Stats Study Guide

# Stats Study Guide - Stats Study Guide Definitions I Type I...

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Stats Study Guide Definitions: I) Type I Error = rejecting H 0 (usually X 1 = X 2 ) when it is true II) Type II Error = not rejecting H 0 (usually X 1 ≠ X 2 ) when it is false III) Central Limit Theorem – Given a population mean (μ) and its variance (σ 2 ), the sampling distribution of the mean will have a mean equal to μ and a variance (σ 2 X ) equal to σ 2 /n (standard deviation of σ/√n). The sampling distribution will approach normality as n increases, regardless of the shape of the raw scores’ distribution. IV) Probability a. A Estimators: V) Mean = √(x – X)/N VI) Variance (σ 2 ) = Σ(x – X) 2 /(N – 1) VII) Standard Deviation (σ) = √(σ 2 ) Working with Tables/Equations: VIII) Z Table a. When to use: when you are testing one score or one mean score against a known population (σ 2 is known) b. z = (X – μ)/σ i. Use when testing individual measure against population c. z = (X – μ)/(σ/√n) i. Use when testing mean against population d. α(.05) = 1.96; α(.01) = 2.58 e. CI(95%): X +/– (s*1.96) IX) T Table a. When to use: when the population variance (σ 2 ) is unknown b. t(df) = (X – μ)/√(s 2 /n); df = n – 1 (mean is fixed) i. Use when testing mean against population c. t(df) = (X 1 – X 2 )/√([s 2 1 /n 1 ] + [s 2 2 /n 2 ]) ; df = n – 1 i. Use when comparing two means and sample sizes are equal d. t(df) = (X 1 – X 2 )/√([s 2 p /n 1 ] + [s 2 p /n 2 ]) ; df = n – 1 i. s 2 p = ([n 1 – 1]s 2 1 + [n 2 – 1]s 2 2 )/(n 1 + n 2 – 2) ii. Pooled variances are done in order to come closer to σ 2 iii. Use when comparing two means and samples sizes are not equal, because t-tests need at least sample sizes or sample variances to be equal (can’t have neither assumption met) e. Standard error of differences (s d ) = √([Σ(D f. CI(95%): X +/- (s p *[t .05 (df)]) g. Welch-Satterthwaite Solution: df’ = ([s 2 1 /n 1 ] + [s 2 2 /n 2 ]) 2 /([( s 2 1 /n 1 ) 2 /(n 1 – 1)] + [( s 2 2 /n 2 ) 2 /(n 2 – 1)])

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i. Use when comparing two samples that have significantly different
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Stats Study Guide - Stats Study Guide Definitions I Type I...

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