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Ш Calculations Sheet
!C Background Information Ў џџџџС С пЎ ќ ; / $ Enter Value for Control (null) Mean:: Enter Value for Biologically Significant Change from Mean:/ Sample Size Required to Detect this Difference:*
n = (Za+Zb)^2 * (2s^2)/(m1-m2)^2 " # % & Enter Value for a:
Enter Value for b:
' Enter Value for Standard Deviation (s):$ %
Power = RSD Change from Mean%
(m1-m2)=sqrt(2s^2/n)*(Za+Zb)
! # $ H Post Priori Calculation of Power (need to then derive 1-b from Z-value): 8 9 & Zb =[(m1-m2)/sqrt(2s^2/n)]-Za
% - Enter Value for Sample Size (each treatment):# Enter Value for Control (null) Mean& Minimal Detectable Difference (m1-m2):
" #
Enter Value for Treatment Mean Mean Difference (m1-m2):
j Type I Error = Probability of rejecting the null (declaring a difference) when there is no difference (a) h i j Type II Error = Probability of accepting the null (declaring no difference) when there is a difference (b)
h i j Power = Probability of rejecting the null (declaring a difference) when there is indeed a difference (1-b) h i Useful Functions in Excel:
n = (Za+Zb)^2 * (2s^2)/(m1-m2)^2
(m1-m2)=sqrt(2s^2/n)*(Za+Zb) Type II Error (b) Correct with Confidence (1-a) % Correct with Power (1-b)# $ & Reject Null (Declare a Difference)% Accept Null (No Change); Minimum Sample Size to detect difference between two means:0 Minimum Detectable Difference between two means:$ E.g., Z(0.05) = -1*normsinv(0.05) = TRUTH# Null is False (Difference Occurred) DECISION MADE UPON ANALYSIS Null is True (No Change) Type I Error (a) Power of Test (1-b):
Zb =[(m1-m2)/sqrt(2s^2/n)]-Za
Za or Zb = -1*normsinv(a or b)
a or b = 1-normsdist(Za or Zb)
3 E.g., If Zb = 0.8416, then b = 1-normsdist(0.8416)=
/ Typical Values of Acceptable Statistical Error: a = 0.05 b = 0.20 (1-b) = 0.8 O Post Priori Calculation of Power (need to then derive b or (1-b) from Z-value):! 6 7 > @ N џ * Пџ
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