You are interested in studying how formal language exposure and deafness affect

Question

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 expressive vocabulary scores obtained using the Peabody Picture Vocabulary Test. You begin with the repeated-measures ANOVA (which can also be used for a 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. The summary ANOVA table for the repeated-measures ANOVA follows. Fill in the F test statistic for this repeated-measures ANOVA. Use the Distributions tool to find the critical value of F for the repeated-measures ANOVA at alpha, alpha = 05. The critical F is __________. At a significance level of alpha = 05, evaluate the null hypothesis that the population means for all treatments are equal using the repeated-measures ANOVA. The null hypothesis is ____. You _____ conclude that deafness and/or the time ASL is learned affects expressive vocabulary. You then ignore the fact that the participants were matched and run an independent-measures ANOVA, as shown in the following ANOVA table. Fill in the F test statistic for this independent-measures ANOVA. Use the tool to find the critical value of F for the independent-measures ANOVA at alpha, alpha = 05. The critical F is ___. At a significance level of alpha = 05, evaluate the null hypothesis that the population means for all treatments are equal. The null hypothesis is ____. You _____ conclude that deafness and/or the time ASL is learned affects expressive vocabulary. Notice that the F statistic for the repeated-measures ANOVA is usually larger than the F statistic for the independent-measures ANOVA, because by matching the participants, ideally you are removing some of the individual differences from the error term in the denominator. Since the numerator is the same (MS_between), the overall test statistic is usually (but not always) greater. The larger F statistic, however, does not mean you will always be more likely to reject the null hypothesis for the repeated-measures ANOVA, because the denominator degrees of freedom are ____. Under which circumstances is the independent-measures research design a better choice than the matched-subjects design? When the treatment effect is small When there are few individual differences

Explanation / Answer

FILL IN THE BLANKS ARE IN BOLD LETTER/NUMERALS

SS due to third treatment=SS due to treatment- SS due to(treatment1+treatment2)=56.1667-(22-75+8.75)=24.6667

n=number of treatment=3

k=number of type of participants=4

N=n*k=4*3=12

(second part) from ANOVA

F=MS(between treatments)/MS(error)=28.0834/6.6389=4.23

The critical F(0.05,2,9) is =4.26.

As critical F=4.26 is less than calcuted F=4.23

so Null hypothesis is Accepted.

You may conclude that

Denominator degree of freedom =9

(last question) when treatement effects is small

Participants Hearing Deaf with early ASL Deaf with late ASL Participants total A 97 96 96 289 n=3 B 102 99 100 301 k=4 C 99 98 91 288 N=12 D 103 100 93 288 T= 401 393 380 G=1166 SS= 22.75 8.75 24.6667

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.