Statistical Symbols Explained
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ABCD
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SymbolNameMeaningType
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dfDegrees of freedom.Abbreviation
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IQRInter-quartile range.Abbreviation
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NHSTNull hypothesis significance testing. The standard method of using data to test a hypothesis.Abbreviation
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Q1Lower quartile (25th percentile).Abbreviation
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Q3Upper quartile (75th percentile).Abbreviation
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sdStandard deviation.Abbreviation
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!factorialMultiple the value by all lower integers, e.g. 4! = 4x3x2x1 = 24Mathematical notation
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<less-than signis less thanMathematical notation
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>greater-than signis greater thanMathematical notation
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|x|absolutePositive numbers stay the same. Negative numbers are changed to positive.Mathematical notation
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square-rootMathematical notation
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less-than-or-equal-to signis less than or equal toMathematical notation
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greater-than-or-equal-to signis greater than or equal toMathematical notation
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ΣsigmaSum ofMathematical notation
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dDifference. Cohen's d is a measure of effect size, which is a standardised difference (Cohen's d = 1 means a difference of one standard deviation).Statistical notation
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H₀H zero or H noughtNull hypothesis.Statistical notation
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H₁ or HₐH one or H aAlternative hypothesis.Statistical notation
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kThe number of levels of an independent variable.Statistical notation
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nSample size.Statistical notation
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NPopulation size.Statistical notation
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pProbabilityStatistical notation
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sStandard deviation of a sample.Statistical notation
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xA particular value of variable X.Statistical notation
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XA particular variable. Often used to denote an independent or predictor variable.Statistical notation
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x barMean of a sample of values of x.Statistical notation
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yA particular value of variable Y.Statistical notation
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YA particular variable. Often used to denote the dependent or criterion variable.Statistical notation
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zA particular standardised value (x / sₓ).Statistical notation
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αalphaCritical level of significance and therefore also probability of a Type I error.Statistical notation
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βbetaProbability of a Type II error and therefore also 1-power.Statistical notation
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μmuMean of a population.Statistical notation
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σsigmaStandard deviation of a population.Statistical notation
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φphiThe probability density function of the normal distribution.Statistical notation
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BUnstandardised regression coefficient, usually used with subscripts where B₀ is the constant.Test statistic
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FANOVA, F-test or F-ratio test statistic. Also used in the Levene's test for homogeneity of variance.Test statistic
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HKruskal-Wallis H test (non-parametric one-way independent ANOVA).Test statistic
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QFreidman test (non-parametric one-way repeated ANOVA).Test statistic
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rPearson correlation coefficient (parametric).Test statistic
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tT-test test statistic.Test statistic
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THistorical test statistic for Wilcoxon signed-rank test (non-parametric paired t-test), which is easier to calculate by hand.Test statistic
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UMann–Whitney U test (non-parametric independent t-test).Test statistic
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WWilcoxon signed-rank test (non-parametric paired t-test).Test statistic
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WShapiro-Wilk test of normality.Test statistic
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WMauchly test of sphericity.Test statistic
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αalphaCronbach's alpha test statistic (reliability).Test statistic
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βbetaStandardised regression coefficientTest statistic
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εepsilonMeasure of sphericity (estimated by both Greenhouse-Geisser and the Huynd-Feldt procedures). Sphericity is the assumption of homogeneity of variance of the differences in a repeated measures design.Test statistic
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η²eta-squaredA measure of effect size use in one-way ANOVA. It is the proportion of the variation (sum of squares) explained by the effect. With the addition of a subscript p it becomes partial eta-squared, which is used in multi-way ANOVA.Test statistic
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ρrhoSpearman's rank correlation coefficient (non-parametric).Test statistic
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τtauKendall tau rank correlation coefficient (non-parametric).Test statistic
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χ²chi-squaredChi-squared test statistic.Test statistic
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