Question

PFOA is a chemical that disrupts endocrine function in amphibians. PFOA acts differently at different dosage levels. This study looked a PFOA at 0, 10, 100, and 1000 ug/L in comparison to thyroid length. The results of the One-way ANOVA of these measurements are listed below along with post hoc Tukey test. Interpret the results of the ANOVA tests and post hoc tukey test and explain what they mean in regards to the effect of different dosage (10, 100, and 1000) on thyroid length.

Thyroid Length
PFOA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	75.30562	3	25.10187	7.618022	0.004099	3.490295
Within Groups	39.54078	12	3.295065
Total	114.8464	15

Tukey Test:

Factor levels: 4	Den df=12		Q=3.52
n= 16	n.= 4		Num df=4

PFOA-Thyroid length	s2pooled=3.295065
Comparison	Absolute difference		Critical range (Q*sqrt(s2pooled/n.)	Results
0 to 10	0.0925		3.19	no sig diff
0 to 100	4.17		3.19	sig diff
0 to 1000	4.58		3.19	sig diff
10 to 100	4.0775		3.19	sig diff
10 to 1000	4.4875		3.19	sig diff
100 to 1000	0.41		3.19	no sig diff

Answer 1

The results of the ANOVA tests:

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃ = µ₄

H_a: At least one means is not equal

The p-value from the output is 0.004099.

Since the p-value (0.004099) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that PFOA acts differently at different dosage levels.

The results of the post hoc Tukey test:

There is a significant difference between 0 to 100 Thyroid length.

There is a significant difference between 0 to 1000 Thyroid length.

There is a significant difference between 10 to 100 Thyroid length.

There is a significant difference between 10 to 1000 Thyroid length.

Thus, PFOA acts differently at different dosage levels.