One mean
If σ known:
Calc: ztest
pv normcdf (a,b,µ, σ) / x±z*σ/n, m =z*σ/n,
Calc: z-interval
z critical value: -invnorm1-C2, μ,σ =invnorm1+C2, μ,σ / µ = µ0 / z=x-μ0σ/n / --
If σ unknown:
Calc: ttest
Pv tcdf(a,b,df) / x±t*s/n, standard error= s/n,
Calc: t-interval
t critical value: invt1+C2, df / µ = µ0 / t=x-μ0s/n / n-1
Difference between 2 means
Matched pairs - Use paired sample t-test on differences D
Calc: ttest
Pv tcdf(a,b,df)
Do a one sample t test on the difference. / D±t*sD/n
Calc: t-interval
t critical value: invt1+C2, df / μD=D0
(D0 is often 0) / t=D-D0sD/n / n-1
If measurements are on 2 independent groups, σ’s unknown and group stdev’s are not equal.
Calc: 2-SampTTest
Pv tcdf(a,b, df)
conservative df
Pop 1 / x1 / n1 / s1
Pop 2 / x2 / n2 / s2
/ x1-x2±t*s12n1+s22n2
Calc: 2-sampTint
t critical value: invt1+C2, df)
the standard error of the difference in sample means iss12n1+s22n2 / usually
μ1=μ2,
μ1-μ2=0 / t=x1-x2s12n1+s22n2 / Smaller of
n1-1, n2-1
Note: conservative df, actual df different
One proportion (large n)
Calc: 1-prop z test
Pv normcdf(a,b,µ, σ) / p±z*p1-pn
Calc: 1-PropZint
z critical value: invnorm1+C2, μ,σ / p=p0 / z=p-p0p01-p0n / --
Type of test, assumptions: / CI / H0 / Test statistic / df
Difference in 2 proportions (large n1, n2), independent samples
Calculator: 2-PropZtest
Pv normcdf(a,b,µ, σ)
Pop 1 / X1 / n1 / p1=X1n1
Pop 2 / X2 / n2 / p2=X2n2
For test Statistic: / p1-p2±z*p11-p1n1+p21-p2n2 / Usually
p1=p2
p1-p2=0 / z=p1-p2p1-p1n1 + 1n2 / --
p=X1+X2n1+n2 / Note: p1=X1n1 p2=X2n2
z critical value: invnorm1+C2, μ,σ / Note: p=X1+X2n1+n2=n1p1+n2p2n1+n2
Association between 2 categorical variables (Chi-square)
Enter data in Matrix A,
X2-Test
Observed [A]
(Calculates [B] for you)
Expected in [B] / n/a / No
association / χ2=O-E2E / (R-1)*
(C-1)
Note: E=Row total × Column totaln
p-values for z p-values for chi-square
If Ha is µ<µ0: P(Z<z)=normalcdf(-∞, z) P(X2> χ2) = X2cdf(χ2, ∞, df)
If Ha is µ≠µ0: P(|Z|>|z|)= 2*normalcdf(|z|, ∞)
If Ha is µ>µ0: P(Z>z)=normalcdf (z,∞)
p-values for t
If Ha is µ<µ0: P(T<t)=tcdf(-∞, t, df)
If Ha is µ≠µ0: P(|T|>|t|)=2*tcdf (|t|,∞, df)
If Ha is µ>µ0: P(T>t)=tcdf (t,∞, df)