Hypothesis Testing and P values

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Q1. Which of the following statements about the P value do you believe to be true?

a)The P value is the probability that the null hypothesis is true. ✔ ✗

b)The P value is the probability that the alternative hypothesis is true. ✔ ✗

c)The P value is the probability of obtaining the observed or more extreme results if the alternative hypothesis is true. ✔ ✗

d)The P value is the probability of obtaining the observed results or results which are more extreme if the null hypothesis is true. ✔ ✗

e)The P value is always less than 0.05. ✔ ✗

Feedback:

The correct answer is d). a) The null hypothesis is either true or false. b) The alternative hypothesis is either true or false. c) The P value is the probability of obtaining the observed or more extreme results if the null hypothesis is true. e) The cut-off of 0.05 is usually used to indicate significance, but the P-value can take any value between 0 and 1.

Q2. Which of the following statements do you believe to be true?

a)In a study of comparing the amount of alcohol consumed by men and women the null hypothesis would be defined as: ”There is a difference in drinking rates of men and women”. ✔ ✗

b)In a study of comparing the weights of men and women the alternative hypothesis would be defined as: “The weight of men is greater than women”. ✔ ✗

c)The P value is the probability that the null hypothesis is true. ✔ ✗

d)If the P value for a hypothesis test is 0.20, we can accept the null hypothesis. ✔ ✗

Feedback:

The correct answer is d). a) The null hypothesis assumes no effect. Therefore, the null hypothesis could be “The difference in alcohol consumed by men and women is zero.” b) Normally we do not specify a direction for the difference. We allow for the difference to be greater or less than zero. This is known as a two tailed test. c) The P value is the probability of obtaining our results, or something more extreme, if the null hypothesis is true. The null hypothesis is either true or false. d) Typically we set the significance value for a test at 0.05. If we obtain a P value of less than or equal to 0.05 then we would reject the null hypothesis and accept the alternative hypothesis.

Q3. Subjects from families with genetic disorders were asked whether they had encountered problems when applying for life insurance. A sample from the general population was also asked the same question (Low L et al. BMJ 1998; 317: 1632-1635). About a third of respondents in the study group (723/2167) reported problems compared with only 5% of the general population. This difference was significant at the 0.01% level. Select all of the following statements which you believe to be true.

a)A suitable null hypothesis would be that subjects from families with genetic disorders in the population are more likely to experience problems when applying for life insurance than those from the general population. ✔ ✗

b)We can reject the null hypothesis at the 5% level of significance. ✔ ✗

c)A suitable alternative hypothesis would be that subjects from families with genetic disorders in the population are more likely to experience problems when applying for life insurance than those from the general population. ✔ ✗

d)The result is significant at the 0.01% level. This means that we are 0.01% certain that the null hypothesis is true. ✔ ✗

e)The differences between the two groups of families are likely to have occurred by chance. ✔ ✗

Feedback:

The correct answer is b). a) A suitable null hypothesis is that subjects from families with genetic disorders in the population are equally likely to experience problems when applying for life insurance as those from families in the general population. c) We do not specify a direction for the alternative hypothesis except in very rare circumstances. Therefore, a suitable alternative hypothesis is that subjects from families with genetic disorders in the population are not equally likely to experience problems when applying for life insurance as those from families in the general population. e) As the P-value is so small, we believe that these results are unlikely to have arisen by chance.

Q4. In a study of workplace bullying in a community NHS trust, staff were asked about whether workplace bullying had affected their working environment (Quine L, BMJ 1999; 318: 228-229). Staff who had been bullied had lower levels of job satisfaction (mean 10.5 [SD 2.7] vs 12.2 [2.3], P<0.001) and higher levels of job-induced stress (mean 22.5 [SD 6.1] v 16.9 [5.8], P<0.001) than those who had not been bullied. Select all of the following statements which you believe to be true.

a)A suitable null hypothesis for this would be that staff in the population who have been bullied at work have similar levels of job satisfaction to staff in the population who have not been bullied at work. ✔ ✗

b)There is a significant difference in the levels of job satisfaction between those who had and those who had not been bullied ✔ ✗

c)The P value for the comparison of job-induced stress was less than 0.001. This means that we cannot reject the null hypothesis at the 5% level of significance. ✔ ✗

d)P < 0.001 means that there is a less than 1 in 1000 chance that we would have obtained these results, or more extreme results, if the alternative hypothesis was true. ✔ ✗

e)We can conclude that work place bullying causes lower levels of job satisfaction and higher levels of job-induced stress. ✔ ✗

Feedback:

The correct answers are a) and b). c) We can reject the null hypothesis at the 5% level of significance (indeed we can reject it at the 0.1% level of significance). d) There is a less than 1 in 1000 chance that we would have obtained these results, or more extreme results, if the null hypothesis was true. e) We do not know that the workplace bullying has caused these results, only that individuals who have been bullied have lower levels of job satisfaction and higher levels of stress than those who have not been bullied. It may be that these individuals already had lower levels of job satisfaction and higher levels of stress before being bullied.

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