Statistical Symbols Explained

Statistical symbols are essential in conveying complex concepts succinctly, with 52 distinct entries detailing their meanings and classifications.

The abbreviation "df" stands for degrees of freedom, while "IQR" refers to the inter-quartile range. The concept of null hypothesis significance testing is denoted by "NHST," a standard method for using data to test hypotheses. For quartiles, "Q1" indicates the lower quartile, or the 25th percentile, and "Q3" represents the upper quartile, or the 75th percentile. The abbreviation "sd" signifies standard deviation, a critical measure of variability.

In mathematical notation, the symbol "!" denotes factorial, which involves multiplying a number by all lower integers, such as 4! equaling 24. The less-than sign is represented by "<," while ">" indicates greater-than. The notation "|x|" signifies the absolute value, changing negative numbers to positive, and "√" represents the square root. The less-than-or-equal-to sign is shown as "≤," and "≥" indicates greater-than-or-equal-to. The sigma symbol "Σ" is used to denote summation.

Moving into statistical notation, "d" represents the difference, particularly in the context of Cohen's d, which measures effect size. The null hypothesis is indicated by "H₀," while the alternative hypothesis is denoted by "H₁" or "Hₐ." The variable "k" refers to the number of levels of an independent variable, and "n" signifies sample size, whereas "N" indicates population size. The symbol "p" is used for probability, and "s" denotes the standard deviation of a sample.

Specific values of variables are represented by "x" for a particular value of variable X, and "X" for the variable itself, which often denotes an independent or predictor variable. The mean of a sample of values of x is indicated by "x̄," while "y" and "Y" represent values and variables for the dependent or criterion variable, respectively. The standardized value is represented by "z," calculated as x divided by sₓ.

In terms of significance, "α" (alpha) indicates the critical level of significance, which is also the probability of a Type I error, whereas "β" (beta) signifies the probability of a Type II error and is related to 1 minus power. The mean of a population is denoted by "μ," and the standard deviation of a population is represented by "σ." The probability density function of the normal distribution is indicated by "φ."

Various test statistics are represented by specific symbols. For instance, "B" refers to the unstandardized regression coefficient, typically used with subscripts, such as B₀ for the constant. The ANOVA test statistic is denoted by "F," which is also used in Levene's test for homogeneity of variance. The Kruskal-Wallis H test is represented by "H," while the Freidman test is indicated by "Q." The Pearson correlation coefficient is shown as "r," and the T-test statistic is represented by "t."

Additionally, "T" denotes a historical test statistic for the Wilcoxon signed-rank test, which is a non-parametric paired t-test, while "U" signifies the Mann–Whitney U test, another non-parametric independent t-test. The Wilcoxon signed-rank test is represented by "W," which is also used for the Shapiro-Wilk test of normality and the Mauchly test of sphericity. The Cronbach's alpha test statistic is denoted by "α," while the standardised regression coefficient is represented by "β."

The measure of sphericity is indicated by "ε," estimated by procedures such as Greenhouse-Geisser and Huyndt-Feldt. The eta-squared measure of effect size used in one-way ANOVA is represented by "η²," which explains the proportion of variation due to the effect. Finally, "ρ" denotes Spearman's rank correlation coefficient, and "τ" indicates Kendall tau rank correlation coefficient, both of which are non-parametric measures. The chi-squared test statistic is represented by "χ²."