Question

Researchers are investigating the effect of storage temperature on bacterial growth for two types of seafood. They set up the experiment to evaluate 3 storage temperatures. There were 9 storage units that were available, and so they randomly selected 3 storage units to be used for each storage temperature, and both seafood types were stored in each unit. After 2 weeks, bacterial counts were made. After taking a logarithmic transformation of the counts, they produced the following ANOVA:

Type 3 Analysis of Variance
Source	DF	Sum of Squares	Mean Square	Expected Mean Square
temp	2	107.656588	53.828294	Var(Residual) + 2 Var(unit(temp)) + Q(temp,temp*seafood)
seafood	1	3.713721	3.713721	Var(Residual) + Q(seafood,temp*seafood)
temp*seafood	2	2.647594	1.323797	Var(Residual) + Q(temp*seafood)
unit(temp)	6	44.050650	7.341775	Var(Residual) + 2 Var(unit(temp))
Residual	6	5.590873	0.931812	Var(Residual)

Questions:

1. Is this a RCBD or CRD design?

2. Calculate the F-test value and F statistic for each effect in the ANOVA, and determine significance for each effect. Please show how you obtain the corresponding values, thank you!

	F (rounded to 4 decimal places)	Fcritical (Table B4, 2 decimal places)	Reject null hypothesis? (Enter only Y/N)
temp
seafood
temp*seafood
unit(temp)

Answer 1

(1).

The given study is based on the RCBD design as the effect of storage temperature on bacterial growth for two types of seafood are analysed by the researcher. Here the storage units into blocks (storage temperature, and both seafood types).

(2).

The F-ratio is calculated by taking the mean square of corresponding effect or treatment and mean square of residual.

The F-critical value obtained at the degrees of freedom of corresponding effect or treatment and residual at the assumed significance level 0.05 from F-table.

The calculation procedure F-ratio values and F-critical values is shown in the following table:

Source	DF	Sum of Squares	Mean Square	F-ratio	F-critical
temp	2	107.656588	53.828294	53.828294/0.931812 = 57.7673	F(2,6) = 5.14
seafood	1	3.713721	3.713721	3.713721/0.931812 = 3.9854	F(1,6) = 5.99
temp*seafood	2	2.647594	1.323797	1.323797/0.931812 = 1.4207	F(2,6) = 5.14
unit(temp)	6	44.050650	7.341775	7.341775/0.931812 = 7.8790	F(6,6) = 4.28
Residual	6	5.590873	0.931812

Decision:

If the F-ratio is greater than the F critical value, then the researcher reject the null hypothesis. It means the result is significant.

If the F-ratio is less than the F critical value, then the researcher fail to reject the null hypothesis. It means the result is insignificant.

The complete table is,

Source	F-ratio	F-critical	Reject the null hypothesis	Significance or insignificant
temp	57.7673	5.14	Y	Significant result
seafood	3.9854	5.99	N	Insignificant result
temp*seafood	1.4207	5.14	N	Insignificant result
unit(temp)	7.8790	4.28	Y	Significant result