Question

My Noles Ask Your Teucta Lconic memory is a type of memory that holds visual inforrmation for about half a second onds). 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 ปั 。s- 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. Beforc 0.3 (aj Complete the F-tahle. (Raund your valuAG ter MS and F tn tin decimal places. Batwcon groupa Witin qrcups (erro) (h) Comp'na ikay's HSD post hoc test and intarprat tha rAGults. (Assum alpha พิ jual to 0.05. Round your anAWer to twa decimal place&J or each pairwise camparison. Which the comparisona had signiticant dirtarnca?(elact all that apnly.) -Recall following ฮ half second delay was significantly different from recall following a one second delay. The null hypothesis of no difference should be retained bccausc nonc of the Pairwisc comparisons demonstrate 교 significant difference. Recall fallowing no delay was aignificantly diffcrent frem recall following a one second delay Recall fallowing no delay was lgnificantly different frem recall followinga half sccond delay. You may need to usa the appropriate table in Appendx C to answer this quastian. Additional Materials

Answer 1

The following table is obtained:

	Group 0	Group 0.5	Group 1
	11	8	2
	6	5	1
	8	6	5
	7	3	4
	10	4	7
	12	10	5
Sum =	54	36	24
Average =	9	6	4
$\Sigma X^2$ =	514	250	120
St. Dev. =	2.366	2.608	2.191
SS =	28	34	24
n =	6	6	6

The total sample size is N = 18.

Number of treatment, k = 3

First, we need to compute the total sum of values and the grand mean. The following is obtained

$\sum_{i,j} X_{ij} = 54+36+24 = 114$

Also, the sum of squared values is

$\sum_{i,j} X_{ij}^2 = 514+250+120 = 884$

Based on the above calculations, the total sum of squares is computed as follows

$SS_{total} = \sum_{i,j} X_{ij}^2 - \frac{1}{N} \left(\sum_{i,j} X_{ij}\right)^2 = 884 - \frac{ 114^2}{ 18} = 162$

The within sum of squares is computed as shown in the calculation below:

$SS_{within} = \sum SS_{within groups} = 28+34+24 = 86$

The between sum of squares is computed directly as shown in the calculation below:

$SS_{between} = SS_{total}- SS_{within} = 162- 86 = 76$

a) Anova table:

Source of Variation	SS	df	MS	F
Between groups	76	k-1 = 2	76/2 = 38	38/5.733 = 6.63
Within groups (error)	86	N-k = 15	86/15 = 5.73
Total	162	N-1 = 17

b) Given n= 6 and k = 3.

Critical value , $q_{\alpha, k, N-k} = 3.68$

$HSD=q_{\alpha, k,N-k}\sqrt{\frac{MS_{within}}{n}}=3.68\sqrt{\frac{5.73}{6}}=\textbf{3.596}$