Question

A study compared three display panels used by air traffic controllers. Each display panel was tested for four different simulated emergency conditions. Twenty-four highly trained air traffic controllers were used in the study. Two controllers were randomly assigned to each display panel–emergency condition combination. The time (in seconds) required to stabilize the emergency condition was recorded. The resulting data and analysis results are given below. Display panel data Emergency condition Display panel 1 2 3 4 A 17 25 31 14 14 24 34 13 B 15 22 28 9 12 19 31 10 C 21 29 32 15 24 28 37 19 Two-way ANOVA results Source of Variation DF SS MS F P Panel 2 218.58 109.29 26.49 0.000 Condition 3 1247.46 15.82 100.80 0.000 Interaction 6 16.42 2.74 0.66 0.681 Error 12 49.50 4.13 Total 23 1531.96 Tasks: Set up null and alternative hypotheses to (a) test the significance of display panel effect, (b) test the significance of emergency condition effects, and (c) test the interaction a between the two factors. Justify the type of ANOVA (one-way or two-way) you will apply to test the hypotheses. Interpret the p values in the results table for an accept/reject decision regarding the hypotheses. State your conclusions including what the ANOVA results do not tell you and your needed actions as a researcher.

Answer 1

Since this a two way ANOVA analysis, three hypotheses are being tested.

The null and alternate hypotheses are defined as,

Null Hypothesis 1: The population means of display panel are equal.

Alternate Hypothesis 1: There is a statistically significant difference among population means of display panel.

Null Hypothesis 2: The population means of emergency condition are equal.

Alternate Hypothesis 2: There is a statistically significant difference among population means of emergency condition.

Null Hypothesis 3: There is no interaction between display panel and emergency condition.

Alternate Hypothesis 2: There is a statistically significant interaction between display panel and emergency condition.

a)

From the ANOVA table, the F statistic and P- value for display panel are,

F-stat	26.49
P-value	0.00

Since,

b)

From the ANOVA table, the F statistic and P- value for emergency condition are,

F-stat	100.8
P-value	0.00

Since,

c)

From the ANOVA table, the F statistic and P- value for emergency condition are,

F-stat	0.66
P-value	0.681

Since,

Hence there is a statistically significant interaction between display panel and emergency condition.

ANOVA result doesn't tell which means are statistically different. ANOVA doesn't compare means pairwise, it only tell atleast one one population mean is different if null hypothesis is rejected.