Question

A	B	C
0.0873	0.0974	0.0956
0.0571	0.0873	0.0974
0.0813	0.0662	0.1352
0.0831	0.0672	0.0817
0.0976	0.0819	0.1016
0.0817	0.0749	0.0968
0.0859	0.0649	0.1064
0.0735	0.0835	0.105
0.0659	0.0725	0.0973
0.0923	0.0703	0.1039
0.0836	0.1026	0.1045
0.0749	0.1064	0.0571
0.065	0.11	0.0814
0.1016	0.0976	0.0835
0.0968	0.0817	0.0725
0.1064	0.0859	0.0703
0.105	0.0735	0.1026

1.) In order to perform an ANOVA on the data to assess if A, B, and C are different, what assumptions must be met? Enter the number of all correct answer choices in numerical order separated by commas in the blank below.

1. The variance between the three groups must be equal.
2. The data in each group must be normally distributed.
3. The members of the sample populations were randomly chosen
4. The variance between each group must be unequal.
5. The variances of each group must overlap with the variance of at least one other group.

Using the data analysis add in for Excel (installation instructions can be found here Win|Mac), perform a single factor ANOVA to deduce if A, B, and C are different. To do this, click the data analysis tool icon, then select "single factor ANOVA", enter the range of cells containing the data, and click okay. Excel will generate a results table you can use to answer the next two questions.

2.) What is the P value?

• Report your answer in the form #.##E##
• For example, 0.00000122 would be reported as 1.22E-6 or 1.22E-06

3.) Is the F value greater than the F_critical value (yes or no)?

4.) Are A, B, and C, different from each other based on the ANOVA (yes or no)?

5.) What test(s) could you perform to deduce if A and B, or B and C, or A and C are individually different from each other? Enter the number of the correct answer in the box below.

1. Kruskall-Wallis
2. Tukey-Kramer
3. Kruskall-Wallis or Tukey-Kramer
4. No further analysis is required. The performed ANOVA already confirmed all 3 groups are each different from each other.

Answer 1

1)

The main assumptions required to perform a one-way ANOVA are:

The groups must come from normally distributed populations

The groups must come from normally populations with equal population variances

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	17	1.439	0.084647	0.000206
B	17	1.4238	0.083753	0.000212
C	17	1.5928	0.093694	0.000322
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.001028	2	0.000514	2.08553	0.135356	3.190727
Within Groups	0.011834	48	0.000247
Total	0.012863	50

2)

P-Value 0.135356

3.) Is the F value greater than the F_critical value (yes or no)?

No

4.) Are A, B, and C, different from each other based on the ANOVA (yes or no)?

5)

Kruskall-Wallis or Tukey-Kramer