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Keep the Highest: Attempts: /4.5 7. Comparing ANOVA and the t test for an independent-measures hypothesis test Aa Aa Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents started a half-hour walk with their infants in a parent-facing or an away-facing stroller and then switched to the other type of stroller midway. Her results suggest that parents talked less to the babies, the babies had higher heart rates, and they were less likely to fall asleep in away-facing strollers than in parent-facing strollers. You are interested in testing the hypothesis that babies who travel in parent-facing strollers have different expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 15 newborns to parent-facing strollers and 15 newborns to away-facing strollers. You then test the babies' expressive vocabularies at age 18 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary The sample means and sums of squares of the scores for each of the groups are presented in the following table. Sample Mean Sum of Squares Group Away-facing Parent-facing 93.5 1,787.66 2,513.84 102.9 You decide to use an ANOVA at a .05 to test the null hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate the F-ratio and enter it into the table. ANOVA Table Vaianice (Chapter Aplia: Student Question Aplia: Assignment Aplia: Student Ques Away-facing Parent-facing 102.9 2,513.84 You decide to use an ANOVA at a .05 to test the null hypothesis that there is no difference between the The ANOVA table follows. Calculate the F-ratio and enter it into the table. ANOVA Table Source of Variation Between Treatments Within Treatments Total Degrees of Freedom Sum of Squares 662.70 4,301.50 4,964.20 Mean SquareF 662.70 28 153.63 5.78 4.31 1.54 0.23 29 Use the Distributions tool that follows to find Fcritical at a significance level of critical region for the F-ratio test statistic. a .05, the value of F that bounds the F Distribution Numerator Degrees of Freedom 26 Denominator Degrees of Freedom 26 .5000 5000 0.00 1.00 1.000 2.003.004.005.006.007.008.00 courses.aplia.com 0 Variance (Chapter.. Aplia: Student Question Aplia: Assignment Aplia: Student Question 1.000 .05 is Fcritical at α Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of α-.05, the null hypothesis is stroller faces influences a child's expressive vocabulary at 18 months. . You find that you conclude that the direction that the Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (Smi-M2) is 4.53, so the t test statistic is Use the following tool to find the critical regions for α = .05. Degrees of Freedom 21 5000 5000 5000 2500 2500 0.0 -0.686 0.000 0.686 2.0 3.0 1.0 3.0 2.0 The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) are Variance (Chapter Aplia: Student Question Aplia: Assignment Aplia: Stud 5000 5000 5000 2500 -3.0 -2.0 0.0 1.0 2.0 3.0 0.686 0.000 0.686 The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) are Now use the tool to evaluate the null hypothesis. At a significance level of expressive vocabulary at 18 months. a .05, the null hypothesis is . You find that you conclude that the direction the stroller faces influences a child's When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in Flash Player MAC 32,0,0,171

Answer 1

Test statistic

F = MS(between) / MS(Within) = 662.70/153.63 = 4.31

F_critical at α = 0.05 is F.INV.RT(0.05, 1, 28) = 4.196

At a significance level of α = 0.05, the null hypothesis is rejected. You find that you can conclude that the direction that the stroller faces influences a child's expressive vocabulary at 18 months.

t test statistic:

M1-M2 93.5-102.9 ー-2.075 4.53 SM1-M2

df = 15+15-2 =28

the critical t score = T.INV.2T(0.05, 28) = +2.048, -2.048

At a significance level of α = 0.05, the null hypothesis is rejected. You find that you can conclude that the direction that the stroller faces influences a child's expressive vocabulary at 18 months.

When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and t test resulted in same conclusion.