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
