Summary of Inference Tests

Stats Cheat Sheet

NameWhen to UseTest StatisticConfidence IntervalAssumptions

Normal Distribution is known

finding z = EQ \F(x - 0,\F(,\r(n))) x z* EQ \F(,\r(n)) REMEMBER: dont read percentages straight, halve gap first1) Independence - SRS2) Normality - normal quantile plot, CLT:

n40 poor approximation (no gross outliers)

Proportion of Successes/ Binomials

(could be represented as two-way table with twins; only consider differences)finding p0

(H0: p0=0.5)z = EQ \F(p-p0,\r(\F(p0(1-p0),n))) p z* EQ \r(\F(p (1- p),n)) 1) Independence - SRS2) Normality if n is large:

np>10 n(1-p)>10

Compared Proportions of Successes - not the tablep1-p2 ~ N(p1-p2, EQ \r(\F(p1(1-p1),n1)+\F(p2(1-p2),n2)) )finding difference in p0z = EQ \F(p1-p2, \r(\F(p1(1-p1),n1)+\F(p2(1-p2),n2))) p1-p2 z* EQ \r(\F(p1(1-p1),n1)+\F(p2(1-p2),n2)) 1) Independence - SRS

2) Normality if n is large:

nipi>10 ni(1-pi)>10 for i=1,2

T-Distribution is unknown

(only s is known)

finding On Formula Sheetx t* EQ \F(s,\r(n)) 1) Independence - SRS

2) Normality - normal quantile plot, CLT

Two-Sample T-Distributiontwo samples with complete independence is unknownOn Formula Sheet(x1- x2) t*sp EQ \r(\F(1,n1)+\F(1,n2)) 1) Independence within sample - SRS2) Independence between samples - SRS

3) Normality - CLT for n1 + n24) Same - within factor of 2, if not n within factor of 2

Paired T-Distributionmatched pair designlook at differences

(H0: =0)as with T-Distributionas with T-Distribution(x and s come from differences)as with T-Distribution

2-testtwo-way categorical tableOn Formula SheetP(2>X2)n/a1) Independence - SRS2) Expected Counts > 10

Linear Regressionslope in regression lineT = EQ \F(b1- 1,SE(b1)) ~ t(n-2) (1=0)

On Formula Sheetb1 t*SE(b1)1) Yi observations are independent - SRS2) i (errors) are normally distributed (=0, =; or n is large by CLT) - normal quantile plot of residuals

3) i has same variance across x (regardless of n) - pattern/distance from 0 in residual plot

4) y (mean of Y) has linear relationship with X - residual plot, no pattern

Independence is important in the normality assumption as then standard error is random (and hence is overall equal) and can be calculated (not dependent upon other variables from a relationshipYears are quantitative, just discreteWhen doing tables and graphs, include FULL titlesPage 2

Oliver Bogdanovski