Symbol formats - Eric L. Peters



Symbol formats

The table below summarizes the correct format of statistical parameters. In many cases, Greek letters are used to indicate the population parameter for a statistic, and corresponding English letters are used to indicate the sample statistic that is an estimate of that population parameter. Symbols should be italicized in all cases where they represent a constant value. Associated subscripts and superscripts are generally not italicized (but see below):

|Population Parameter |Population Parameter Symbol |Sample Parameter |Sample Parameter Symbol |

|population size |N |sample size |n |

|population mean (arithmetic) |( (m in Symbol font) |sample mean (arithmetic) |[pic] (created using the Insert menu ( |

| | | |Object… ( Microsoft Equation function in|

| | | |Microsoft Office). The word “mean”, as |

| | | |in “mean = 27.2 is also acceptable. |

|population mean (geometric) |(G (mG in Symbol font) |sample mean (geometric) |[pic] (created using the Insert menu ( |

| | | |Object… ( Microsoft Equation function in|

| | | |Microsoft Office). The abbreviation |

| | | |“GM”, as in “GM = 27.2 is also |

| | | |acceptable. |

|population mean (harmonic) |(H (mH in Symbol font) |sample mean (harmonic) |[pic] (created using the Insert menu( |

| | | |Object… ( Microsoft Equation function in|

| | | |Microsoft Office) The phrase “harmonic |

| | | |mean”, as in “harmonic mean = 27.2 is |

| | | |also acceptable. |

|population median |[pic] (“μ-tilde” created using the |sample median |[pic] (“x-tilde”created using the Insert|

| |Insert menu ( Object… ( Microsoft | |menu ( Object… ( Microsoft Equation |

| |Equation function in Microsoft Office)| |function in Microsoft Office). The word |

| | | |“median”, as in “median = 27.2 is also |

| | | |acceptable. |

|population variance |σ2 (s2 in Symbol font) |sample variance |s2 |

|population standard deviation |σ (s in Symbol font) |sample standard deviation |s |

| | |standard error of the mean |SE or SEM |

| | |coefficient of variation |CV |

|population skewness |γ1 (g1 in Symbol font) |sample skewness |g1 |

|population kurtosis |γ2 (g2 in Symbol font) |sample kurtosis |g2 |

|population correlation coefficient |ρ (r in Symbol font) |sample correlation coefficient |r |

|(Pearson’s) | |(Pearson’s) | |

|coefficient of determination (population) |ρ2 (r2 in Symbol font) |coefficient of determination (sample) |r2 |

|regression line intercept |β0 (b0 in Symbol font) |Regression line intercept (estimated |b0 |

| | |from sample data) | |

|regression line slope(s) |βi (bi in Symbol font, where i = the |Regression line slope(s) estimates from |bi (where i = the variable number) |

| |variable number) |sample data) | |

|regression line variables: y and x(s) |Your call: can be upper or lowercase, italicized or not. |

Symbols used in statistical tests:

Probability should be expressed as P, and “alpha” as α (a in Symbol font).

Critical values are generally not reported.

There should always be a space on either side of any “equals sign” ( = ).

The test statistics z, t, chi-squared, and F should be represented as:

zα (or zα/2) neither subscript is italicized, but the numerical value for α or α/2 is substituted for the α (or α/2). Often (n = the sample size) is also included. The P-value may or may not be reported

tα (or tα/2) neither subscript is italicized, but the numerical value for a or a/2 is substituted. Always report the P value and the degrees of freedom or include the alpha and degrees of freedom in the subscript (e.g., t0.975,35 = the test statistic). Alternatively, report t = the test statistic (df, the degrees of freedom); P = the P-value).

χ2 needs to have the alpha and degrees of freedom reported, as well as the P-value: χ2α,df = the test statistic (e.g., χ20.05,12). Alternatively, report χ2 = the test statistic (df , the degrees of freedom); P = the P-value).

For F, always report both the numerator and the denominator degrees of freedom (e.g., F2,35 = the test statistic; P = the P-value) or include it in parentheses, e.g., (F(2,35) = the test statistic; P = the P-value).

Other symbols of potential value:

> greater than

≥ greater than or equal to (option >)

>> much greater than

< less than

≤ less than or equal to (option ................
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