Confidence Interval on Linear Combination of Means, Independent Groups (5
of 5)
Next section: Pearson's correlation
Summary of Computations

Compute the sample mean (M) for each group.
 Compute the sample variance
(s²) for each of the k groups.
 Find the coefficients (a's) so that Σ a_{i}μ_{i} is
the parameter to be estimated.
 Compute L = a_{1}M_{1} +
a_{2}M_{2} + ... +
a_{k}M_{k}
 Compute MSE = Σs² /k
 Compute
 Compute
df = k(n1) where k is the number of groups and n is the number of subjects
in each group.
 Find t for the df and level of confidence desired using a t
table
 Lower limit = L  t s_{L
}
 Upper limit = L + t SL_{}
 Lower limit ≤ Σa_{i}μ_{i} ≤ Upper
limit
Assumptions:
 All populations are normally distributed.
 All population variances are
equal (homogeneity of variance)
 Scores are sampled
randomly and independently from k different populations.
 The sample sizes
are equal.
Next section: Pearson's correlation