The t test. Peter Shaw RIl. "Small samples are slippery customers whose word is not to be taken as gospel" (Moroney). Introduction. Last week we met the Mann-Whitney U test, a non-parametric test to examine how likely it is that 2 samples could have come from the same population.
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"Small samples are slippery customers whose word is not to be taken as gospel" (Moroney).
Remember Z scores? These apply to the idealised normal distribution
How many s.d.s is this data point from the mean? Zi = (Xi- μ)/σ
We can look up Z in tables, but these assume that the values of μ and σ are known perfectly.
You have 2 samples which may be from 1 distribution or 2. To assess the likelihood, find how many s.d.s the means of the 2 populations are apart:
How many S.D.’s?
Calculate t = (μ1 - μ2) / pooled sd
Number of groups:
Mann-Whitney U test
Analysis of variance (ANOVA)
= sqrt[2.2675] = 1.506
Hence t = (61.25 - 56.21)/1.506 = 3.35 with 12df
This is significant at p<0.05