Question

12.26  Does haptic feedback improve performance?

A group of technology students is interested in whether haptic feedback (forces and vibrations applied through a joystick) is helpful in navigating a simulated game environment they created. To investigate this, they randomly assign 20 students to each of three joystick controller types and record the time (seconds) it takes to complete a navigation mission. The joystick types are (1) a standard video game joystick, (2) a game joystick with force feedback, and (3) a game joystick with vibration feedback. Using the table below of group means and standard deviations, construct an ANOVA table. Based on the F statistic and degrees of freedom, compute the P-value. What do you conclude?

Joystick	Group mean	Group sd.	n
1	279	78	20
2	245	68	20
3	258	80	20

Answer 1

Since the significance level is not mentioned, we use the default which is 0.05.

The Hypothesis:

H0: There is no difference in the mean times of the three types of joysticks used.

Ha: There is a difference in mean times between at least 2 types of joysticks used.

The Calculations for ANOVA are below:

The overall mean = [(20 * 279) + (20 * 245) + (20 * 258)] / 60 = 1564060 = 260.67

SS treatment = SUM n* ( - overall mean)² = 20 * (279 - 260.67)² + 20 * (245 - 260.67)² + 20 * (258 - 260.67)² = 11773.33

df1 = k - 1 = 3 - 1 = 2

MSTR = SS treatment/df1 = 117733.33 / 2 = 5886.67

SSerror = SUM [(n - 1) * Variance] = 19 * 78² + 19 * 68² + 19 * 80² = 325052

df2 = N - k = 60 - 3 = 57

Therefore MS error = SSerror/df2 = 325052/57 = 5702.67

F = MSTR/MSE = 5886.67/5702.67 = 1.03

The ANOVA table is as below.

Source	SS	DF	Mean Square	F	Fcv	p
Between	11773.33	2	5886.67	1.03	3.16	0.3628
Within/Error	325052.00	57	5702.67
Total	336825.33	59

The p value is calculated for F = 1.03, df1 = 2, df2 = 57 and p value is = 0.3628

The Decision Rule: If p value is < Alpha , then reject H0.

The Decision: Since p value is > Alpha , we fail to reject H0.

The Conclusion. Fail to reject the null hypothesis. There is insufficient evidence at Alpha = 0.05 to conclude that there is a difference in the mean times between at least 2 of the joysticks used.