Hypothesis testing

1. Thomas Holland: Ho: The C drug is no more effective than the traditional medication. Ha: The drug treatment is more effective. With a degrees of freedom of 2, significance value of 0.035 Chi-Square value of 6.38. From these results we accept the null hypothesis and conclude that the C-drug is no better than the antidepressant. A type 1 error occurs when we reject the null hypothesis when it is actually true. A type II error is when we do not reject the null hypothesis and the null hypothesis is actually false. Both errors are serious issues when using hypothesis testing. In this example, the type 1 error could be that we reject Ho but the c drug is actually more effective. Type two error in this case could occur if we do not reject Ho and conclude that the c drug is more effective when in fact it is not. I believe that in this case the type 1 case is more serious as it could mean people are receiving ineffective medication.

1.1. Tracy Hong Define: C = proportion of subjects given C-drug who suffer relapse A = proportion of subjects given traditional antidepressant who suffer relapse P = proportion of subjects given placebo who suffer relapse Hypotheses: H0: C ≤ A H1: C > A H0: C ≤ P H1: C > P H0: A ≤ P H1: A > P If the study results provide sufficient basis for rejecting all 3 null hypotheses above then it can be said that (at the chosen significance level) that taking C-drug and taking a traditional antidepressant each is correlated with a reduced rate of relapse and that C-drug is correlated with a greater reduction in relapse rate than the traditional antidepressant. If 1 or more of the null hypotheses fail to be rejected then the effectiveness of C-drug and/or traditional antidepressant at reducing relapse would be much more doubtful. The chi-squared test can be used to determine whether 2 sets of (categorical) data are independent of each other. In the given scenario, a null hypothesis that can be tested is that the likelihood of a cocaine user relapsing is independent of the treatment given (C-drug vs. traditional antidepressant vs. placebo), with a corresponding alternative hypothesis that relapse rate is dependent on the treatment given. (As also pointed out by Gary), the hypotheses can be tested by comparing C to both, or one only, of A and P. A Type I error occurs when H0 is true but is incorrectly rejected. A Type II error occurs when H0 is false but, incorrectly, fails to be rejected. For this study, a Type I error would occur if C-drug were concluded to be effective at reducing relapse when in fact it is ineffective, whereas a Type II error would occur if C-drug were concluded to be ineffective when in fact it is effective. The Type I error could lead to investment in further developing and marketing of C-drug without conferring benefit on the community. The Type II error could lead to C-drug being abandoned as a candidate for reducing relapse despite having the potential to confer benefit on the community. Both types of errors are associated with considerable costs (financial / social / personal) to the community.

2. GARY) Q1) State the hypotheses This is a study looking at the effects of two different interventions, anti-depressants the new C-Drug. The placebo is the control group. We are trying to determine whether or not the treatments are effective at reducing relapse to drug usage and how the treatments compare. H1 Antidepressants are not effective at lowering the relapse rate. U(AD and No relapse) – U(Placebo and No relapse) <=0 H1A U(AD and no relapse)-U(Placebo and no relapse) > 0 H2 C-Drug is not effective at lowering the relapse rate. U(C-Drug and no relapse) – U(Placebo and no relapse) <= 0 H2A U(C-Drug and no relapse) – U(Placebo and no relapse) > 0 H3 C-Drug is not more effective at lowering the relapse rate than anti-depressants. U(C-Drug and no relapse) – U(Antidepressants and no relapse) <= 0 H3A U(C-Drug and no relapse) – U(Antidepressants and no relapse) > 0 The reported chi-squared result rejects the probability of independence of this set of data. However, if we remove the placebo data and focus on the difference between Antidepressants and C-Drug, a new Chi-squared value of 0.0847 (higher values are more significant) does not reject the hypothesis of independence. These results are not significantly different from random when comparing these two treatments. A type 1 error is when we reject the null hypothesis and we should not have. H1 – Type 1 error. Antidepressants not effective and we recommend their use. Costs to patients include both financial and side-effects. H2 – Type 1 error. C-Drug is not effective and we recommend their use. Costs to patients include both financial and side-effects. Very important with known digestive side-effects. H3 – Type 1 error. C-Drug is not more effective than anti-depressants, yet we recommend this new drug’s use over anti-depressants. Costs to patients include both financial and side-effects. Very important with known digestive side-effects. As well as missing out on the benefits of anti-depressants if they are found to be effective. A type 2 error is when we fail to reject the null hypothesis when we should have. H1 – Type 2 error. Antidepressants are useful and we miss out on the benefits. H2 – Type 2 error. C-Drug is useful and we miss out on the benefits. H3 – Type 2 error. C-Drug is more useful than anti-depressants and we miss out on the benefits.

3. Stephen: Ho: The antidepressant will have a lower rate of relapse than the Cdrug. Ha: The Cdrug will have a lower rate of relapse than the antidepressant Using these results, we cannot reject the null hypothesis. The antidepressant performed better than the cdrug. A Type 1 error is when the Null hypothesis is rejected, when it is actually true. In this example, a type 1 error would be saying that the Cdrug performed better than the antidepressant. A type 11 error is when the null hypothesis is not rejected and it is actually false. Using this example, a type 11 error could occur if the Cdrug was actually more affective, yet we stated that the antidepressant had the lower rate of relapse

4. Dawei Jia : HO: in the experiment C-drug cause a good result than antidepressant. Ha: in the experiment antidepressant cause a better result than C-drug we have know the significant value is 0,035 however we have to know the chi-square value. so we can't decide which one is better. type 1 erro is when the null hypothesis will be rejected, how could we know the result is true, type 2 euro is when the null hypothesis will not be rejected, how could we the result is wrong.

5. Truc Thuy Le Ho: the C-drug is better than the antidepressant Ha: the C-drug is not as good as the antidepressant We don’t have enough information to know which one is better. Type I error is we reject the null hypothesis when we should not. For example, we reject C-drug but it actually works. Type II error is we do not reject the null hyphothesis and it is false. For example, we do not reject the antidepressant when it does not work.

6. Kevin Koo: H0: C drug is equally or more effective than antidepressants HA: C drug is less effective than antidepressants Type I error: When the null hypothesis is wrongly rejected. In this example, a Type I error could occur if C drug was effective on a patient but categorised as ineffective. A type I error is generally considered as a more significant error than a type II error. Type II error: When the null hypothesis is not rejected, but is actually false. A type II error could occur if C drug was incorrectly labelled as effective although it was ineffective on a patient. A chi-squared value tests for data independence, and whether two variables have significant association with each other. In this example, the chi-square test is used to assess whether C drug has been effective or whether C drug has a similar effect to a placebo. In this case, a value of 0.035 shows that the data is not independent. The C drug or the antidepressant needs to be compared solely with the placebo in order to infer a more meaningful result.