

Q

Stands for Quartile: Q1 (1st Quartile), Q2 (2nd Quartile), Q3 (3rd Quartile) and Q4 (4th Quartile). Quartiles divide a distribution into four groups of equal frequency.

Pearson’s Coefficient of Skewness

Σ

Σ (capital Greek letter Sigma). It means the operation of summation or addition

σ (Population Standard Deviation, sigma)

s (Sample Standard Deviation, s)

σ2 (Population Variance, sigma-squared)

s2 (Sample Variance, s-squared)

Sample Standard Deviation, Grouped Data

Skewness or SK

Trimean

Upper Outlier (Extreme Upper Outlier)

X

X stands for the random variable

Symbol/Formula

Description

Fisher’s Ideal Index

Laspeyres Index

Paasche Index

Simple Aggregate Price Index

Simple Index Number

Simple Price Index

Value Index

Symbol/Formula

Description

Bayes Theorem

Combinations

nCr

nCr is pronounced “the combination of r things selected from n things.”

Note: With combinations, the order of selection matters.

Complement Rule (Subtraction Rule)

Factorial Number

n! (The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n:
4! = 1 x 2 x 3 x 4 = 24.)

General Rule of Addition (for non-mutually exclusive events

or

Note: Ç is pronounced as “intersection.” It is the equivalent to the word “and.”

General Rule of Multiplication (for dependent events

or

Multiplication Formula

(o)

Permutations

nPr

nPr is pronounced “the permutation of r things selected from n things.”

Note: With permutations, the order of selection matters.

P(A)

The probability of event “A”

P(~A)

The probability of the event not A. This is called the complement of event A. It is sometimes written as P(AC) or P(not A).

P(A|B)

The probability of event A given than event B has happened. This is called conditional probability.

Special Rule of Addition (for mutually exclusive events)

or

Note: È is pronounced “union” and is the equivalent to the word “or”

Special Rule of Multiplication (for independent events

or

Symbol/Formula

Description

Solving for X

X = μ + zσ

Note: z can be either a positive or negative number.

Standard Error for the Mean, sigma sub x-bar or SEM

Standard Normal Value

z-value, μ and σ known

Symbol/Formula

Description

Mean of the Sample Means (mu sub x-bar)

Sampling Error

X̅ - μ = 0 or X̅ ≠ μ

Standard Error of the Mean, SEM, or

z-value for sample

Symbol/Formula

Description

c

The selected confidence level; usually 95%, but in some cases 99% or 90%.

Confidence Interval for Means using t

Confidence Interval for Means using z

Confidence Interval for Proportions

Critical Value

The value a test statistic must exceed to be out of the confidence interval or the value a test statistics must exceed to reject the Null Hypothesis. A test statistic is a value derived from a sample for the purposes of hypothesis testing and confidence intervals. Do not report the Critical Value as CV. CV is the Coefficient of Variance.

d.f., df, or ν (the lower-case or small Greek letter nu)

Note: The formula for degrees of freedom depends on the type of distribution used.

Margin of Error for the Mean using t

Margin of Error for the Mean using z

Population Proportion

Population Proportion = π. Some use a capital P to symbolize the Population Proportions. In Clear-Sighted Statistics population parameters are always symbolized with Greek letters.

Sample Proportion, p

Sample Proportion = p (a lower-case p). A commonly used symbol for the sample proportion is p-hat, .

Sample Proportion formula

Standard Error of the Mean ( or SEM)

Standard Error for the Proportion (σp or SEP)

Symbol/Formula

Description

Estimating Sample Size for the Mean

Estimating Sample size for the Proportion

Symbol/Formula

Description

α (alpha)

The level of significance. The level of significance is selected by the researcher or analyst. Alpha is also the likelihood of a Type I Error.

P(α)

The probability of a Type I Error, or rejecting a Null Hypothesis when we should fail to reject it.

β (beta)

A Type II Error or failing to reject a Null Hypothesis that should be rejected.

H0

The Null Hypothesis. H0 is pronounced “H sub-zero” or “H sub naught.” H0 is a hypothesis about a population parameter. The Null Hypothesis states that there is no effect. Any difference between the parameter and the statistic is due to sampling error.

H1 or HA

The Alternate Hypothesis, sometimes called the Research Hypothesis. The Alternate Hypothesis is pronounced “H sub-one” when the H1 symbol is used or “H sub-A” when the HA symbol is used. Like the Null Hypothesis, the Alternate Hypothesis is a statement about a population parameter. The Alternate hypothesis states that there is an effect, which means the difference between the parameter and statistic is too big to have occurred by chance.

p-value

The p-value represents the likelihood of obtaining a test statistic as extreme or more extreme than the one obtained. If the p-value is greater than the level of significance, fail to reject the Null Hypothesis. When the p-value is equal to or less than the level of significance, reject the Null Hypothesis.

Statistical Power

Symbol/Formula

Description

Cohen’s d Effect Size

delta, δ, for the mean

delta, δ, for the proportion

One-Sample test for the Mean when σ is known

One-Sample test for the Mean when σ is unknown

One-Sample test for the Proportion

Probability of a Type II Error P(β)

Statistical Power

Symbol/Formula

Description

Cohen’s d

Cohen’s h (ES for population)

d

The difference between paired or dependent samples.

(d-bar)

The mean of the difference between paired or dependent samples.

df for Unequal Variance t-test

F-Test for comparing two sample variances

Paired t-test for dependent samples

Pooled Proportion

Pooled Variance

Pooled Variance t-test for Means (equal Variance)

Pooled Standard Deviations

Two-sample z-test of Means

Two-sample z-test of Proportions

Two-Sample t-test for Means (Unequal Variance)

Variance of the Distribution of differences in Means

Symbol/Formula

Description

Confidence Interval for difference in Treatment Means

Eta-squared, η2, Effect Size

Sum of Square, error

Sum of Square, total

Sum of Square, treatment

Symbol/Formula

Description

Chi-Square (χ2) Goodness of Fit Test

Where fo stands for the Observed Frequencies for each category and fe stands for the Expected Frequencies for each category.

Chi-Square Expected Frequency for a Contingency Table

Cohen’s w Effect Size

Degrees of Freedom for a Goodness of Fit

df = k – 1

Degrees of Freedom for a contingency table

Degrees of Freedom for a Goodness of Fit test for Normality

df = k – 3

(The two extra degrees of freedom are needed because we use the sample mean and sample standard deviation.)

Symbol/Formula

Description

Coefficient of Correlation or r

Coefficient of Determination or r2

or

Confidence Interval

Intercept of the Regression Line

Linear Regression Equation (y-hat)

Prediction Interval

ρ, or the lower-case Greek letter rho

Slope of the Regression Line

Standard Error of the Estimate

Test for Zero Slope

Test statistics for the significance of r

Greek
Letter

Upper
Case

Lower

Case

Statistical Symbol

Alpha

Α

α

α = level of significance, Type I Error