A sample of adults with hearing aids were randomly assigned to one of three cond
ID: 3150774 • Letter: A
Question
A sample of adults with hearing aids were randomly assigned to one of three conditions that focused on lists of practice words that are typically challenging for individuals with hearing loss to accurately perceive. Following 12 weeks of structured practice with a speech-language pathologist, they were assessed using a testing of speech perception to yield a “hearing score”. State the null and research hypotheses, assess the assumptions of ANOVA, and interpret the results (F-ratio, post hoc results when applicable), and describe the outcome of the study with respect to null hypothesis.
Explanation / Answer
Here dependent variable is hearing score.
In the first table testing the equality of variances.
The test of hypothesis is,
H0 : Variances are equal.
H1 : Variances are not equal.
Assume alpha = level of significance = 5% = 0.05
We are given that test statistic F = 0.509
P-value = 0.677
We see that P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : Variances are equal.
In the second table,
The test of hypothesis is,
H0 : Bj = 0 Vs H1 : Atleast one of the Bj is differ than 0.
Test statistic F = 4.919 and P-value = 0.003
In this table we can see that all the P-values are less that alpha (0.05).
Reject H0 at 5% level of significance.
Conclusion : Atleast one of the Bj is differ than 0
R-squared = 0.138
It expresses the proportion of the variation in dependent variable which is explained by variation in independent variable.
The 95% confidence interval for population mean of hearing score is 26.712 and 29.913.
And the mean is 28.313.
Thus we conclude that we are 95% confident that the population mean for hearing score is in between 26.712 and 29.913.
Also for list1, list2, list3 and list4 we are 95% confident that the population means are in between confidence limits.
Post HOC analysis :
In the List1 :
The P-value for list3 and list4 are 0.009 and 0.013.
P-value < 0.05
Reject H0 at 5% level of significance.
Conclusion : The differences are significant.
list2, P-value = 1
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : The differences are insignificant.
In the List2 :
The P-value for list3 and list4 are 0.335 and 0.459.
P-value > 0.05
Accept H0 at 5% level of significance.
Conclusion : The differences are insignificant.
For list1 , P-value = 1
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : The differences are insignificant.
In the List3 :
The P-value for list2 and list4 are 0.335 and 1.
P-value > 0.05
Accept H0 at 5% level of significance.
Conclusion : The differences are insignificant.
For list1 , P-value = 0.009
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The differences are significant.
List4 ::
For list1, P-value = 0.013
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The differences are significant.
And P-values for list2 and list3 are > alpha
Accept H0 at 5% level of significance.
Conclusion : The differences are insignificant.