KNR 445
Statistical Applications in Science & Technology

Assignment 18
Independent t-test

This assignment introduces the concept of the independent t-test, used to compare the mean difference between two uncorrelated sets of data. The data to be used includes the CDC smoking data, and data sets accessed from this page.

Homework

1. Conduct an independent t-test on the following sets of data:
Group 1: 3, 6, 9; Group 2: 7, 11, 12.
    a. By hand
        i. Use = alpha 0.05
        ii. Does the outcome of the comparison change if alpha = 0.01 is used?
    b. Enter the data into SPSS, and conduct the independent t-test
        i. Are the results at alpha = 0.05 and alpha = 0.01 the same as in questions 1.a.i and 1.a.ii above?
SPSS Output

2. Using the region variable assigned to each state in earlier assignments:
    a. Run independent t-tests between ALL possible pairs of regions using the variable Tax per pack of smokes.
        i. How many t-tests were conducted in total?
        ii. How many of the observed differences between regions were statistically significant (alpha = 0.05)?
SPSS Output

3. Create an SPSS file with the data in file indep_t2
    a. Conduct independent t-tests between the two groups (CHO_sup and Regular diet).
        i. Is the difference statistically significant at alpha = 0.01?
        ii. Is the difference statistically significant at alpha = 0.05?
        iii. Is the difference statistically significant at alpha = 0.10?
    b. How could the difference be statistically significant at one level but not at another?
    c. Write a paragraph to justify your selection of an level.
    d. Write a paragraph presenting the results of the independent t-test, using the format presented in your lecture overhead notes.
SPSS Output

4. Create an SPSS file with the data in file indep_t3
    a. Conduct independent t-tests between the two groups (CHO_sup and Regular diet).
        i. Is the difference statistically significant at alpha = 0.01?
        ii. Is the difference statistically significant at alpha = 0.05?
        iii. Is the difference statistically significant at alpha = 0.10?
    b. Create a new variable CHO_2sup by adding 10 minutes to each case of CHO_sup..
    c. Conduct all possible independent t-tests between the three groups (CHO_sup, CHO_2sup and Regular diet).
        i. Are any differences statistically significant at alpha = 0.01?
        ii. Are any differences statistically significant at alpha = 0.05?
        iii. Are any differences statistically significant at alpha = 0.10?
    d. Use the procedure Graph==>Interactive to create a graph showing the mean & SD of  the three groups (use Excel as an alternative).
    e. Write a paragraph to justify your selection of an alpha level.
    f. Write a paragraph presenting the results of all possible independent t-tests, using the format presented in your lecture overhead notes.
SPSS Output