(A)
- In the opinion of Bosq (2013), independent variables are variables which can be controlled, which can be selected and manipulated. Example here can be marital status.
- According to Dybvig and Hieb (2010), dependent variables are what can be measured within an experiment and is affected in an experiment. Example in this case is degree of happiness.
(B) Null hypothesis: There is no difference in happiness with regard to marital status.
(C) Degree of freedom for
- Gender=(p-1)=2-1=1
- Marital status=(b-1)=3-1=2
- Interaction between marital status and gender=99-(1+2+96)=0
- Error or within variance=(n-b-p+1)=100-3-2+1=96
(D) Mean square for
Mean square = sum of squares ÷ degree of freedom
- Gender = 68.15 ÷ 1= 68.15
- Marital status = 127.37 ÷ 2 = 63.69
- Interaction between marital status and gender = 41.90 ÷ 0 = ∞
- Error or within variance = 864.82 ÷ 96 = 9.00
(E) F ratio for
F ratio = Sum of squares ÷ Mean square
- Gender = 68.15 ÷ 68.15 = 1
- Marital status = 127.37 ÷ 63.685 = 2
- Interaction between marital status and gender = 41.90 ÷ ∞ = 0
(F) Identifying critical Fs at α = 0.05
- Gender = F0.05 1,96 = 3.96
- Marital status = F0.05 1,96 = 3.09
- Interaction between marital status and gender = F0.05 0,96 = 0
(G) With α set at 0.05; the null hypothesis which states that, there is no difference in happiness with regard to marital status is accepted. According to Fallahian (2008), when the calculated F ratios are less than the tabulated F ratios, the null hypothesis is usually accepted.
References
Bosq, D. (2013). Mathematical Statistics and Stochastic Processes. London: Wiley.
Dybvig, R. K., & Hieb, R. (2010). A new approach to procedures with variable arity. Bloomington, Ind: Computer Science Dept., Indiana University.
Fallahian, N. A. (2008). Study of the association between exposure to transuranic radionuclides and cancer death.
