A school psychologist tests the effects of environmental noise on the reading co

Question

A school psychologist tests the effects of environmental noise on the reading comprehension scores of high school students through three different conditions: silence, white noise, and rock music. The reading comprehension scores are as follows. Use independent measures ANOVA to determine if these data indicate any significant differences among the three groups. Test with a = 0.05. Perform Tukey's post hoc test to Complete: Use appendix to find q (k = 3, df = 15, 0.05 level of significance), calculate HSD, calculate differences between means, and identify significance

Explanation / Answer

Here the test of the hypothesis is,

H0 : mu1 = mu2 = mu3 Vs H1 : atleast one of the mean is different.

alpha = 0.05

We can find MS by using the formula,

MSB = SSB / df (between) = 70.34 / 2 = 35.17

MSW = SSW / df(within) = 68.16 / 15 = 4.544

F = MSB / MSW = 35.17 / 4.544 = 7.739877

The complete ANOVA table is,

P-value we can find by using EXCEL.

syntax :

FDIST(x,deg_freedom1, deg_freedom2)

where x is test statistic value

deg_freedom1 = degrees of freedom for between. = 2

deg_freedom2 = degrees of freedom for within. = 15

P-value = 0.0049

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the mean is different.

We have to check which mean is different between three groups for that we do post hoc analysis.

q(k = 3, df = 15, 0.05 level of significance) is 3.140

mean for silence (m1)= 7.17

mean for white noise (m2)= 5

mean for rock (m3)= 2.33

m1 - m2 = 2.17

m1 - m3 = 4.84

m2 - m3 = 2.67

MSE = 4.544

HSD = q * sqrt [MSE /n ]

HSD = 3.140*sqrt[4.544/6 ]

HSD = 2.7326

m1 - m3 > HSD

m1 - m2 < HSD

m2 - m3 < HSD

one difference is significant with LSD are now not significant.(m1 - m3)

Source SS Df MS F between 70.34 2 35.17 7.739877 within 68.16 15 4.544 total 138.5 17

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