Abbreviation Standard Error Mean
Contents |
operator precedence) abs(x), |x| absolute value of x without regard to sign alpha, α significance level of a hypothesis test (also type I error rate). 1-a is standard error abbreviation excel the level of the confidence interval ANOVA analysis of variance beta, β
Abbreviation For Standard Deviation
type II error rate (1-power) CI confidence interval, see confidence intervals df degrees of freedom e base abbreviation for standard deviation apa of natural logarithms (2.718281...) k! factorial , in simplest terms factorial of k is the product of all integers from 1 to k, with 0! defined as 1, a fuller definition relates factorial to the gamma function
Standard Error Of The Mean Definition
as gamma (k+1) which enables the calculation of fractional factorials ln(x) natural (base e) logarithm of x, the natural logarithm of x is the value of y such that x is equal to the e constant raised to the power of y, remember that ln(1) = 0, ln(0) = minus infinity and ln(a/b)=ln(a)-ln(b), see also transformations MS mean square μ mean of a population - see also n sample size abbreviation for personal (population sized is usually referred to as N) P probability of the data (or more extreme data) arising by chance, see P values p proportion of a sample with a given characteristic q hat, the hat symbol above the q means "estimate of" r Pearson's product moment correlation coefficient SD standard deviation (of a sample, ) - a measure of variability around the mean - Greek lower case sigma (σ) is used for population standard deviation. SE standard error (of sample mean, ) - a measure of uncertainty of the estimate of a statistic (e.g. sample mean) and used to derive confidence intervals for the population value of the statistic sqr(x) square root of x, or sum of all (1 to n) x values product of all (1 to n) x values (x1 * x2 * x3 etc.) VAR variance (of the mean, ), greek σ² for populations and s² for samples vs. versus x individual value from a population or sample x bar (bar symbol above the x denotes mean) is a sample mean (arithmetic mean, ), see also μ z, Φ standardized normal deviate (from standard normal distribution) Copyright © 2000-2016 StatsDirect Limited, all rights reserved. Download a free trial here.
Lee In the social sciences, the worlds of grammar and mathematics intersect, as authors must not only run statistical tests but also write about their results in a clear, consistent way. To
Scheduled Abbreviation
help achieve that end, this post focuses on some of the grammar of mathematics:
Abbreviate Scholarship
how to introduce and use statistical terms in text when you are reporting your results. The sixth edition Publication Manual provides standard error of the median a listing of many mathematical variables and terms that commonly appear in APA Style papers (see Table 4.5 on pp. 119–123). The table below excerpts some of the most common statistics, showing their written-out and http://www.statsdirect.com/help/references/glossary.htm abbreviated forms in both the singular and the plural. Following that, we discuss the ins and outs of using them in an APA Style paper. Written-out form Abbreviation/symbol Singular Plural Singular Plural Cohen’s d Cohen’s ds d ds degree of freedom degrees of freedom df dfs F statistic or F value F statistics or F values F Fs mean means M Ms sample size (subsample) sample sizes (subsample) n http://blog.apastyle.org/apastyle/2011/08/the-grammar-of-mathematics-writing-about-variables.html ns sample size (full sample) sample sizes (full sample) N Ns p value p values p ps r value r values r rs R2 value R2 values R2 R2s standard deviation standard deviations SD SDs standard error standard errors SE SEs t value t values t ts z score z scores z zs Cronbach’s alpha Cronbach’s alphas Cronbach’s α Cronbach’s αs beta betas β βs chi-square chi-squares χ2 χ2s delta deltas Δ Δs Singular Versus Plural The syntax of your sentence will dictate whether you need to use the singular or plural form of the variable. All plural abbreviated forms are made by adding a nonitalic lowercase “s.” Do not use an apostrophe plus an “s,” an italic “s,” or a capital “S.” Correct: ps < .05; Ms = 3.70 and 4.22; degrees of freedom. Incorrect: ps < .05, p’s < .05; Ms= 3.70 and 4.22; Means = 3.70 and 4.22; degree’s of freedom. Written-Out Form Versus Abbreviated Form Use the written-out form of the variable in prose; use the symbol in conjunction with all mathematical operators (such as the equals sign or the greater than/less than signs). As usual, use singular or plural as needed by the context. Italic Versus Nonitalic Variables are italicized. Superscript numbers are no
the values of a variable, whereas the standard error of the mean (SEM) represents the spread that the mean of a sample of the values would have if you kept taking samples. So the SEM http://www.sportsci.org/resource/stats/meansd.html gives you an idea of the accuracy of the mean, and the SD gives you an idea of the variability of single observations. The two are related: SEM=SD/(square root of sample size). Some people think you should show SEMs with means, because they think it's important to indicate how accurate the estimate of the mean is. And when you compare two means, they argue that showing the SEMs gives you an idea of whether standard error there is a statistically significant difference between the means. All very well, but here's why they're heading down the wrong track: For descriptive statistics of your subjects, you need the SD to give the reader an idea of the spread between subjects. Showing an SEM with the mean is silly. When you compare group means, showing SDs conveys an idea of the magnitude of the difference between the means, because you can see how big abbreviation for standard the difference is relative to the SDs. In other words, you can see how big the effect size is. It's important to visualize the SDs when there are several groups, because if the SDs differ too much, you may have to use log transformation or rank transformation before you compute confidence limits or p values. If the number of subjects differs between groups, the SEMs won't give you a direct visual impression of whether the SDs differ. If you think it's important to indicate statistical significance, show p values or confidence limits of the outcome statistic That's more accurate than showing SEMs. Besides, does anyone know how much SEMs have to overlap or not overlap before you can say the difference is significant? And does anyone know that the amount of overlap or non-overlap depends on the relative sample sizes? Most importantly, when you have means for pre and post scores in a repeated-measures experiment, the SEMs of these means do NOT give an impression of statistical significance of the change--a subtle point that challenges many statisticians. So if the SEMs don't show statistical significance in experiments, what's the point of having them anywhere else? Here's a figure to illustrate why SEMs don't convey statistical significance. It's for imaginary data in an experiment to increase jump height. The change in he