Question

7. Gravetter/Wallnau/Forzano, Essentials Chapter 12 End-of-chapter question 22 Aa Aa 을 The following data have the same sample means and variances that appeared in the preceding question but the sample size is increased to n = 10. n 10 n=10 n 10 T-10 T=50 T=60 s2-9.00 s2 = 10.00 s2-11.00 SS-81 SS = 90 SS = 99 G=120 Σχε = 890 Predict how the increase in sample size should affect the F-ratio for these data. Use an ANOVA to check your prediction Larger samples should the F-ratio. Source df MS Between treatments Within treatments Total Predict how the increase in sample size should affect the value of η 2 for these data compared to the η2 in problem 10. Calculate n2 to check your prediction. Increasing the sample size should effect on η 2,

Answer 1

large samples should increase the F ratio

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
1	10	1	9.000	90.000	81.00
2	10	5	10.000	10.000	90.00
3	10	6	11.000	40.000	99.00
	grand mean=	4.0000		140.000	270.00
				SSTr	SSE
Source	SS	df	MS	F
between	140.00	2.000	70.0000	7.00
within	270.00	27.000	10.0000
total	410.00	29.0000

increasing the sample size should decrease the effect on $\eta$²

$\eta$² =SSR/SST =140/410=0.3415