Treating Insomnia Patients: Scientific Method Testing

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Table of Contents

Introduction
Testing the two Population Means using a two-sample t-test
Conclusion
References

Introduction

In this assignment, we are testing the population means of two independent samples. We test the data using the two-sample t-test for random samples and the sample sizes are less than 30. The data are obtained from Martha who experimented with 20 samples. The aim is to determine whether special visualization therapy reduces the time taken to fall asleep in patients affected with mild insomnia.

Testing the two Population Means using a two-sample t-test

Choice between independent and dependent samples t-test

Martha should use an independent samples t-test. The samples of twenty numbers of the treatment are chosen randomly and the treatment is assigned randomly. The treatment samples are independent of each other. If the treatment X1 and X2 are given to the same samples and time was recorded, then the samples are related. Here the treatments X1 and X2 are given to different samples. Hence Martha should use independent samples t-test. (Fisher, R. A)

Independent and dependent variables

Time taken to fall asleep is the dependent variable as it is believed to depend on the treatment and the dichotomous data of with treatment and without treatment is the independent variable, as the selection for treatment is random.

Defining the hypothesis

Null hypothesis: The therapy does not affect the time taken to fall asleep. That is, there is no difference between the means of both treatments X1 and X2.

Alternate hypothesis: The therapy reduces the time taken to fall asleep. That is the mean of treatment X1 is less than the mean of treatment X2.

H₀: µ2 = µ1 H₁:µ2 > µ1

One-tailed or two-tailed test?

We would use a one-tailed test as the critical region for the hypothesis is in one direction of the right side. Also, the hypothesis is to test whether the meantime is reduced after treatment. Hence the hypothesis is a one-sided test. Suppose if Martha has to test whether there is any difference in the meantime, then it is a two-tailed test as the critical region lies on both sides.

Degree of freedom

The degree of freedom for two samples t-test is n1 + n2 – 2 where n1 and n2 are the sample sizes of the two samples respectively. Here n1 = n2 = 10. Hence df = 10 + 10 – 2 = 18.

Critical value

The critical value for a =.05 is 1.734. This value is found at the intersection of df = 18 and P = 5% (since one-tailed test) from the table.

Statistical interpretation

The tobt = 1.49. Since this value is less than the critical value, we have no evidence against the null hypothesis. Hence the null hypothesis can withstand at a 5% level of significance (Weisstein, Eric W).

Decision

Martha should conclude that the treatment does not affect the time taken to fall asleep as the test result show that both means are the same.

Conclusion

We have learned to do a hypothesis test to check the population means of two independent random samples. Inferential statistics provide us most important results so that we can take decisions. A more detailed test and further test like a test for variances will also provide good information about the population.

References

Fisher, R. A. “Applications of ‘Student’s’ Distribution.” Metron 5, 3-17, 1925.

Weisstein, Eric W. “Hypothesis Testing” from MathWorld–A Wolfram Web Resource. Web.

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