Assume we have a group of 10 rats daily injected with 50 µg Pb/kg b. wt. At the end of experiment, the Pb concentrations in the liver and kidney were measured and tabulated as mean ± standard error in the following table: Pb contentMeanStandard error liver (µg/g dry tissue) kidney (µg/g dry tissue) Is there any significant difference between the liver and kidneys in the levels of accumulated Pb at confidence level 95%? Revision

2 So we want to test the null hypothesis H 0 : σ 2 2 = σ 1 2 against the alternate hypothesis H A : σ 2 2 ≠ σ 1 2 (2-tailed) Solution: F (9,9) = 4.03 d.f.= 10 – 1 = 9 In this case, F calc (17.78) > F tabulated (4.03), so we reject H 0 that the two standard deviations are unequal, so P < 0.05

 Does the type of diet significantly affected the body weight of mice at confidence levels of 95% and 99 %? Three diets (I, II, III) for mice were tested for differences in body weight (in grams) after a specified period of time. The results are recorded in the following table: DietBody weight (g) I II III  Compare between group I and II.

Solution DietBody weight (g)meansizeS I II III

SourceSSdfMSFP Between (Factor) SSBdf B MS B MS B /MS W Within (Error) SSWdf W MS W TotalSST

df B = h-1= 3-1= 2 MS B = SS B /df B =

df W = N-h= 12-3= 9 MS W = SS W /df W = 52.5

SourceSSdfMSF Cal P Between (Factor) <0.01 Within (Error) Total F 0.05 (2, 9)= 4.26 F 0.01 (2, 9)= 8.02

f-distribution Table

Tukey’s HSD (Honestly significance difference) Post-hoc test The critical value for comparison between two averages Sample size /group Number of groups = number of means Total number of Samples Critical q value (tabulated)tabulated

Tukey’s HSD (Honestly significance difference) Post-hoc test Q= 3.95 (3.62)=14.31

N (total sample size)- g (number of groups) g (3) 12 – 3= 9

The data below represent the levels of blood glucose before and after injection with a certain herbal extract. Experimental conditionsBlood glucose levels (mg/dl) Before2, 3, 3, 2, 4, 2 after9, 8, 9, 8, 8, 7 Did the herbal extract cause increased blood glucose levels??

After (X 2 ) Before (X1)After (X 2 ) D D2D d.f. = n t tabulated at d.f. 5 = t Cal (12.84) > t tabulated (2.015) Significant, P<0.05

In an experiment to study the effect of pH value on the hepatic Cd content, the data below were recorded. Test the claim that Cd content at pH 8 is significantly higher than at pH 5? pHHepatic Cd content (mg /kg b. wt.) 54, 8, 8, 30, 10, 12, 12 84, 7, 10, 11, 14, 16,16, 21, 23, 25, 26

pH5 (X 1 )pH8 (X 2 ) (X 1 ) (X 2 ) d.f. = n 1 + n = = 16

t tabulated at d.f. (7+11-2) = t Cal (1.001) < t tabulated (1.746) Insignificant, P>0.05

t-distribution Table