Question

Use Random number generator (under Data Analysis) to simulate the following data set. Create 10 columns, each 20 points long and use the following parameters: Number of variables (10), number of data point (20), Distribution (Normal), Mean (40), Standard Deviation (10), Random seed (1234). The data should be in columns: A,B,C,….,I,J.

Randomly pick two columns (say Column B and Column H) and perform 2-sided t-test on these two data columns. Record the P-value and repeat this procedure several times (at least 5 times). That is, each time randomly pick two columns, perform 2-sided t-test and record the P-value. And answer the questions. (Pick the closest answer)

17. What did you observe?

• a. Most of the P-values are very small, and some below 5%.
• b. P-values are very different, some small and some large, but very few, if any, below 5%
• c. Most of the P-values are very large, around 0.9 and 0.95 range.
• d. ​​Essentially all P-values are below 5% and some even below 1% range.

18. What is the Statistical interpretation?

• a. Since data are created randomly one expect to see small P-value for t-test.
• b. The t-test worked as designed, since in most cases it detected the difference, sometimes even with 1% threshold.
• c. The t-test worked as designed, in most cases it did not detect the difference since the data are created with equal means (equal averages).
• d. None of the above

Create one more random column of data. This time use the following parameters: Number of variables (1), number of data point (20), Distribution (Normal), Mean (50), Standard Deviation (10), Random seed (3434). CUT &PASTE this data in the same sheet as the previous 10 columns and put it in column M.

Randomly pick one column out of A,B,…,J (say Column F) and perform 2-sided t-test based on this randomly picked column and the newly created column M. Record the P-value and repeat this procedure several times (at least 5 times). That is, each time randomly pick one data from the ten previously created and perform 2-sided t-test versus the newly created column M. Record the P-value. And answer the questions. (Pick the closest answer)

19. What did you observe?

• a. Most of the P-values are very small, and some below 5%.
• b. P-values are very different, some small and some large, but very few, if any, below 5%
• c. Most of the P-values are very large, around 0.9 and 0.95 range.
• d. Essentially all P-values are below 5% and some even below 1% range.

20. What is the Statistical interpretation?

• a. Since data are created randomly one expect to see small P-value for t-test.
• b. The t-test worked as designed, since in most cases it detected the difference, sometimes even with 1% threshold.
• c. The t-test worked as designed, in most cases it did not detect the difference since the data are created with equal means (equal averages).
• d. None of the above

Answer 1

The obtained p-values are given below:

0.127024684

0.609651501

0.339961999

0.866233798

0.26958763

17)

The p-values are very different, some small and some large, but very few, if any, below 5%. Hence the second option is correct.

18)

The t-test worked as designed , in most cases, they didnt detect the difference since the data are created with equal means (equal averages).Hence the third option is correct.

Now the observed p-values are given by

0.000968376

0.000946191

0.001960953

0.009606169

1.74726E-05

19)

Essentially all p-values are below 5% and some even below 1% range. Hence the last option is correct.

20)

The t-test worked as designed, since in most cases, it detected the difference, sometimes even with 1% threshold. Hence second option is the correct option.