Question

Based on the findings for the delivery below, determine if a post hoc test is necessary. If necessary:

1. Run and report the results for the Tukey HSD (1 point)
2. Present the M and SD (in table form) for each condition; use the Excel ANOVA variance for the basis of these calculations! (2 points)
3. Identify which conditions have an honestly significant difference. (2 points)

condition 1	condition 2	condition 3
0	6	6
4	8	5
0	5	9
1	4	4
0	2	6

Answer 1

We used the excel data analysis tool pack to get the summary and one way ANOVA of the data, which is given below:

The Mean and standard deviation if the given data is as below:

Groups	Count	Sum	Average	Variance	Standard deviation
condition 1	5	5	1	3	1.73
condition 2	5	25	5	5	2.24
condition 3	5	30	6	3.5	1.87

We have to test

H0: all µi are same i.e. µ1= µ2= µ3

H1: all µi are not same i.e. at least one mean is significantly different than others

The ANOVA of the data is given below:

ANOVA
Source of Variation	SS	df		MS	F	P-value
Between Groups	70	2		35	9.13	0.0039
Within Groups	46	12		3.83
Total	116	14

We have the p-value=0.0039 which is less than 0.05 and it indicates that we have strong evidence against H0 to reject it so we reject the null hypothesis and conclude that mean is significantly different than others.

We have a significant ANOVA (rejected H0) so we will proceed for Tukey’s HSD post hoc test

We have q(0.95,3,12)= 3.772929

EMS = 3.83

r=5

The 95% Tukey’s confidence interval for mean difference in condition 1 and condition 2 can be given as below:

Lowe limit= 0.696

Upper limit= 7.304

Above confidence interval does not include the value 0 which indicates that there is significant mean difference between condition 1 and condition 2.

The 95% Tukey’s confidence interval for mean difference in condition 1 and condition 3 can be given as below:

Lowe limit= 1.696

Upper limit= 8.304

Above confidence interval does not include the value 0 which indicates that there is significant mean difference between condition 1 and condition 3.

The 95% Tukey’s confidence interval for mean difference in condition 2 and condition 3 can be given as below:

Lowe limit= -2.304

Upper limit= 4.304

Above confidence interval includes the value 0 which indicates that there is not significant mean difference between condition 2 and condition 3.

So finally we can conclude that condition 1 is honestly significant different than condition 2 and condition 3 while condition 2 and condition 3 are not honestly significant different.