Question

Scientist warn that food shortages are an impending future issue for humans. A potential solution is eating non-traditional foods in the western world. An experimental psychologist knows that westerners are uncomfortable eating food other cultures have no trouble eating. The psychologist developed a method to help individuals tolerate more the eating of non-ordinary food. However, the psychologist is unsure which type(s) of foods the method will be more effective on. The psychologist has some participants go through the method and then asks them to eat each of the following out of the ordinary foods: stick insects, bovine testicles, fish eyes, and Witchetty grubs. On each occasion, participants are measured on how many seconds it takes before they gagged while eating the food. The data are in the table below. What can the psychologist concluded with α = 0.01?

stick	bovine	fish	grub
7 8 6 4 8 7 9 11	6 4 1 2 3 4 1 5	1 2 3 1 4 4 6 7	5 4 7 8 7 6 1 0

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Input the appropriate value(s) to make a decision about H₀.
p-value =_______________ ; Decision:  ---Select--- Reject H0 Fail to reject H0

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

1) At least one of the foods differed on time before gagging.

2) None of the foods differed on time before gagging.    

Answer 1

1)

one-way ANOVA

2)

count, ni =	8	8	8	8
mean , x̅ i =	7.500	3.25	3.50	4.75
std. dev., si =	2.070	1.832	2.204	2.92
sample variances, si^2 =	4.286	3.357	4.857	8.500
total sum	60	26	28	38	152
grand mean , x̅̅ =	Σni*x̅i/Σni =	4.75

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	7.563	2.250	1.563	0.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	60.500	18.000	12.500	0.000	91
SS(within ) = SSW = Σ(n-1)s² =	30.000	23.500	34.000	59.500	147.0000

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   32
df within = N-k =   28
  
mean square between groups , MSB = SSB/k-1 =    30.3333
  
mean square within groups , MSW = SSW/N-k =    5.2500
  
F-stat = MSB/MSW =    5.7778

P value =   0.0033

conclusion :    p-value<α , reject null hypothesis

3)

Effect Size = SSR / SST

= 91 / 238

= 0.3824

LARGE

4)

1) At least one of the foods differed on time before gagging.

Thanks in advance!

revert back for doubt

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