Statistical Reasoning in Psychology

Question 1 

Baseball Players		Basketball Players	Football Players
32		27	27
27		36	23
26		25	26
35		30	20
	120	118	96
	3654	3550	2334

Graph for the data 

Grand Total (G): Y.. = 120 + 118+ 96 =334 

∑∑ Yᵢj² = 3654 + 3550 + 2334 =9538 

(b) The hypothesis testing 

Step1 

The model for this experiment is Yᵢ j = u. + αᵢ + e ij 

j = 1 , 2 , 3 ; 1=Baseball 2= Basketball 3= Football 

i= 1, 2, 3, 4. 

Where Y ij is the jth observation on the ith treatment 

u. – the overall mean scab index = 1/3[u1 +u2 + u3] 

αᵢ -- the effect of the ith treatment assumed to be a constant. 

e ij – random error. 

Step2 

Hypothesis to be tested 

H ₀ : αᵢ =0 versus H ₁ : αᵢ ≄ 0 for some i 

Step3: computation of ANOVA Table Components. 

SS(TOTAL) = ∑∑Y ij ² –G²/N 

Where N = 12 

= 9538 – (334²/12) 

=9538 – 9296.33 

=241.67 

SS(Treatment) = [∑Yi²]/n - G²/N 

= [(120²/4) + (118²/4) + (96²/4)] – (334²/12) 

=9385 – 9296.33 

=88.67 

SS(ERROR) = SS(TOTAL) – SS(treatment) 

=241.67 – 88.67 

153.00 

ANOVA TABLE 

Source	Df	Sum of square	MSS	F-Ratio
Treatment	2	88. 67	44.335	2.609
Error	9	153.00	17
Total	11	241.67