Q. 89  If we want to ensure that a statistical test picks up a significant effect, what will we want to increase - confidence or power of test?

 

 

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Power of test is more significant 

If we want to ensure that a statistical test picks up a significant effect, what will we want to increase - confidence or power of test?

 

Before proceeding to find the answer of above question, we should know about Null Hypothesis, Alternate Hypothesis, confidence and power of test.

Null Hypothesis: This Hypothesis indicates that there is no significant effect.

Alternate Hypothesis: This Hypothesis indicates that there is a significant effect. 

Confidence: It is the probability that the test accepts Null Hypothesis when Null Hypothesis is True.

Power: It is the probability that the test rejects the Null Hypothesis when Alternate Hypothesis is True.

             The statistical Power ranges from 0 to 1 and as statistical power increases, the probability of making type 2 error decreases.  For a type 2 error probability of β, the corresponding statistical power is 1-β. Means we are accepting the Alternate Hypothesis Test when it is true. Type 2 error is not rejecting the Null Hypothesis when in afcr the Alternate Hypothesis is true. SO by decreasing type 2 error, we are decreasing the probability of Null Hypothesis.

 

            Alpha, the Type 1 error that you are willing to accept. Its value is set from 0.1 to 0.5. An alpha of 0.5 means that you are willing to accept that there is a 5% chance that your results are due to chance not by test.Type 1 error is rejecting the Null Hypothesis when it is in fact true. Confidence level is 1- α. If we want to increase confidence level, then there is need to decrease value of α which indicates that we are accepting Null Hypothesis when Null is True, means that a statistical test is not picking of any significant effect when confidence is increasing.

 

So, from above explanation we can say that, if we want to ensure that a statistical test picks up a significant effect, then we will want to increase power of test. 

 

 

 

 

Decision based on test	Reality
	Ho is True	Ho is False
Accept Ho	Correct Decision (1 – alpha) Confidence Level	Type II error (Beta)
Reject Ho	Type I error (alpha)	Correct Decision (1 – Beta) Power of the Test

 

If we want the test to pick up a significant effect, it means that whenever H1 is true, it should accept that there is significant effect.

 

In other words, it means that whenever H0 is false, it should accept that there is significant effect.

 

Again, in other words, it means that whenever H0 is false, it should reject H0. This is represented by (1-Beta). As seen from the above table, this is defined as the power of the test.

 

Thus, if we want to increase the assurance that the test will pick up significant effect, it is the power of the test that needs to be increased.

 

Hypothesis testing.

In the given situation... Where we want to check whether the pick up choice has a significance effect... We have to ensure the H0 and HA which is better... Here Significant level HA is given means power is to be increased...i.e (1-beta).

Great job, Vastupal and Venugopal for providing a detailed and well explained answer. The chosen best answer is that of Venugopal as the table makes the description easy to read and understand.