In a 1993 study from the British Medical Journal, the researchers compared the n

Question

In a 1993 study from the British Medical Journal, the researchers compared the number of emergency room visits due to car accidents on Friday the 6th and Friday the 13th in order to see if Friday the 13th was a more dangerous time to be out driving. Use a sign test to test whether there is a significant increase (alpha = 0.05) in accidents on the 13th. The original researchers used a paired t test and found a significant increase in the number of accidents. Why might we prefer the t test to our sign test? Why might the sign test be more appropriate in this case?

Explanation / Answer

Part a

Here, we have to use the sign test to test whether there is a significant increase or not.

Null hypothesis: H0: There is no significant increase.

Alternative hypothesis: Ha: There is a significant increase.

The sign table is given as below:

#

X

Y

X - Y

Sign

1

9

13

-4

-

2

6

12

-6

-

3

11

14

-3

-

4

11

10

1

+

5

3

4

-1

-

6

5

12

-7

-

Number of negative signs = 5

Number of positive signs = 1

Sample size = 6

Now, we have to find the p-value by using binomial distribution table with n = 6, x = 1 and p = 0.5

P-value = 0.109375

Alpha value = 0.05

P-value > Alpha value

We do not reject the null hypothesis that there is no significant increase.

Part b

The original researchers used a paired t test and found the significant increase. We might prefer the paired t test because the above sign tests do not given exactly correct results and it is used as approximation to the paired t test. The sign test is only based on the signs of the differences but this test does not count the magnitude of differences.

Part c

The sign test is more appropriate in this case because most of the pairs show the negative difference while only single pair shows the positive difference. When parametric test violated then non parametric tests are most useful. For the given scenario we don’t know about the parent distribution.

#

X

Y

X - Y

Sign

1

9

13

-4

-

2

6

12

-6

-

3

11

14

-3

-

4

11

10

1

+

5

3

4

-1

-

6

5

12

-7

-

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.