Question

SHOW ANY WORK

Computational problems:

One-way ANOVA

A researcher wants to investigate different formats for taking an exam. She randomly assigns one-third of the class to an open book exam, one-third to no notes, and one-third to one page of notes only. The data appear below.

1.       What is the F statistic reported in appropriate APA style?

2.       What is your decision? (use alpha = .05)

3.       Do you need to conduct a follow-up test?

4.       Do you need to determine the effect size? If yes, what are the results?

          Open book                  No notes            One page only

          65                        88                        70

          70                        94                        72

          72                         89                        76

          78                        98                        80

          82                        93                        81

          79                        94                        82

Answer 1

treatment	A	B	C	D
count, ni =	6	6	6
mean , x̅ i =	74.333	92.67	76.833
std. dev., si =	6.408	3.670	4.997
sample variances, si^2 =	41.067	13.467	24.967
total sum	446	556	461		1463	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	81.28
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	48.225	129.707	19.753
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	289.352	778.241	118.519		1186.111111
SS(within ) = SSW = Σ(n-1)s² =	205.333	67.333	124.833		397.5000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   18
df within = N-k =   15
  
mean square between groups , MSB = SSB/k-1 =    593.0556
  
mean square within groups , MSW = SSW/N-k =    26.5000
  
F-stat = MSB/MSW =    22.3795

anova table
	SS	df	MS	F	p-value	F-critical
Between:	1186.1111	2	593.056	22.379	0.0000	3.682
Within:	397.5000	15	26.500
Total:	1583.6111	17
					α =	0.05

F(2,15) = 22.379

   Decision:   p-value<α , reject null hypothesis    

yes, we need to conduct follow up test to check which pairs of means are significantly different

eta square ,effect size = SSbet/SST = 0.7490