Statistical Calculator

Difference Between Two Means

Formula

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Large (Infinite) Populations

test statistic:  t = |m₁-m₂ |/s

where:

m₁ =  mean 1
m₂ =  mean 2

s = sqrt(s₁² /n₁ + s₂²/n₂)    s₁ = standard deviation 1  s₂ = standard deviation 2

significance test:
t > 
2.576 for 99% level of confidence
1.96 for 95% level of confidence
1.645 for 90% level of confidence

Finite Populations

test statistic:  t = |m₁-m₂ |/s

where:

m₁ = mean 1
m₂ = mean 2

s = sqrt(s₁²/n_1adj + s₂²/n_2adj)   
s₁ = standard deviation 1 
s₂ = standard deviation 2
n_1adj = (N-1)n₁/(N-n₁)
n_2adj = (N-1)n₂/(N-n₂)
n₁ = sample size 1 
n₂ = sample size 2

significance test:
t > 
2.576 for 99% level of confidence
1.96 for 95% level of confidence
1.645 for 90% level of confidence