p population proportion. Formula Sheet and List of Symbols, Basic Statistical Inference. α significance level For example: Where is the center of the data located? Math symbols are easy enough to decipher with a simple review of algebra. sample proportion. t= x 0 s= p n and H 0: = 0: H 1 Critical region P-probability 0 t t 1 F(t) Symbols (or notation) found in statistics problems fall into three main categories: math symbols, symbols referring to a population, and symbols referring to a sample. s sample standard deviation. How spread out is the data? Probability Density Function (PDF) Mean Standard Deviation Student’s t Distribution This distribution was first studied by William Gosset, who published under the pseudonym Student. Nn i i i i. xx x Nn. µµ ss −− = − − = − − ∑ ∑ ∑∑ Percentile Locator: Coefficient of Variation: CV = 100 s µ × % (population) cv = 100. s x × % (sample) Probability . STATISTICS FORMULAS DESCRIPTIVE STATISTICS: MEAN: VARIANCE: STANDARD DEVIATION: STANDARD ERROR: SAMPLE SIZE FOR A GIVEN m: Z-SCORE: REGRESSION LINES: For a data set , where ( ) are the centroids (means) of the data set, and is the correlation coefficient: LEAST-SQUARES REGRESSION LINE: + RESIDUALS: SSM SSE SST = SSM+SSE COEFFICIENT OF DETERMINATION: r2 = … statistics to get a feeling for the data. Level 3 Mathematics and Statistics (Statistics), 2013 9.30 am Wednesday 20 November 2013 FORMULAE AND TABLES BOOKLET for 91584, 91585 and 91586 Refer to this booklet to answer the questions in your Question and Answer booklets. Seeing What Statistical Symbols Stand For. X variable. Testing expectations z= x 0 ˙= p n and H 0: = 0: H 1 Critical region P-probability 0 z z 1 ( z) < 0 z z ( z) 6= 0 jzj z =2 2min ( z);1 ( z) is the standard normal cumulative distribution function. σ population standard deviation. Symbol What it Represents. for mutually exclusive events if and are independent if and are dependent ( ) () ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) μ population mean. µ= === ∑∑ 22 2 22 2 () () 11. ii i i. xx NN x x ss nn. MIDTERM EXAM FORMULA SHEET 1 1 . σ2 population variance. sample mean. How correlated are the data from two variables? q 1-p. n sample size. The most common descriptive statistics are in the following table, along with their formulas and a short description of what each one measures. Degrees of Freedom = df = degrees of freedom = −1 A positive whole number that indicates the lack of restrictions in our calculations. However, this Cheat Sheet summarizes many of the basic methods and formulas used in data analysis. Statistically Figuring Sample Size Check that this booklet has pages 2–4 in the correct order and that none of these pages is blank. s2 sample variance. Basic Formula: σ= √SS R Computational Formula: s= √ ∑X2− ∑X ;2 n n − 1 Basic Formula: s= √SS n − 1 D) Variance (Ch.
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