ANOVA is a time consuming method (calculating SSC, SSE, and so on). How can we manually test a hypothesis that there is no difference in means of three (or four) samples?
Assuming sample data are taken from normally distributed populations.
suggest you use a computer. R is free downloadable software. Any R book or google ANOVA R and you should get instructions. Best, D. Booth
PARAMETRIC TEST is not relevant to the data testing that you are looking for. You are looking for the difference between the means of four samples: A, B, C, and D. Use these simple procedures (just excel is good enough, no need for statistical software):
1. EQUAL SAMPLE SIZE
Td = d^ / [Sd/sqrt(n)]
where d^ = d1 + d2 + ... + dn) / n ; Sd = standard deviation of di, and n = sample size. The difference: di = (Xai - Xbi). This is called d-Bar analysis. It works only when the two samples are equal. if your samples are of equal size then construct the following pairs: (A;B), (A:C); (A;D); (B:C); (B:D); (C:D). The possible pairs are: k = n(n - 1)/2 = 4(3)/2= 12/2 = 6.
2. UNEQUAL SAMPLE SIZE
T = A / (BC)
A = (X^a - X^b) - (mua - mub)
B = sigma(ab)
C = sqrt(1/n1 + 1/n2)
LINK:
See this book for basic statistical tests by Kanji Gopal:
https://www.pdfdrive.com/100-statistical-tests-e97177.html
Anova is your best bet, download the mini tab it’s easy and user friendly
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