Question

Looking for some help with this stats problem - will give good reviews!

Attempts Average: /19 10. Comparing repeated-measures ANOVA to independent-measures ANOVA Aa Aa You are interested in studying how formal language exposure and deafness affect language acquisition. You want to compare three groups: a hearing group, a deaf group that began learning American Sign Language (ASL) before age 1, and a deaf group that did not begin learning ASL until age 1. You are trying to decide whether to use a matched-subjects or an independent-measures design. To determine which research design is more robust, you decide to compare hypothetical data analyzed first using a matched-subjects design and then using an independent-measures design. The results of the studies are displayed in the tables that follow. All scores are receptive vocabulary scores obtained using the Peabody Picture Vocabulary Test. You begin with the repeated-measures ANOVA (which can also be used fora matched-subjects design) to test the null hypothesis that the three population means are equal. Note that each participant row in the table that follows actually corresponds to the data from three different participants, but since they are matched, you can look at the results as if they are repeated measures from one participant. Begin by filling in the seven missing values in the data table. Participant Hearing Deaf with Early ASLDeaf with Late ASL Participant Totals 92 96 104 108 90 94 98 106 90 93 95 98 P 272 P 283 P = 297 T = 388 T = 376 SS 160.00 SS 140.00 SS EX2113,314 The summary ANOVA table for the repeated-measures ANOVA follows. Fill in the Ftest statistic for this repeated-measures ANOVA. Repeated-Measures ANOVA Table Source Between Treatments 72.0000 2 36.0000 Within Treatments334.00 9 37.1111 MS Between subjects 300.6667 3100.2222 33.3333 6 5.5556 Total 406.0000 11

Answer 1

Participants	Hearing	Deaf with early ASL	Deaf with late ASL	Total
A	92	90	90	P = 272	n = 4
B	96	94	93	P = 283	k = 3
C	104	98	95	P = 297	N = 12
D	108	106	98	P = 108+106+98 = 312
	T = 92+96+104+108 = 400	T = 388	T= 376		G = 400+388+376 =1164
	SS =160	SS=140	SS = 34		= 113.314

Repeated measured ANOVA :

MSbeteen36.0000 een.5556 M Serror 5.55566.4799

At = 0.05 and df1 = 2, df2 = 6, Critical value , F_c = 5.1443

As F = 6.4799 > F_c = 5.1443, we reject the null hypothesis.

The null hypothesis is rejected. you can conclude that deafness ans/or the time ASL is learned affects receptive vocabulary.

Independent measured ANOVA:

between 36.0000 MSuǐithin 37.1111

At = 0.05 and df1 = 2, df2 = 9, Critical value , F_c = 4.2565

As F = 0.9701 >  F_c = 4.2565, we fail to reject the null hypothesis.

The null hypothesis is not rejected. you cannot conclude that deafness ans/or the time ASL is learned affects receptive vocabulary.

Independent measured design better choice than repeated measured design under-

When there are few individual differences.