Question

You operate a travel advisory website and want to give your users advice on airline timeliness. You select three airlines and monitor their delays at 5 airports. You record average delay times for each airline at each airport. THen you run a 2way ANOVA and get the following partial result:

ANOVA results

Source of Variance SS df MS F

Airline 383

Airport    296

Error

Total 723

What is the sum of squares for error?

WHat are the degrees of freedom for the variability associated with the airlines?

What is the mean square for the variability associated with airports? (2 decimal places)

WHat is the f-statistic for variability associated with arilines?

If you are testing for significant effects at the 0.05 level of significance, what would be the critical value of F for assessing the effect of airlines?

Is the effect of airlines significant at the 0.05 level of significance?

Is the effects of airports significant at the 0.05 level?

Could you please go step by step? Thank you very much

Answer 1

Level of Factor A Airlines, a = 3

Level of Factor B, Airport, b = 5

df(A) = a-1 = 2

df(B) = b-1 = 4

df(error) = (a-1)*(b-1) = 8

df(total) = N-1 = 14

sum of squares for error, SSE = SST-SSE-SSB = 723-383-296 = 44

MSA = SSA/df(A) = 191.5

mean square for the variability associated with airports, MSB = SSB/df(B) = 74

MSE = SSE/df(error) = 5.5

F for airline = MSA/MSE = 34.8182

p-value = F.DIST.RT(34.8182, 2, 8) = 0.0001

Critical value Fc = F.INV.RT(0.05,2,8) = 4.459

As F = 34.8182 > 4.459, we reject the null hypothesis.

The effect of airlines is significant at the 0.05 level of significance

------

F for airport = MSB/MSE = 13.4545

p-value = F.DIST.RT(13.4545, 4, 8) = 0.0013

Critical value Fc = F.INV.RT(0.05,4,8) = 3.838

As F = 13.4545 > 3.838, we reject the null hypothesis.

The effect of airport is significant at the 0.05 level of significance

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Airline	383	2	191.5	34.8182	0.0001	4.459
Airport	296	4	74	13.4545	0.0013	3.838
Error	44	8	5.5
Total	723	14