Question

The following data were collected

Determine if there are any significant differences among the four treatments. Use the .05 level of significance.

Participant	A	B	C	D
1	6	3	3	0
2	4	4	2	2
3	4	2	0	2
4	6	3	3	0

For the given data above, calculate the f-ratio. Show ALL your work

Answer 1

Null Hypothesis, Ho: There is no significant difference in the means of four treatment groups i.e.

Alternative Hypothesis, Ha: There exists at least one treatment group for which the mean is significantly different i.e.       for at least one

Test Statistics: Under Ho,

  

where k = number of groups = 4 and,

n = number of observations = 16

Calculations:

Treatment Groups	ni		si
Group 1	4	5	1.1547
Group 2	4	3	0.8165
Group 3	4	2	1.4142
Group 4	4	1	1.1547

So,

and ,

Decision:

Since, p-value = 0.0024 < , so we reject the Null Hypothesis at 5% level of significance.

Conclusion:

There exists at least one treatment group for which the mean is significantly different i.e. for at least one