Question

Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

Delay Before Recall
0	0.5	1
8	6	5
11	8	7
9	4	2
12	4	4
7	11	5
7	3	1

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

Source of Variation	SS	df	MS	F
Between groups
Within groups (error)
Total

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is  for each pairwise comparison.

Which of the comparisons had significant differences? (Select all that apply.)

Recall following no delay was significantly different from recall following a one second delay.The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.Recall following a half second delay was significantly different from recall following a one second delay.Recall following no delay was significantly different from recall following a half second delay.

Answer 1

	Delay 0	Delay 0.5	Delay 1	Total
Sum	54	36	24	114
Count	6	6	6	18
Mean, Sum/n	9	6	4
Sum of square, Ʃ(xᵢ-x̅)²	22	46	24

a)  

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 18

df(between) = k-1 = 2

df(within) = N-k = 15

df(total) = N-1 = 17

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 76

SS(within) = SS1 + SS2 + SS3 = 92

SS(total) = SS(between) + SS(within) = 168

MS(between) = SS(between)/df(between) = 38

MS(within) = SS(within)/df(within) = 6.1333

F = MS(between)/MS(within) = 6.20

p-value = F.DIST.RT(6.1957, 2, 15) = 0.0109

Decision:

P-value < α, Reject the null hypothesis.

ANOVA
Source of Variation	SS	df	MS	F
Between Groups	76	2	38	6.20
Within Groups	92	15	6.13
Total	168	17

b)

At α = 0.05, k = 3, N-K = 15, Q value = 3.67

Critical Value, CV = Q*√(MSW/n) = 3.67*√(6.1333/6) = 3.71

Comparison	Diff. = (xi - xj)	CV	Results
x̅1-x̅2	3	3.71	Means are not different
x̅1-x̅3	5	3.71	Means are different
x̅2-x̅3	2	3.71	Means are not different

All that apply:

• Recall following no delay was significantly different from recall following a one second delay.